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!:ST EXAMPLES
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MY HISTORY LESSONS
And Th«
BOOKS I HAVE READ
Outjine Note-books for Both
FLExiBUt BOAkDs — ^25 Cents each — blank book styl«
These two new nottbooh are a new device that make pos-
sible tlie keeping of a systematic^ uniform^ concise and complete
record oK one's history lessons and of the books one reads. They
will be eminently serviceable for recording the data of history les-
soris, cr for recalling impressions of books read j and will be pecu-
liarly piacticable for teachers — to place iii the hands of students for
recording and preserving unpretentious analyses of the studies in his-
tory, or of books read in class and in general reading. These two
notebooks embody an original device. 1 he many advantages of this
leally successful and popular device are ;
It enables teachers to keep track of home work and
to secure uniformity throughout the schnol
It h logical. It is pedagogical
It is simple, concise, complete
It economizes time and labor ^
It develops thought, attention, discrimination
It provides permanent data
It assists the memory
It will develop the critical faculties
It encourages self-activity, self-direction
It encourages systematic habits and neatneai
It is inexpensive
The few well-arranged headings are so simple and obvious that
the teacher can tell at a glance whether the pupils' history study or
prescribed book-reading has been done attentively, intelligently and
thoroughly. * Tis a teachers' ^oon, simply as a teacHers* r»«- ■-•/' * /
HINDS, NOBLE & ELDREDGE, Publishers of
How To Study Literature, 75 cents
Smyth's American Literature, 90 cents
Trimble's Handbook Eng. and Amer. Literature, $1, 3c
31-33-35 West J5th Street New York Qty
From
The Rostrum (Chicago)
SEELEY'S A NEW SCHOOL MANAGEMENT
This is a readable book. It is sure of a latere
sale. Normal schools must make it a text 1 ook.
Teachers will prize it as a vade mecum while teaching.
Teachers' meetings will take it up for discussion, and
we p-edict for it an unusual popularity. It is the
latest and best book on a live stibjed and is a credit alike
to tlie author and the pubHshers.
What Page's "Theory and Practice of Teaching"
was to young teachers years ago, this new work by
Dr. Seeley is to young teachers of the present age.
It is in the highest degree a practical, helpful work,
especially for teachers in their first gear's work.
And for this very reason it is practical and helpful
for older teachers also. Educational principles are
the same everywhere; they are not graded. The
perf. ct school is a structure. Its higher depart-
ments are built upon the lower, and the pedagogy
applicable to them all rests upon that of the ele-
mentary school. Hence a sound body of principles
illustrated and explained as clearly and fully as in
this new book by Dr. Seeley cannot lose its value to
a teacher, even though he may have passed on from
the rank of a beginner to that of a veteran.
HINDS, NOBLE & ELDREDGE, Publishers of
School Management (Seeley,) $1.25
Foundations of Education (Seeley), $1.00
Page's Theory and Practice (with Quest, and Ans.), $i,oo
Gordy's New Psychology (for teachers), $1.25
Gordy's A Broader Elementary Education, $1.25
Best Methods in Country Schools, $1.25
Character: A Moral Textbook. $1,50
Moore's Science of Study, $i.oo
Parliamentary Usage, 50c.
3J-33-35 West J5th Street, New York City
Page's
Theory and Practice of Teaching
The popularity of Page's book is perennial. It is,
so to speak, a staple with educators — as flour is, or
sugar is, with a grocer. For more than a generation
it has been a standard in normal schools, training
schools, and reading circles. Superintendents who
themselves studied it twenty years ago when they were
just beginning to teach, now prescribe it at regular
intervals for the professional study of young teachers
whom they are now training!
More copies of Page's theory and practice
have been sold than of any other work on teach-
ing. In States which have a State reading
circle it is always one of the first works officially
adopted, and then gets re-adopted every-so-many
years. Its chapters cover :
The Spirit of the Teacher
Responsibility of the Teacher
Habits of the Teacher
Literary Qualifications of the Teacher
Right Views of Education
Right Modes of Teaching
Conducting Recitations
Exciting an Interest in Study
School Government
School Amusements
Teachers Relations to Parents of Pupils
Teacher's Care of His Health
Teacher's Relation to His Profession
Miscellaneous Suggestions
The Rewards of the Teacher
To impart to the book still greater value for
teachers who have to take grade examinations
we have added numerous questions and answers
ON THEORY AND PRACTICE OF TEACHING.
A teacher is sure to be well-equipped who possess-
es Page's book, if in addition he (or she) also possesses
Seeley's A new school management, which many
teachers tell us is the only rival that, possibly, excels
Page's theory and practice.
HINDS, NOBLE & ELDREDGE, Publishers of
Page's Theory and Practice (with Quest, and Ans.), $i.oo
Seeley's A New School Management, $1.25
Gordy's New Psychology (for teachers), $1.25
3J-33-35 West J5th Street New York City
IN THB SaMK SKRIKS
lOOI QUESTIONS AND ANSWERS ON
U. S. HISTORY.
(Including the Federal Constitution and Amendments.)
lOOI QUESTIONS AND ANSWERS ON
GEOGRAPHY.
(Embracing Descriptive, Physical and Mathematical Geography.)
XOOI QUESTIONS AND ANSWERS ON
GRAMMAR.
(With copious Illustrations, Parsing and Analysis.)
lOOI QUESTIONS AND ANSWERS ON
ARITHMETIC.
(Including nearly 300 Test Examples, with Solutions.)
lOOI QUESTIONS AND ANSWERS ON
THE THEORY AND PRACTICE OF TEACHING
ICX)I QUESTIONS AND ANSWERS ON
FHYSIOI.OGY AND HYGIENE.
(Containing a Chapter on the Physiological effects of Alcohol ani
Narcotics.)
XOOI QUESTIONS AND ANSWERS ON
ORTHOGRAPHY AND READING.
lOOI QUESTIONS AND ANSWERS ON
GENERAIv HISTORY.
1001 QUESTIONS AND ANSWERS ON
BOTANY.
lOOI QUESTIONS AND ANSWERS ON
TEST EXAMPI.es IN ARITHMETIC
lOOI QUESTIONS AND ANSWERS ON
PHYSICS OR NATURAL PHILOSOPH n'
EXTRA ClyOTH, Prick 50c. Each. Postage Prepaid^
HINDS. NOBLE & ELDREDGE, Publishers
»* :'3 35 West 15th Stret.;. New York Cit>
• lOOl • ^
THST EXAMPLKS i
IN
ARITHMETIC
WlTk AiNSvvcRS.
REVISED EDITION.
HINDS, NOBLE & ELDREDGE,
31-33-35 West 15th Street, New York City.
^ GIFT .
Copyright. 1896,
THE BURROWS BROTHERS CO.
CONTENTS. 'Z-fi-u,^,
h^^
Example. Solution.
PAGE. PAGE.
Fractions, 5 84
Percentage, 14 92
Interest 23 loi
Stocks and Bonds, 27 106
Discount, 35 113
Exchange, 38 117
Insurance, 42 121
Taxes, 45 124
Duties or Customs, : . . . . 46 125
Proportion, 48 127
Partnership, 50 129
Equation of Payments, 52 132
Alligation, 54 135
Arithmetical Progression, 56 137
Geometrical Progression, 57 138
Time, 58 139
Application of Square Root, 59 140
Application of Cube Root, 60 141
Measurements, 61 142
Miscellaneous, 65 146
M669ia6
HOW TO BECOME
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Price $1.00.
FRACTIONS.
1. A "boy engages to cut each stick of a cord of wood in two
pieces at 50 cts. per cord. What should he receive per
cord for cutting each stick in three pieces ? Ans. : $1.
2. Two consecutive numbers are such that \ of the less ex-
ceeds ^ of the greater by one ; find the numbers. Ans. :
80 and 95.
3. Two numbers differ by 28, and one is f of the other ; find
them. Ans. : 252 and 224.
4. Find a number whose | part is less; than its J by 3. Ans.:
60.
5. What number is that whose ^ and | are equal to 15?
Ans.: 54.
6. I of A's money is equal to B's, and | of B's is equal to C's;
all together have $770 ; what has each ? ANS. : A, $450 ;
B, $180 ; C, $140.
7. The width of a room is f of its length ; if the width had
been 3 ft. more and the length 3 ft. less the room would
have been square. What are the dimensions ? Ans. :
12 and 18.
"8; A, B and C together have 6450 sheep. C has twice as many
as B, and if 120 be taken from A he will have ^ as many
as B. How many has each? Ans.: A, 753; B, 1899; C,
3798.
9. The difference between J and J of a number is 6 less than
I of the number. What is the number ? Ans. : 180.
10. f of a number of persons received 15 cts. each and ^ re-
ceived 9 cts. each. They all received $4.68, How many
persons were there ? Ans. : 36.
11. If $45 is f of my money, T»hat part of it will that sum
plus $4^ be ? Ans.
FRACTIONS.
12. A and B can do a piece of work in 12 days. Assuming
that A can do | as much as B, how long will it take each
to do it ? Ans. : A, 28 ; B, 21 da.
13. A and B together had $5,700. | of A's money was equal
to f of B's. How much had each ? Ans. : B, $3,000 ; A,
$2,700.
14. A, B and C have $540. \ of A's share is equal to \ of B's
and f of B's share is equal to f of C's. How many dol-
lars has each 1 Ans. : A, $240 ; B, $160, and C, $140.
15. Two men found a purse, the contents of which they
divided equally. A takes for his share $1,000, and y\ of
remainder. How much did the purse contain ? Ans. :
$2,444f.
16. The sum of two numbers is 490, and one bears the same
relation to \ as the other does to f . What are the num-
bers ? Ans. : 196 and 294.
17. The sum of two numbers is 1,357. Their difference is xt
of the smaller number. Find the numbers. Ans. : 649
and 708.
18. A sold B a horse for \ more than it cost him. B sold it to
C for $36, which was \ less than it cost him. What did
A pay for it ? Ans. : $40.
19. A can do a piece of work in 5 days ; B can do the same in
7 days. How long will it take them together to do the
work ? Ans. : 2\\ da.
20. A man and his wife use a bag of meal in 16 days ; it will
last his wife alone 48 days. How long will it last the
man ? Ans. : 24 da.
21. A's land is \ less in quantity than D's, but 2V better in
quality; how do their farms compare in value. Ans. :
A's i»o of D's.
22. If \ of A's sheep equals f of B's, what part of B's equals |
of A's? Ans.: f.
23. A has f more money than B, and B f more than C. How
many times C's is A's ? Ans. : 2|.
24. f of my capital equals \ of yours ; if we put both together
what part of the whole will I own ? Ans. : xV
FRACTIONS.
25. After selling \ and \ of my horses I had 8 more than I had
sold ; how many had I at first ? Ans. : 80.
26. In 12 years I shall be \ of my present age ; how long since
was I f of my present age ? Ans. : ^\ yrs.
27. Four times f of a number is 100 less than twice the num-
ber ; what is the number ? Ans. : 90.
28. A man left y\- of his money to his wife, f of the remainder
to his sou and the balance, $2,100, to his daughters ;
what was the estate ? Ans. : $10,800.
29. I sold an article to A for | less than it cost me ; A sold it
for $21, which was f more than it cost him. What did
it cost me ? Ans. : $25.
30. A is J older than B ; their father, whose age is equal to
the sum of theirs, is 54; how old are A and B? Ans. :
24 and 30.
31. A tree stands f under water ; the water rose 8 ft, and then
there was as much under water as had been above water
before. Find height of tree. Ans. : i8f ft.
32. A is f as old as B ; if he were 6 yrs. older he would be y\
as old as B ; how old is each ? Ans. : 48 and 60.
33. A's money is $9 more than | of B's and $6 less than \ of
B's ; how much has each ? Ans. : $99 and $120.
34. f of A's age is f of B's, and A is 2 yrs. the older. How
old is each ? Ans. : A, 32 ; B, 30.
35. If 4 boys do a work in 8 hrs., how long will it take a man
who works five times as fast as a boy? Ans. : 6| hrs.
36. If 10 men can do a work in 5 days, how much time will
be saved by employing 2 more ? Ans. : | da.
37. A left I of his estate to his wife ; the remainder to his
son, who received $900 less than his mother. What was
the estate ? Ans. : $4,500.
38. B is worth 7 times A ; what part of B is f of A and B both
worth ? Ans. : fi-
39. Divide 102 into two such parts that | of the first is equal
to f of the second. Ans. : 54 and 48.
40. What number is that whose \ increased by 8 is 12 less
than its \. Ans. : 80.
FRACTIONS.
41. Bight men hire a coach ; by getting four more passengers
their expenses are reduced $1 each. What do they pay
for the coach ? Ans. : $24.
42. I sell eggs at 10 cts. per doz. and lose | ct. apiece. How
much must I sell them for to gain \ ct. apiece ? Ans. :
25 cts.
43. One-tenth of a dollar is what part of 2| cts ? Ans. : \\.
44. I gain \ ct. apiece by selling pears 3 for a dime ; how much
apiece will I lose by selling them 4 for a dime? Ans. :
ict.
45. How much grain must I take to mill so that I shall bring
back 6 bu. after paying toll at the rate of 4 qt. to the
bu. ? Ans. : 6f bu.
46. After doing f of a work in 30 days, I called an assistant ;
we both completed it in 6 days. In what time could the
assistant do it alone ? Ans. : 2if da.
47. The sum of two numbers is 4816. Their difference is f of
the larger. Find the numbers. Ans. : 3612 and 1204.
48. A can do a piece of work in \ da., B in ^ and C in a day ;
in what time can all do it ? Ans. : xV-
49. A can do a work in 40 days, B in 60 ; after both work 3
days A leaves ; when must he return that the work may
occupy but 30 days ? Ans. : At the end of the i3th day.
50. A and B can do a work in 12 days, A and C in 8 days, B
and C in 6 days. How long will it take all together to
do it ? Ans. : 5 J da.
51. A can plow f of a field in 6 days, B f in 10 days ; in what
time can they both plow it ? Ans. : 5f da.
52. A and B can cut a field of corn in 12 days, and A alone in
20 days. In what time can B cut it ? Ans. : 30 da.
53. A, B and C together do a work in 12 days ; A alone can do
it in 24 days ; B alone in 34 ; in what time can C do it
alone? Ans.: 8if da.
54. A can mow 3 acres in 4 days, B 5 acres in 6, and C 2^ acres
in 5 days. In how many days can the three mow 2\
acres? Ans.: i^ da.
55. Two-thirds of a number plus \ of the number plus 34
equals twice the number. What is the number ? Ans. : 30
FRACTIONS.
56. The age of B is 2* times that of A, and the sum of their
ages is 76 years ; what is the age of each ? Ans. : A, 20 ;
B, 56.
57. Divide 88 sheep among A, B and C, giving to B |, and to
C f as much as to A. Ans. : A, 42 ; B, 28, and C, 18.
58. Divide $440 among three persons, A, B and C, so that the
share of A may be f that of B, and the share of B | that
of C. Ans. : A's, $90 ; B's, $150, and C's, $200.
59. The age of A is twice that of B, and B's twice C's, and the
sum of all their ages is 98 years. What is the age of
each ? Ans. : A, 56 ; B, 28 ; and C, 14 yrs.
60. A man having spent $3 more than | of his money had $7
more than \ of it left ; how much had he at first ?
Ans.: $75.
61. It is required to divide 91 into two such parts that the
greater, being divided by their diflference, the quotient
will be 7. Ans. : 49 and 42.
62. Two persons can drink a cask of water in 6 days and one
alone in 10 days ; how many days will it last the other ?
Ans. : 15 da.
63. A could mow a field in 20 days, but if B assisted him 6
days he could mow it in 16 days; in how many days
could B mow it alone .■* Ans. : 30 days.
64. What is the value of | of f of f of a pound at $y% for f of
a pound? Ans. : $|j.
65. If a certain number be diminished by its ^, and f of the
remainder be added to the first number, the sum will
be 18.24; find the number. Ans.: 11.52.
66. Divide $125 J among A, B and C, giving C $7^^ more than
B, and $I2| more than A. Ans.: A, $35!; B, $41^; and
c. $^^.
67. What number is that which being increased by its f and
diminished by 20 is equal to 45 ? Ans. : 35.
68. I have in my mind two numbers; one is 3J times the
other and their difference is 100. Find the numbers,
Ans : 40 and 140.
69. What number is that to which if you add its J ^nd \ the
sum will exQ.^d its ^ by 51 ? Ans. : 36, "
FRACTIONS.
70. A person bought a number of lemons for 94 cts. ; having
lost 7, he sold \ of the remainder at cost for 20 cts.
How many had he at first ? Ans. : 47.
71- i + i + i^ of my money is $18. How much money have I?
Ans.: $24.
72. The sum of two numbers is 9f and their difference is 4|.
4 times the larger is how many times the smaller?
Ans.: ii.
73. The owner of y\ of a mine sold ^-^ of his share for $40,500.
What should a person who owns f of it get for f of his
share? Ans.: $70,714!.
74. I of A's money is to f of B's as 3 to 4. They both to-
gether have $1,520. How much has each ? Ans. : A
$720 and B $800.
75. A and B together have 153 sheep ; | of A's equals | of B's.
How many has each? Ans. : A, 81 ; B, 72.
76. A man in walking 18 miles finds that the distance he
walks in 100 min. is f of the remaining distance. Find
his rate of walking. Ans. : One mile in 13J min.
77. A can do as much in 3 hrs. as B can do in 5. How long
will it take A to finish a piece of work of which B has
done I in 20 hrs. ? Ans. : 4 hrs.
78. If 20 men do a work in 12 days, how many men can per-
form another work three times as large in \ of the time?
Ans.: 300.
79. A has \ of if- times $2,660, which is 2f times as much
again as B has. How much has B ? Ans. : $420.
80. Divide 7,250 sheep between A and B so that A shall have \ as
many asB, increased by 1,250. Ans. : A, 4,050; B, 3,200.
81. A had f of f of 7^ times 7,862 sheep, and sold \ of \ of
them. How many had he left ? Ans. : 35,379.
82. There is a fish whose head is 12 inches long, and whose
tail is as long as its head plus \ of its body, and whose
body is as long as its head and tail. What is the length
of the fish ? Ans. : 96 in.
83. A man lost | of all his money ; he then found $24 ; he now
lost I of all he had, and had only $48 left. How much
bad be at first ? Ans. : $360.
FRACTIONS. II
34. B sold a cask of acid and water ; f of the whole plus 3
gallons is acid, and \ of the whole plus t\vo gallons is
water. How many gallons of each ? Ans. : Acid, 43
gal.; water, 17 gal.
85. Find the result of i + fXf^f — i-^TV + f X I Ans.: i
86. A bought a lot for $68, which was f of twice what he sold
it for, lacking $1 ; how much did he gain ? Ans. : $12.50.
87. Divide $542 between A and B so that f of A's part plus 24
shall equal f of B's. Ans. : A's, $270; B's, $272.
88. I of A's age plus 8 yrs. equals | of B's, and the sum of
their ages is 148 years. Find their ages. Ans. : A's, 64 ;
B's, 84.
89. What will 10 yds. of cloth cost at $i.o.^|3^ per yd.? Ans.;
$1010.
90. If f of A's number of sheep plus f of B's equals 180, and
\ of B's number is to | of A's number as f to f , how
many sheep has each ? Ans. : A, 126 ; B, 128.
91. A, B and C have $645. C has twice as much as B, and: if
$12 be taken from A's he will have \ as much as B.
How much has each ? Ans. : A, $75.30 ; B, $189.90 ; C,
$379.80.
92. A man owns a pig and a horse ; \ the value of the horse
equals four times the value of the pig. Both together
are worth $170. Find the value of each. Ans.: Pig,
$10 ; horse, $160.
93. If the J of 6 is 3, what would the \ of 50 be ? Ans. : 15.
94. What will 100 yds. of silk cost at $1.00. of ^ per yd. ? Ans. :
$600.
95. A is 20 yrs. of age; B's age is equal to A's and \ of C's;
and C's is equal to A's and B's together. Find the age
of each. Ans. : B, 60 yrs. ; C, 80 yrs.
96. A is 35 yrs. old and his son is 10. How soon will the son
be \ the age of his father ? Ans. : 15 yrs.
97. A and B can do a work in 20 hrs. If A does f as much as
B, in how many hours can each do it ? Ans. : A, 46!
hrs. ; B, 35 hrs.
FRACTIONS.
98. If to a certain number you add \ of itself the result will
be 20 less than double the number. Find the number.
Ans.: 26|.
99. \ of A's sheep is equal to f of B's, and the diflference is 8.
' How many has each ? Ans. : A, 48 ; B, 40.
ICO. James Boone sold -f^ of his sheep and then bought 65.
He then had | of all he had killed by dogs, and had left
10 less than he had at first. How many had he at first ?
Ans.: 33.
loi. A man spent fV of ^ ^^is money and then received $65,
and then \ of what he first had equaled 3^/^ of all his
money. How much had he at first ? And what did he
spend? Ans. : $33 at first; spent $6.
102. f of 5J furlongs is \ of y^ of how many miles ? Ans. : lizf .
103. A merchant gains a sum equal to | of his capital ; the \
of his gain multiplied by \ of his increased capital
equals 4 times his gain. How much had he at first .'
Ans.: $24.
104. A and B have equal sums of money ; A loses \ of his
money and B gains $100 \ B then has three times as
much as A. How much had each at first ? Ans. : $100.
105. A hare has 100 yds. the start of a hound ; the hare runs
'j\ yds. in f of the time that the hound takes to run 12.
How many yds. will the hound run to catch the hare ?
Ans.: 600.
xo6. A owns ^0 of a mine and B j\. A bought from B enough
to make his share equal to what B had left, paying
therefor $3,500. What was the value of the mine .?
Ans.: $60,000.
107. Ten years ago the sum of the ages of two sons was \ of
their father's age ; one is two years older than the
other and the present sum of their ages is 14 less than
their father's age. How old are they? Ans. : 17 and 15
yrs.
108. A man earns twice as much as he had to begin with, and
then spends $16; he loses ^ of what remained, and af-
terwards earns as much as he had at first ; he then had
$80. What had he at first? Ans. : $52.
PR ACTIONS. 13
109. $40 is divided among a number of men ; if the number
had been increased by-^, each would have received 20
cts. less. Find the number of persons. Ans. : 40.
110. I spent $15 more than | of my money, and then had $13
less than f of it left. How much had I at first ? Ans. :
$80.
111. A boy gives f of his apples to A, J to B and the rest to
C. C gives 10 to B, and A then has 6 more than B.
How many had each at first ? Ans. : A, 96 ; B, 80 ; C, 64.
112. Four times B's age exceeds A's age by 20 yrs., and J of
A's age is less than B's age by 2 yrs. Find their ages.
Ans. : a, 36 yrs. ; B, 14 yrs.
113. y^y of A's age is greater by two years than \ of B's, and
twice B's age is equal to what A's age was 13 years ago.
Find their ages. Ans. : A, 55 ; and B, 21 yrs.
114. J of the sum of two numbers is 14, and \ of their differ-
ence is 4. What are the numbers? Ans. : 25 and 17.
115. \ of the difference between two numbers is 4, and i\
times their sum is 75. Find the numbers. Ans.: 7
and 43.
116. \ of the sum of two numbers is 16, and 4 times their sum
and difference is 480. Find the numbers. Ans.: 60
and 20.
117. Bought 4 yds. of silk for $.00,-^-^^^ per yd. and sold it at
$i.oo2__ per yd. Find my gain on the whole. Ans. : $4.
118. A man walks to town at the rate of 4J miles an hour and
walks back at the rate of 3 miles an hour. He was
gone 7J hours. How far was it to town ? Ans. : 13J
miles.
119. \ of the difference between two numbers is equal to \ of
their sum. The smaller number is 287. Find the
larger. Ans.: 451.
120. B buys goods at a discount of | and \ off and sells them
at a discount of y^ and ^^ off- What does he gain on
the dollar ? Ans. : $|.
121. f of a quantity of milk and water is milk. When I add
10 gal. of water the milk is 217 of the whole. What was
the mixture at first ? Ans. : 70 gal.
14 PERCENTAGE.
122. Divide 12J into two parts so that one shall be \2\ times
the other. Ans. : | f and iif^.
123. I bought a watch and chain for $48. \ the cost of the
watch plus the difference between the watch and chain
equals the chain. Find the cost of each. Ans. : Chain,
$18; watch, $30.
124. I buy calico and sell it at a profit of \ of the cost. Find
the cost per yard if the selling price of 125 yds. is
equal to the profit on $30 outlay. Ans. : 6 cts.
125. If f of $1 buy 5 of a sheep and f of a sheep be worth j^j
of an ox, what will 10 oxen cost ? Ans. : $200.
126. A is 20 yrs. old ; the sum of the ages of B and C equals 4
times A's age. C's age is |^ of A and B together. What
is the age of each? Ans. : C, 10 ; B, 70 yrs.
127. If J of 8 is 3, what would the half of 90 be ? Ans. : 67J.
PERCENTAGE.
1. A man sold a horse for $84, and by so doing gained \ of
what it cost him. What % would he have gained if he
had sold it for $100 ? Ans. : 42f %.
2. A sold I of a lot for $72 and gained $6. What would have
been his rate of gain had he sold the whole lot for
$100? Ans.: I3tV%-
3. A sells pork at $ro a bbl., \ of which equaled his gain.
How many % would he have gained if he had sold it at
$12 a barrel ? Ans. : 50%.
4. Sold a horse for $440 and thereby gained 10%. How
ought I to have sold it to lose 25^? Ans. : $300.
5. A and B invest equal sums in business. A gains a sum
equal to 25% of his stock. B lost $225. A's money at
that time is twice B's. What did each invest ? Ans. :
$600.
PERCENTAGE, 15
6. I sold two lots for $300 each. On one I gained 25%; on
the other I lost 25 % . How much did I lose ? What per
cent.? Ans. : $40 loss; dY/c,
7. I sold goods at a gain of 20%. If they had cost me $250
more I would have lost 20% by the sale. What did the
goods cost ? Ans. : $500.
8. Isold two lots for $597, gaining by the sale 25% on the
first and 10% on the cost of the second. If | of the
cost of the first equals -| of the cost of the second, what
was the cost of each ? Ans. : ist, $270 ; 2d, $240.
9. If I sell I of an article for what \ of it cost, what is my
gain ^? Ans.: i6f^.
10. I sell goods so that f of the cost is received for \ of the
quantity of goods. Find gain %. Ans. : 42f.
11. A man pays |6oo for rent ; f of this sum is 33^% of \ his
income. What is his income? Ans. : $2,700.
12. A man owning 33^% of a farm sold 25% of his share for
$3350.50. Whai was the whole farm worth ? Ans. :
$40,206.
13. I of ^ of 60 is 75% of 33^% of what number? Ans.: 20.
14. 66f % of I of 100 is 5% of 10 times 25% of what number?
Ans : 213J.
15. A man paid me $80, which was 8^% of ^ the amount he
still owed me. How much does he still owe ? Ans. :
$I,882yV
16. A farm cost $3,000. \ of this sum was 62^% of what the
house and barn cost. Find cost of house and barn.
Ans.: $1,600.
17. What is that number to which, if 37^% of \ of 20% of 480
be added, the sum will equal | of | of 50% of 324?
Ans.: 27.
18. By selling a cow for $21 I lost 12^%. At what price should
I have sold her to have gained 12^%? Ans. : $27.
19. In building a house I paid 3 times as much for material
as for labor. Had I paid 5% less for material and 4^
more for labor the house would have cost $2,334. What
did it cost me ? Ans. : $2,400.
i6 PERCENTAGE.
20. In a building I paid three times as much for material as I
did for labor. Had I paid 5% less for material and 4%
more for labor it would have cost me $66 less. What
did I pay for the labor and material? Ans. : f6oo and
$r,8oo.
21. I sold a carriage to B and gained 7^%. B sold it to C for
$141.90 and lost 12%. What did it cost mc ? Ans. :$ 150.
22. A hog was sold for 75% of its cost, but had it cost me $1 00
more it would have sold for 60% of its cost. Find its
cost. Ans. : $4.00.
23. On a bill of $425, what is the difference between 50% off
and 30 and 20% off? Ans. : $25;50.
24. A buys a $60 sewing machine at a discount of 30 and i6|%
off and sells it at 5% above the list. How much does
he make ? Ans. : $28.
25. I bought goods amounting to $725.16 at \ and 5 off. What
did I pay for them ? Ans. : $459.27.
26. I of what I received for an article is equal to | of its cost.
What is the gain %? Ans. : 12^%.
27. I marked goods to gain 60%, but on account of an incor-
rect measure I gained only 40%. What was the length
of the measure? Ans.: 41^ in.
28. An article is marked to gain 40%, but I throw off \o% and
afterwards pay 20% for collecting the debt. What is my
gain or loss? Ans.: |% gain.
29. I buy vinegar at 40 cts. per gallon. I then add water
so that by selling the mixture at 30 cts. per gallon I
make 50% . What % of each gallon is water? Ans. : 50% .
30. If I buy for 20% less I will make 30% more. What is my
gain %? Ans.: 20%.
31. If f of the selling price is 20^ less than the cost, what is
the gain or loss? Ans.: 6|% gain.
32. 66|^ of 240 is ii^% less than 20% of what number?
Ans. : 900.
33. If f of the selling price equals f of the cost price, find the
^ gain or loss. Ans. : 2of^ loss.
34. Two houses sold for $300 each. On one I gained 20;^ and
lost 25% on the other, What did I gain or lose ? Ans. ;
$50 loss.
PERCENTAGE. 17
35. I bought a watch for $30, which was 40% less than its
value, and sold it for 50% more than its value. Find
my gain. Ans. : $45.
36. I sold a horse at a gain of 20% . With the money I bought
another and sold it for $60 and lost 37^%. Find my
gain or loss. Ans. : $16 loss.
37. If an article had cost me 8% less my gain would have been
15% more. Find my rate of gain. Ans. : 72^%.
38. I bought corn at 50 cents a bu. ; 5% wasted. At what price
must I sell it to gain 33^%? Ans. : 7oi§c.
39. What % of .005 is $100? Ans. : 2,000,000%.
40. If an article had cost me 10% more my rate of ^ain would
have been 20% less. What is my rate of gain ? Ans. :
120%.
41. If I of what I receive for a horse is equal to | of its cost,
find rate of gain. Ans.: \2.\%.
42. If cost had been 20% less, loss would have been 15% less.
What was the loss %? Ans. : 10%.
43. If goods cost $180, how should I mark them so that I may
fall 10% and still make 20%. Ans.: $240.
44. A, B and C are partners. A receives 35% of the profits.
Of the remainder B's share is 60% more than C's. C's
income is increased by $150, when the profits rise from
10% to 12%. What did each invest ? Ans. : A, $10,500;
B, $[2,000 ; and C, $7,500.
45. I bought a number of lbs. of tea for $12. If I had bought
10 lbs. more, I would have been allowed a discount of
10% on the whole and the price would have been $18.
How many lbs. did I buy at first ? Ans. : 15 lbs.
46. I lost 25% on the purchase. What % must I gain on the
remainder to gain 25% on the whole ? Ans. : 66|%.
47. What must I ask for a hat that cost $4 so that I can fall
20% an 1 still make 20% on the cost? Ans. : $6.00.
48. A and B have $12,550; A's money is 125% of B's plus $400.
How much has each ? Ans. : A, $7,150; B, $5,400,
i8 PERCENTAGE.
49. A farmer sold two horses for |8io, receiving f as much for
the first as for the second. On the jEirst he gained 33^%,
and on the second he lost ii^fc. What did he gain?
Ans. : I33.75.
50. I bought 5 chests of tea of 74 lbs, each at 45 cts, per pound
at 2% off for cash. "What will be my profit if I retail it
at i2j% advance? Ans.: $20.12.
51. If my horse had cost 25% less than 80% of what he did
cost, I would have received 66f % more than I did. What
% did I gain or lose ? Ans. : iB^f % gain.
52. I sold two horses for the same sum ; on one I gained 25%;
on the other I lost 25%. I lost $30. Find the cost of
each? Ans.: $180, first; $300, second.
53. I bought 150 pounds of sugar at 6 cts.; after selling 100
lbs. at a loss of 5%, at how much a pound must I sell the
remainder in order to gain 10 fo on my investment ?
Ans. ! 8 1 cts.
54. I sold my goods for $1,125 5 ? is sold for 25% gain, | at 12^
^ gain, and the remainder at ^ of the cost. What did
I pay for the goods ? Ans. : $1,000.
55. What is the difference between 15% and 5% off, and 5%
and 15% off? 7Vns. : o.
56. I bought an invoice of goods which at retail sells for $850
at 30% off and 2^% oflf for cash. What did they cost?
Ans.: $580. i2|.
57. The sum of two numbers is 4655, and 40% of one is equal
to 60% of the other. What are the numbers? Ans.:
1862 and 2793.
58. A teacher spent 24% of his money and had $760. What is
his income ? Ans. : $1,000.
59. What must I ask for a hat that cost $1.60 so that I may
reduce my asking price 30% and lose i2j%? Ans.:
$2.00.
60. I bought a wagon for $72, and sold it for 25% more than
it cost and 10% less than I asked. What was my asking
price? Ans. : $100.
61. i^% of my money is 12^% more than $480. How much
have I ? Ans. : $36,000.
PERCENTAGE.
19
A sold B a horse for $120. If B had paid 10% less A would
have lost 8%. What did the horse cost A? Ans. :
63. I sold two horses for $105 each ; on one I gained 25% and
on the other I lost 25%. Did I gain or lose? How
much ? Ans. : $14 loss.
64. I pay $600 a year for rent ; 75% of this is just 33^% of \ of
my income. What is my income? Ans. : $2,700.
65. I own J of a vessel and sell 25% of it for $350; at that rate
what is the whole vessel worth ? Ans. : $4,200.
66. I bought tea for 20% less than its marked value and got
5% off for cash. I sold it for 15% above the marked
value. Find ^ gain. Ans.: 5ij%jc.
67. A merchant asked 25% more for his goods than they cost
him, but sold them at 10% less than his asking price,
realizing $4684 profit. What was the cost of the goods ?
Ans.: $37,472.
68. I sold goods at a gain of 20%. If they had cost me $60
less I would have gained 25%. Find cost of goods.
Ans. : $1,500.
69. I sold two houses for the same price ; on one I gained
25% and on the other I lost 25%. I lost $60. Find the
cost of each house. Ans. : $360 and $600.
70. Sold a horse at a gain of 33^% and with the money bought
another and sold it for $120 and lost 25%. What was
my gain or loss %? Ans. : 0%.
71. Bought for 20^ off and sold them for 20% above list price.
I gained $90. Find the cost. Ans. : $225.
72. I buy goods for $1200 and sell ^ at a profit of 15%. I then
raise the price from 15 to 17I cts. per yd., and sell the
remainder. Find my profit. Ans. : $190.
73. I gained 30% on f of my investment and lost 5% on the
remainder. My profits were $720. What did I invest ?
Ans.: $4,500.
74. I sold goods and gained .^0% on | and lost 5% on |. I had
I sold goods and gained 30% on | and lost 5^ on
invested $4500. Find my gain. Ans. : $405.
i^ PEkCENTAGE.
75. I bought a horse for $240. What must I ask for it that I
may deduct 25% from ray asking price and still make
25%? Ans.: I400.
76. I bought rice, tea, coffee and sugar. The tea cost 60%
more than the rice; coflPee 50^ more than the tea;
sugar 25% more than the coffee The whole cost was
$240. Find the cost of each. Ans. : rice, $30 ; tea, $48;
coflfee, $72 ; sugar, $90.
77. I sold \ of my goods at 20% gain, and the remainder at a
loss of 10%; my gain was $100. What was the cost of
the goods ? Ans. : $2,000.
78. A farmer sold 38% of his land, and afterwards bought 25%
of as much as he had left. He then had 9 acres less
than at first. What had he at first ? Ans. : 40 acres.
79. I bought 300 yds. of cloth. Sold \ at 20% gain, and the
remainder at a loss of \i\%. My whole gain was $30.
What was the cost of the cloth per yard ? Ans. : $2f .
80. I sold two city lots for $1200; gained 20% on one and lost
7.0% on the other. I lost $50. What did each cost me ?
Ans. : I500 and $750.
81. I bought sugar at 8 cts. alb.; the wastage is 10^. How
must I sell it to gain 30%? Ans. : ii§ cts. a lb.
82. I bought a barrel of wine containing 46 gal. at $2.50 per
gallon ; if 6 gallons leak out, how must I sell the re-
mainder to gain 25%? Ans. : $3.59! per gal.
83. Silver is y% pure. What % would it take to make it \\
pure? Ans.: if%.
84. Silver is \\ pure. How pure would it be if vou would add
2|%? Ans.: i| pure.
85. The cost of publishing a book is 50 cts. a copy ; if the ex-
pense of sale be 10% of this, and the profit 25%, what
does it sell for ? Ans. : 67^ cts.
86. My retail gain is 33^%, and I sell at wholesale for 10%
less than at retail. What is my gain ^ at wholesale ?
Ans.: 20%.
87. Bought dishes; lost 15% by breakage; at what % above
cost must I sell the remainder to clear 20% on the
whole? Ans.: 4IxV
PERCENTAGE.
88. If I pay for a lb. of sugar, and get a lb. troy, what % do I
lose? Ans. : 25%.
89. Sold my lot at 40% gain ; with the proceeds bought
another and sold it for $238, losing 20%. What did each
lot cost me ? Ans.: ist, $21250; 2d, I297.50.
90. I spent 50% of my money the first day; the second, 50%
of the remainder, and so on for 10 days, when I had left
only |i.oo. What had I at first? Ans. : |i,024.
91. I made this year $2400, which is 120% of my gain last, and
that is 44f % of my gain the year before. What were
my gains the two previous years ? Ans. : last year,
$2,000; year before, $4,500.
92. I bought goods by dry measure and sold at cost by wine
measure ; I bought another lot of same by wine meas-
ure and sold at cost by dry measure. Required the rate
of gain or loss. Ans. : 2^f^yc gain.
93. Bought wheat, and 6% was wasted ; 30% moulded, which I
sold at 40% less than the same amount cost ; at what %
advance on the first cost must the good wheat be sold
so as to yield a profit of 14% on the investment ? Ans. :
50%.
94. A's money is 3% of B's and 4% of C's ; B has $100 more
than C. How much has A ? Ans. : $12.
95. If 25% of what I receive for an article is gain, what is my
rate of gain ? Ans. : 32,} fc
96. I sell atSfo gain ; I invest and sell again for 12 J % gain ;
invest again and sell at a loss of 4%, and have $1,166.40.
What had I at first ? Ans. : $1,000.
97. Henry spent iSf-y^ of his money, and then received $65 ;
he then lost 75^ of all his money, and had $10 less than
he had at first. What had he at first ? Ans. : $33.
98* 75% of the difference between two numbers is equal to
i6| % of their sum. The smaller number is 287. Find
the larger. Ans.: 451.
I bought a certain number of hats at $2.50 each ; I sold f
of them at 25% profit, and on the sale of the remainder
I lost $15. My total loss was equal to 5%. Find the
number of hats. Ans. : 120.
22 PERCENTAGE.
loo. A merchant bought loo yds. of cloth at lo francs per
yard. \o% was lost by damage, and he sold the re-
mainder at lo marks per yard. Find the rate of gain
or loss. Ans. : 9t¥3% g^i^-
loi. A has 50% more money than B. E's money is what % of
A's ? Ans. : 66|.
102. Sold a horse at a profit of 40% on the cost, and at a dis-
count of 12^% from the asking price. What was my
asking price if cost was $100? Ans. : $160.
103. 10% of f of anything is what ^ of f of it? Ans. : T%.
104. I bought cloth and marked it at an advance of 40^. In
selling, I used a yard-stick one inch too short. My to-
tal gain was $330. Find cost of cloth. Ans. : $770.
105. A buys an article and sells it to gain 12^%. If he had
bought it for 10^ less and sold it for $18 less he would
have gained $20. Find the cost. Ans. : $i68f.
106. I sold a piece of cloth for $24, losing 25%. If I had sold
it for $34, would I have gained or lost, and what %?
Ans.: 6J% gain.
107. A and B invested equal sums in business. Againsasum
equal to 25% of his stock and B lost $225, when A's
money at this time was double that of B's. What
amount did each invest ? Ans. : $600.
108. 10% of 120 is 8 less than 5% of what No. ? Ans. : 400.
109. Sold a wagon for $25, losing i6f ;^; bought another ard
sold it at a gain of 16%. I neither gained nor lost on
the two. What did each cost.? Ans.: ist,$3o; 2d,|3[.2j.
no. By selling for $5 less than cost I lose \%. Had I sold i'
for $6 more than I did what % would I have gained ?
Ans.: 4V %•
111. I marked goods to gain 60%, but on account of using an
incorrect yard- stick I only gained 40%. What was the
length of the measure ? Ans. : \\ yd.
112. I buy vinegar at $4 a bl. and add water so that whea I
sell it at $3 a bl. I make 50%. What % of the mixture
is water? Ans.: 50%.
INTEREST. 23
.13. Isold goods at a certain gain %. If they had cost me
50% less my gain would have been 6 times as great.
What % did I gain ? Ans. : 10%.
114. I spent equal sums for rice, coffee and tea. I gained 20%
on the rice, io% on the coffee, and lost 8% on the tea.
My total receipts were $3,864. Find the cost of each.
Ans.: $1,200.
INTEREST.
1. I gave my note, 10 per cent, from date, for $2,442.04. What
sum, paid annually, will have discharged the whole at
the end of 5 years? Ans. : $644,204.
2. If the true annual rate of interest be 10^, what would be
the true rate for each 73 days, if the interest be com-
pounded throughout the year ? Ans.: 1.924 per cent.
3. I get 24 cents per day, which is f of a mill per day on $1.
How much have I at interest? Ans. : $1,080,
4. I pay 6% int. payable semi-annually, and lend it at 12%,
payable quarterly. I clear $2,450.85 a year. What is the
sum? Ans.: $38,485.87.
5. A debt is to be paid in 4 equal installments at 4, 9, 12, 20
months, respectively; its cash value is $750, allowing
5% simple interest. What is the debt? Ans. : $785,156.
6. I bought a lot for $156 due in 8 months, and sold it at
once for $180. What is my gain %, int. ^\% ? Ans.:
i8H%.
7. I sell my farm for $4,850 ; $250 payable at 6 mon., i J yr.,
2\ yr., 3^ yr., and 4^ yr. each, and the balance in 5 yrs. ;
if money is worth 10% per annum to me, what is the
cash value of the sale? Ans.: $3,413.08-1-.
8. What must I loan Jan. ist, at 9% , to be repaid by 5 install-
ments of $200 each, payable on the first day of the 5
succeeding months? Ans. : $978.15.
24 INTEREST.
9. I owe $1500, due in i yr. 10 mo. I pay $300 cash, and a note
for 6 mo. for the balance ; what is the face of the note,
interest 6%? Ans. : |i, 080.56.
13. What rate do I make by charging 12% per annum, com-
pound interest, payable quarterly ? Ans.: i2j%VWoV-
II What is my gain in i yr., on $100 deposited at 6% and
loaned 11 times for 33 days. Int. 2% a mon.? Ans.:
1 1 8. 20.
i2o Principal, $3,325, time 10 mo. 24 days. Int. $119.70; find
the rate. Ans.: 4%.
13, Ac what rate per annum will any sum double by simple
interest in 6 years ? Ans. : i6f %.
14, At what per cent, will $6,000 produce $45 in one month ?
Ans.! 9%.
15, What principal will produce $17 interest in 68 da. at 1% a
month.? Ans.: $750.
Lo. At what rate per annum will any sum treble itself at sim-
ple interest in 30 yrs. ? Ans. : 6f %.
17. What is the rate of interest when stock bought at 40%
discount yields a semi-annual dividend of 5%? Ans.:
i6|f..
18. At what rate per annum will any sum quadruple itself at
simple int., in 24 yrs. ? Ans. : 12^%.
19. What sum, drawing simple int. at 5% per annum, will
amount to $819.45 in i yr. 8 mo. 5 da. ? Ans. : $755.93.
20. In what time will $100 double itself by simple interest at
8%? Ans.: 12J yrs.
21. The interest on twice A's and 3 times B's money for 5 yrs.
6 mo. at 6% is $2,640; how much has each if twice A's
equals 3 times B's? Ans.: A, $2,400; B, $1,600.
22. How long must I deposit $1,37450, at 10^^, to pay a debt
of $1,480.78? Ans. : 9 mo. 8^— da.
23. How long would it take $175.12 to produce $6.43, interest
6%? Ans.: 7 mo. 10 da.
24. How long will it take $3,642.08 to amount to $4,007.54 at
i2'i^? Ans.: 10 mo. i da.
INTEREST. 25
25. What is the rate of discount when a 60-day note yields 2%
interest a mouth? Ans. : "^.^iz-hfo-
26. Find the face of a 90-day note, to net |i,ooo when dis-
counted at 6^. Ans. : $1,015.74.
27. At what rate should I discount a 60-day note to get 20%
per annum interest ? Ans.: 19/07% -
28. What is the rate when the interest on $200 for 2 years is
$48? Ans.: 12%.
29. How much must I loan at 6% to produce $48 in 2 yrs. ?
Ans.: $400.
30. I invest \ of my annual income in mortgages paying 6%
annual interest. In 6 mo. 12 days my interest from
them was $640. What is my annual income ? Ans. :
$100,000.
31. Find the difference between the annual and compound
interest of $400 for 2 yrs. at 8% , Ans. : o.
32. Find the difference between the annual and compound
interest of $200 for 3 yrs. at 6%, Ans. : $04+.
33. Find the difference between the simple and compound
interest of $200 for 2 yrs. at 8% , iiNe. " li 28
34. What must I save annually commencing at 18, so that I
may have $25,000 when I am 37 yrs. of age if I get 6%
compound interest? Ans. : $698,744-.
35. If the interest on the sum of A's and B's money, for 3 yrs.
9 mo., at 8%, is $3,213, and | of A's money is equal
to \ of B's, how much has each ? Ans. : A, $5,680 ; B,
$5,040.
36. \ of the cost of A's house, increased by \ of the cost of
his farm for 2 yrs. at 5% amounts to $4,950. What was
the cost of each if \ of the cost of the house was only
f as much as f of the cost of the farm ? Ans. : House,
$r,666.66|; farm, $4,375.
The sum of f of A's plus \ of B's money being on interest
for 8 yrs. at 6% gives $960 interest. What has each if \
of B's is 3 times | of A's ? Ans. : A's, $750; B's, $3,000.
A's money added to \ of B's, which is to A's as 2 to 3,
being put on interest for 6 vrs , at 4% , amounts to $744.
What has each ? Ans. : A, $360; B, $360.
26 INTEREST.
39. In what time will $13 at 6% give $0,975 interest? Ans. : i
yr. 3 mo.
40. The interest of $325 for 2 mo. is $3.25. Find the rate.
Ans.: 6%.
41. By lending a sum of money at 4% and another sum at 5%
the total interest is $68. If the rates are changed the
interest is $67. Find the principal lent at each rate.
Ans. : $700 and $800.
42. The interest on my money for 9 mo. at 5% is $150 less than
the same for 15 months at 4%. Find the sum. Ans. :
$12,000.
43. A sum of money doubled itself in 16 yrs. at simple inter-
est. Find the rate. Ans. :6^%.
44. The amount of a certain sum at simple interest for 3 yrs.
is $558 ; for 4^ yrs. it amounts to $612. Find the rate and
principal. Ans. : Rate, 8%; prin., $450.
45. The interest is | of the principal, and the difference be-
tween the interest and principal is $120. Find the in-
terest. Ans.: $80.
46. The interest is \ of the principal. The difference between
the interest and principal is $120. Find the principal.
Ans. : $150.
47. The interest on a sum of money in 5 yrs. is f of the sum.
What is the rate ? Ans. : \2\%.
48. At 3^% for 8 yrs. what fraction of the principal is \ of the
interest. Ans.: 2V
49. The interest of a sum of money at the end of 15 yrs. was
f of the sum itself. What was the rate ? Ans. : 4%.
50. A sum of money in 9 yrs. at 11% at simple interest
amounts to $597. In how many years will it amount to
$663 ? Ans. : 1 1 years.
51. The interest of $1,460 for one day is 25 cents. Find the
rate % per annum (365 da.) Ans. : 6^fc.
52. In what time at simple interest will $723. 16 J return | of
itself at 7^%? Ans. : 8 yrs. 4 mo.
53. A certain sum in 8 months amounts to $790, and in 19
months to $845. What is the rate ? Ans. : Sfo,
STOCKS AND BONDS.
5 1. What is the difference between the simple interest of $139
for 600 days and $600 for 139 days ? Ans. : o.
55. The interest of a certain sum is \ of tlic principal. The
amount is $640. Find the principal. Ans. : $560.
5O At what rate simple interest will a sum become 4 times
itself in 20 yrs. ? Ans.: 15%.
STOCKS AND BONDS.
What do I receive for 32 shares of telegraph stock which
a broker sells for me at 15% discount, charging \'fo
brokerage? Ans. : $2,712.
I purchased 18 shares of telegraph stock for $500 per share
at a premium of 2% and sold them for 28^ below par.
What was my loss ? Ans. : $2,700.
How many shares of stock must be sold at 4% discount,
brokerage ifo, to realize $4,775? Ans. : 50.
i received a 6% dividend on certain stock and invested
the money in the same stock at 75%. My stock had
then increased to $16,200. What was the amount of my
dividend ? Ans. : $900.
If I buy 6% stock at 90%, what rate of interest do I re-
ceive on my investment ? Ans. : 6|%.
At what rate must an 8^ stock be purchased to yield the
purchaser 7% interest? Ans. :ii4f.
At what price must 6% stock be purchased in order to ob-
tain Sfc income on the investment? Ans : 75%.
What sum must be invested in 8% stock at 130 to produce
an income of $2,000 ? Ans. : $32,500.
Sought 120 shares of canal stocks, $10 each, at j\% ad-
vance and sold at §% discount. Find my loss. Ans. : $23.
28 STOCKS AND BONDS.
10. ^.t what discount must I buy stocks so that -by selling at
2% premium I may gain 20% on my investment?
Ans. : 15%.
11. If I receive an annual dividend of 6% on Michigan stock,
which cost me but 37^%, what % income do I receive
on my investment? Ans. : 16%.
12. I bought bonds at 4% discor.nt and sold them at 5% pre-
mium. I gained $450. How many shares of $50 each
did I buy ? Ans. : 100.
13. When N. Y. Central is quoted at %|, how much stock can
be bought for $6,894, brok. J%? Ans. : $7,200.
14. I buy stocks at 25% below par and r,ell 20% above par.
What % do I make ? Ans. : 60^.
15. If I buy stock at 30% discount and every 6 months re-
ceive a dividend of 4^, what is my annual rate of inter-
est? Ans.: iif%.
16. A person exchanged 250 shares of 6% bonds at 70, for
bonds bearing 8% at 120. What is the difference in his
income ? Ans. : $333^.
17. How many shares of stock $100 each must be sold at 4%
discount, brok. ^%, to realize $4,775. Ans. : 50.
18. My broker sells 50 shares of stock, brok. J%. He remits
me $2,348.20. At what rate did the stock sell? Ans.:
19. At what price must I purchase 15% stock that it may yield
the same income as 6% stock purchased at 90. Ans. :
225.
20. If stock bought at 15% premium pays 8% on the invest-
ment, what % would it pay if bought at 10% discount?
Ans.: iof%.
21. What should I pay for a 6% bond of $50 that I may realize
8%? Ans. : $37-50.
22. When gold is at 115 and U. S. ia-40's at 105, what is a $500
bond worth ? Ans. : $456.52/3.
23. A party investing in 5% bonds realizes 8% income on his
investment. How did the bonds stand? Ans. : 62^.
24. How much must be invested in U. S. 8's at 95 to receive
an annual income of $3,000? Ans. : $35,625.
»
STOCKS AND BONDS. 29
-25. What % on his investment will a person receive who buys
f U. S. 6's at 107 when gold stands at 150 ? Ans. : 8j%\%.
26. When gold is worth 129 what yearly % income will a per-
son receive Who invests $7,540 in U. S. 6's when selling
at 104? Ans.: 7|f%.
27. What must gold sell for that a party investing in 5^40's at
105 may realize 8% on his investment ? Ans. : 140.
28. When gold is at 115 what is the semi-annual interest in
currency on $9,500 in io-40's ? Ans. : $273,125.
29. When gold is at 115 what amount in currency can be
bought for $8,500 in gold ? Ans. : $9,775-
A broker invested $21,300 in 5-20's at 106J and sold them
at 109. How much did he gain ? Ans. : $500.
31. When gold is 105 what is the value in gold of a dollar in
currency? Ans. : 95/x *^^^^®'
32. Bought $800 in gold at no, brok. 1%. What did I pay for
gold in currency ? Ans. : $881.
33. What face value of stock paying if % quarterly dividend
will yield an annual income of $513.50? Ans. : $7900.
34. What must be invested in 6\% bonds bought at 105 to
realize an income of $1,000? Ans. : $16,153.84x^3.
35. At the end of 6 mos. I received 4% dividend in stock; at
the end of the year, a 5% dividend in stock. I then
had $12,012 worth of stock. How many shares had I at
first? Ans.: no.
36. When U. S. 4's are worth 106, what will be my yearly in-
come in gold from bonds that cost $4,982 ? Ans. : $188.
37. If I pay 70 for bonds that yield an annual income of 7%,
what % do I get on my investment? Ans. : 10%.
38. How many shares of railroad stock bought at 95^ and sold
I at 105. brokerage i^% on each transaction, will yield an
' annual income of $925 ? Ans. : 100.
39. What must I invest in U. S. 5's at 118 to yield an annual
income of $1,921 in currency when gold is worth 113 ?
Ans : $40,120.
3o STOCKS AND BONDS. i
40. I own 25 shares in an electric light plant which declares '
a 5% annual dividend. I take the dividend in lighting ;
at the rate of $2.50 per lamp. How many lamps can I j
burn 10 mos. of each year ? Ans. : 60. i
41. What will be the cost of 25 $1,000 5-20 U. S. bonds of 1865 ,
at 1 14^, brokerage J%? Ans.: $28,593.75. !
42. My broker sells a certain amount of stocks and remits me ]
$25,734.37 J. His brokerage at yV% was $15.62^. What j
was the price of the stocks ? Ans. : 103. '
43. What is my currency income if I invest $5,220 in U. S. 5-20 i
6fo bonds at 116 when gold is 105? Ans. : $283.50. j
44. Find the cost of 125 shares U. P. R. R. stock at 68^, brok- \
eragei%? Ans.: $8,593.75. j
45. What will $8,000 U. S. io-40's of '65 cost at 108^^, brok. J%?
Ans. : $8,670. •
46. How much will 55 shares of railroad stock cost at 28|,
brok. $13.75? Ans.: $1,595- j
47. If I pay $5,418.75 for 50 U. S. 5-20's at 8J% premium, what
is the rate of brokerage? Ans. : i%. j
48. Bought 35 shares of canal stock at 86J and sold them at \
8i% premium. Find my gain. Ans. : $761.25. |
49. I sold 135 shares of stock at a discount of i$\%, paying ,
\% brokerage. How much did I receive for it ? Ans. : ■
$11,407.50. ^
50. How many shares of bank stock at 5% discount can be 1
purchased for $3,790 if \% is paid for brokerage? Ans. : !
40. i
51. What will be my income if I invest $4,196.25 in 5% stock \
purchased at 93, allowing \fc for brokerage ? Ans. : $225. \
52. What will be my annual income if I invest $1,299 ^^ ^% i
stock purchased at 37^, allowing \% brokerage. Ans.: i
$209,234-. ;
53. If I receive $622.80 by investing $4,696.95 in bonds at 45%, '
brokerage \%^ what rate do the bonds bear ? Ans. : 6%. [
54. Which is more profitable, and how much, to invest $5.':;j)0 1
in 6% stock purchased at 75, or 5% stock purchased al ■
60%? Ans.: 5^ at6oby $i6.66f.
I
STOCKS AND BONDS. 31
55. U. S. 5-20's pay 6% iuterest iu gold. What will be my in-
come in currency by investing $11,212.50 at 112J when
gold is at 106P Ans. : $641.25.
56. Which is more profitable, to buy 6% bonds at 90, interest
payable in currency, or 5% bonds at 95, interest payable
in gold, when gold is at io6| ? Ans. : 6% at 90.
57. Which affords the greater % of income, bonds bought at
125 which pay 8%, or bonds which pay 6% bought at a
discount of 10% ? Ans. : 6% at 10% discount.
^ 58. Which is more profitable, and how many % , to buy New
' York 7's at 105, or Louisiana 6's at 98 ? Ans. : N. Y. 7's
59. What must I pay for stock which pays a dividend of 15 fo
so that I may realize 7% on my investment ? Ans. : 2i4f.
60. I bought stock at 225 which yielded the same income as
6% stock bought at 90%. What rate did my purchase
bear? Ans.: 15^.
61. I sold $5,000 of U. S. 6's of '81 at 115 and invest in io-40's
at 105. Do I gain or lose and how much annually (lat-
ter bearing 5%)? Ans. : $26.20 loss.
62. What is a dollar in currency worth wh^n gold is quoted
at 125 ? Ans. : 80 cents.
63. If stock bought at 105 pays 6% on the investment, what
will it pay if bought at 15% discount? Ans.: 7tV%-
64. What must be the price of gold so that a person investing
in 5-20's at 108 may realize 7% ? Ans. : 126.
65. If I invest a certain sum in 6's at 85 and the same in 7's at
95 and receive $5 more a year from the latter investment,
how much do I invest in each ? Ans. : $1,615.
66. What sum must I invest in U. S. 5-20's of '82 at 96!%,
brokerage |%, to secure an annual income of $1,500?
Ans. : $24,250.
67. If I invest $10,200 in U. S. 6's at 30%, what is my income ?
Ans. : $2,040.
68. If I pay 125 for 10% bonds, what % do I make ? Ans. : Sfc,
69. When gold is 50% premium over paper money, what is a
paper dollar worth ? Ans. : 66f cents.
32 STOCKS AND BONDS.
70. At what price will a ^^Q% government bond of $1,000 pay
the purchaser 6% interest ? Ans. : I2i|.
71. At what price will a 10% bond of $50 pay 9% interest?
Ans. : $55f •
72. If gold were worth 125 and U. S. 5-20's worth 105, what
size of bond could I buy for $420 in gold ? Ans. : $500.
73. I pay $150 for two 6% bonds of $100 each. What rate do
I realize on the investment ? Ans. : 8^ .
74. I pay through a broker $29,840 for 6% Cleveland Water
Works bonds at 93^ % , including brokerage. The owner
afterwards refunds the brokerage, $240. What rate do
I realize on the investment? Ans. : d^-fc.
75. I have $8,475 invested in U. S. io-40's at 113. What is my
semi-annual income in currency, gold being worth no?
Ans.: $206.25.
76. When gold is worth 128, what half-yearly income in cur-
rent funds will a person receive who invests $7,540 in
U. S. ia-40's when selling at 104 ? Ans. : $232.
77. What % on my investment will I make by buying U. S.
7iV's at 104 ? Ans. : ^i^.
78. What must gpld sell for that a party investing in U. S. 6's
may realize 8% ? Ans. 1133^.
79. My semi-annual interest in currency is $276 on $9,600 U.
S. bonds when gold is at 115. What rate do the bonds
bear? Ans.: 5%.
80. When gold is at 115, what amount in currency can be
bought for $8,500 in gold ? Ans. : $9,775.
81. A broker invested $26,250 in 5-20's at 106.V and sold them
at 109. How much did he gain? Ans. : $616.19-!-.
82. Bought $8,000 in gold at no, brok. \fc. What did I pay
in currency? Ans.: $8,810.
83. Bought stock at 20^ discount, sold out at 112, realizing
$2,240. What did I invest? Ans. : $1,600.
84. When gold is at a premium of 25%, what is the discount
on greenbacks ? Ans.: 20%.
85. What income will be obtained by investing $6,840 in
stocks bearing 6% interest at 95 ? Ans. : $432.
STOCI^S AND BONDS. 33
86* U. S. 5-20's pay interest in gold. What will be my in-
come in currency by investing $11,212.50 at ii2j^wlien
gold is at a premium of 6^ ? Ans. : $641.25.
87. Bonds at 20^ premium, brokerage |%, cost $300.87 J more
than their face. What was the face of the bonds?
Ans. : $i,458ff.
88. A owned .075 of all the stock of a bank. The stock in-
creases .015 the first year. The increase was invested
in stock. He gave his son .025 of all the stock then
owned by him. What % of the whole stock of the bank
did he give away ? Ans. : .001875= j\%.
89. Bought a check at 55%; traded it for canal stock at 60%,
which bears 7% interest. What % interest do I receive
on my investment ? Ans.: 21/^%.
90. I invested $2,700 in bonds at 25% discount, which pays 8%.
How much must I invest in bonds at 4% discount and
paying 10% dividend to secure an equal income.? Ans.:
$2,764.80.
91. I sold canal stocks at a loss of 15%. I invested the pro-
ceeds in R. R. stocks and sell at 15% gain. Do I gain
or lose on the two speculations? How many %? Ans.:
2\% loss.
92. Bought bonds at lofo discount, which rose to 5% pre-
mium, and sold for cash. After paying a debt of $33, 1 in-
vested the remainder in stocks at 102, which at par left
me $11 less than at first. How much had I at first?
Ans.: $148.50.
93. I buy bonds at 94 ; sell at 100 ; my gain is $666 ; how many
$50 shares ? Ans. : 222.
94. I exchanged 72 N. Y. bonds ($1,000 each) at 6\% premium
for Ky. bonds ($500 each) at 2% premium. How many
of the latter did I get ? Ans. : 150.
195. 4% canal stock brings an income of $300, but sells in
market for 92%. What amount is invested? Ans.:
$6,900.
I
96. I invested in 5% furnace stock at 75. My income is $180.
How much must I invest in 6% state stock at 102 to
have the same income ? Ans. : $3,060.
34 STOCKS AND BONDS.
97. Which is the better investment, canal 4's, registered at
99f, or U. S. 4i's at 106. Ans. : Latter ^^^% better.
98. What is the value of 18 shares R. R. stock ($75 each) at 8%
discount? Ans. : $1,242.
99. What must be paid for fifteen $100 shares of mining stock
at 18% advance ? Ans. : $1,770.
ICO. How much money must I give with nine $100 shares at
15% discount in exchange for eight $100 bonds at 2%
discount ? Ans. : $19.
loi. How many $50 shares at 8% discount must be given for
23 bonds of $100 each at 2% premium ? Ans. : 51.
102. I bought 18 shares of $50 each at J% discount and sold at
f % premium. What is my gain ? Ans. : $11.25.
103. Bought 120 shares of R. R. stock ($10 each) at i\% ad-
vance and sold at 1% discount. Find my loss. Ans.:
$23.
104. I bought stock at 65 and after receiving a dividend of
S\% sold it at 82 and made $1,125. How much stock
had I and what % did I realize ? Ans. : 50 shares ;
realized 22 J%.
105. I bought stock at 73, and then received $945 as a dividend
at 2j%, when I sold my stock at 86|. How much stock
had I and what did I make ? Ans. : 420 shares ; made
$6,510.
106. I bought $9,040 worth of stock at $113, and after receiv-
ing a dividend of 5^%, sold at in J. How much did I
make and how much stock did I buy ^ Ans. : Made
$320; had $8,000 stock.
DISCOUNT. 35
DISCOUNT.
What sum is it whose true discount by simple interest for
4 yrs. is $25 more at 6% than at 4% per annum ? Ans. :
$449.50.
2. I bought a lot for $156 due in 8 months, and sold it at once
for $180. Find my gain %, int. 4^%. Ans. : i2^ii^%,
3. If I discount a note at 20% per annum I make 22^% inter-
est per annum ; how long does the note run ? Ans. :
200 da.
4. I discount a 6 mos. note at |% a month and it yields
$4,800. What was its face ? Ans. : $5,057.06+.
5. Paid $180 for a claim due in 6 mo. A broker bought the
claim same day, taking bank discount at 6%. I cleared
$13.90. What was the amount of the claim. Ans. : $200.
6. The true discount on a sum for 3 yrs. 4 mo. at 2 J % is $60 ;
and the interest on the same sum for the same time
and rate $65. Find the principle and rate. AnS. : $780
prin.; |f% rate.
7. How long must a note run discounted at 8% to yield 9^
per annum .? Ans. : i yr. 4 mo. 20 da.
8. The true discount of a debt of $405 due in 10 mo. 20 da. is
$30. What is the rate ? Ans. : 9%.
9. Sold flour for $3,275.60, half cash, the balance a note at 60
days. If the note is discounted in bank at 10%, what
will be the net proceeds of the sale ? Ans. : $3,272.83-}-.
Sold 50 bl. of rum, each containing 31 gal. 2 qt., at $2.40
a gal., receiving a note at 90 da. What would be the
proceeds of this note discounted at 7j%? Ans.;
$3,706.76+.
What will be the proceeds of a note of $999, payable in
97 days, int. 8% ? Ans.: $977.27.
36 DISCOUNT.
12. The discount of a certain sum at 6% for i8o days was
$185.49. What would have been the true discount?
Ans. : $180.
13. The present worth is $326,40, true discount $114.24, time
7 yrs. 9 mo. 10 da. Find the rate. Ans. : \Yfc.
14. A bank paid $336.43 for a note of $340 discounted at 6^.
How long did the note run ? Ans. : 60 days.
15. The discount on a debt due in 2 yrs. was $45. What would
have been the discount on the same note 10 months be-
fore due ? Ans. : $26^^.
16. The discount was $3.96 on a note of $396 for 57 days.
What was the rate of discount? Ans. : 6^.
17. Find the true discount of a debt of $405 due in 10 mo. 20
da. at 9%. Ans.: $30.
18. The bank discount of a note of $750 was $8.50. What was
the time, interest 8% ? Ans. : 48 days.
19. What is the present worth of a debt due in 4 yrs. 8 mon
10 da,, the true discount at 6% being $169 ? Ans. : $600,
20. The bank charged $33.20 and paid $2,366.80 for a note dis
counted at 6%. How long had it to run ? Ans. : 2 mo
20 da.
21. Rate 8%, discount $105, debt $245. Find the time. Ans.
9 yrs. 4 mo. 15 da.
22. I received $792 for a note of $800 payable in 42 days. Find
the rate. Ans.: 8%.
23. A bank gave $1,385.30 for a note payable in 60 da. How
much did they charge for discounting at 6% ? Ans..
$14.70.
24. A bank charged $27.30 for discounting a note of $2,600,
payable in sixty days. Find the rate. Ans : 6%.
25. The bank discount on a note having 2 mos. to run was
$72.66, int. (i%. Find the face. Ans.: $6,920.
26. The proceeds of a note dated Feb. 19th, 1892, payable Jan.
ist, 1893. and bearing 8% int., was $105. 51J, when dis-
counted Oct. 12th, 1892, at 6%. What was the face of
the note ? Ans. : $100.
DISCOUNT.
27. For what sum must I give my note for 6 mos. to realize
$1,500; int. 10^? Ans. : $1,580.33.
28. What is the present worth and discount at 8% of a note of
$500, due in 3 yrs., and bearing interest at 6%? Ans.:
P. W., $475.81 ; dis., $114.19.
29. Find the true discount at 6% of a note of $300, due in 2
yrs., and bearing 8% interest. Ans.: $37.29.
30. Find the present worth and discount of a note of $368.75
for 5 mos., at 10%. Ans.: $354; $14.75.
31. I bought goods amounting to $775, on 4 mos. credit. What
would I pay cash if money is worth 10% ? Ans. : $750.
32. If money is worth 6%, what sum in cash will pay for a
bill of goods amounting to $260, bought on 8 months'
credit ? Ans. : $250.
33. I can have 4 mos. credit or 5% off for cash. What will be
my gain by paying cash on a bill of goods amounting
to $2,480, if money is worth 10 fc ? Ans. : $45.47.
34. The difference between the true and bank discount of a
certain principal is $2.45 for i year. What is the princi-
pal, int. 7% (omitting days of grace)? Ans.: $535.
35. I was oflfered $r,i22 for my farm in cash, or $1,221 payable
in ID mos., without interest ; I chose the latter. How
much did I lose, money being worth 12%? Ans. : $12.
36. I bought goods on 9 mos. credit, amounting to $840.40.
How much money will pay the debt at the time of re-
ceiving the goods, int. being 8%? Ans.: $792,83.
37. A 30-day note yields $1,650, when discounted at ij% a
month. Find the face. Ans. : $1,677.68.
38. A note discounted at 8% for 40 days yields $2,072.60. Find
the face. Ans. : $2,092.60 — .
39. At what should I discount a 60 day note to get interest at
the rate of 20%? Ans.: 19/07%-
40. What is the rate of discount when a note running i yr.
will produce 25% interest without grace ? Ans. : 20^.
41. I offered to sell my farm for $8,000 cash, or for $10,296 in
three equal payments, at the end of i, 2 and 3 yrs., with-
out interest. If money is worth 10^, what will be the
gain to the buyer by Dayiug cash ? Ans. : $620*
38 EXCHANGE.
42. What will be the face of my note if I wish to obtain $400
from a bank for 30 days when discounted at 6%? Ans. :
$402.21.
43. The bank discount on a certain principal for i yr. at 6%
is $3 60 greater than the true discount for the same time
and rate. Omit days of grace and find the principal.
Ans.: $1,060.
EXCHANGE.
1. What is the cost of a draft on Augusta for $5,680, payable
in sixty days, exchange being 2X \% prem., int. 6^?
Ans.: $5,648.76.
2. What is the cost of a draft on Albany for $1,575, payable
in 30 days, exchange being at f % premium, int. 6%?
Ans.: $1,578.15-
3. The face. of a draft payable in 60 days is $2,625, exchange
being at \\Jo premium, int. 6%. Find the cost. Ans.:
$2,636.81+.
4. Find the cost of a draft for $500, payable in 30 days after
sight, exchange being 1% premium, int. dfo. Ans.:
$502.25.
5. How large a draft payable 30 days after sight can be
bought for $502.25, exchange being 1% premium and
int. 6%? Ans.: $500.
6. How large a draft payable in 60 days can be bought for
$798.80, exchange being \\% premium and interest 8%?
Ans.: $800.
7. A draft payable in 30 days was bought for $352.62, ex-
change being \\% discount, and int. 6%. Find the face.
Ans.: $360.
8. What must be paid in Baltimore for a draft on Cincinnati,
drawn at 90 days for $4,8 jo, the course of exchange be-
ing loif, int. 6%? Ans.: $4,791.60.
EXCHANGE. 39
9. A commission msrchant in Albany wishes to remit to his
employee, in Columbus, by draft at 60 days, $512.36.
What is the face of the draft he can purchase with this
sum, exchange i^'fo discount? Ans. : $531.2184-.
10. What must be paid in New York for a draft on Concord,
at 30 days for $5,400, exchange \ % premium ? Ans. :
$5,397-3o-
11. An agent in Harrisburg, Pa., having $1,324.74 due his em-
ployee, is instructed to remit the same by a draft drawn
at 30 days. What will be the face of the draft, ex-
change being at i|^ premium .? Ans. : $1,309.03.
12. Exchange on Augusta, Me., for $5,000, cost $5,075. What
was the course of exchange ? Ans. : 1^% premium.
13. What is the market price of a sight draft on New York
for $890, exchange being ioiJ%? Ans. : $901. 12J.
14. Find the market value of a sight draft on New York for
$1,800, exchange 99%. Ans.: $1,782.
15. Find the cost of a draft on Cincinnati for $1,400, payable
in 60 days after sight, exchange being worth io2j%, and
int. being 7%. Ans.: $1,420.18^.
16. What is the cost of a draft on Peoria, 111., for $2,400, paya-
ble in 90 days, int. being 10%, and exchange 103%?
Ans. : $2,410.
17. Find the value of a draft on Boston for $1,650, payable 60
days after sight, exchange being 98J, and int. 6% . Ans. :
$1,607,925.
18. If exchange is ioiJ%, how large a sight draft can be
bought for $7,900 ? Ans. : $7,783.25.
19. What is the face of a draft that can be bought for $5,000,
when exchange is 98^ ? Ans.: $5,076.14.
20. What is the face of a draft at 60 days sight, which costs
$r,ooo, exchange being 103^ and interest 6%? Ans.:
$980.87.
21. What is the cost of a si^ht bill for ^87, when £1 is wortl]^
$4.82 in gold, gold being worth 106 ? Ans. : $444.5o-f .
22. How large a bill can be bought for $2,000 in currency,
when sterling exchange is quoted at $4.85 and §old at
jp6? Ans.: ^389 7+d,
40 EXCHANGE.
23. What will a check on New York for $1,505.40 cost 2X\^c
discount? Ans.: $1,501.64—.
24. What will a 60-day draft on Columbus for $12,692.50 cost
at f % premium, int. off atSfc? Ans. : $12,654.42-}-.
25. Find the face of a draft on New York that will cost $2,000
at 1^ premium. Ans. : $1,987.58—.
26. A draft cost $4,681.25, at il% discount. Find the face.
Ans.: $4,740-51— •
27. What must be the face of an 18-day draft costing $5,264.15
at ^^ premium, int. off at 6%? Ans.: $5,256.27 — .
28. A 21-day draft cost me $6,836.75, at f % discount and in-
terest off at 6^. Find the face. Ans. : $6,925.04. .
29. What is the cost of a 60-day draft for $850 on New York,
exchange being at loij, int. 6fo per annum? Ans.:
$853-825.
30. The cost of a 30-day draft was $2,128,525, exchange being
102, int. yfo. Find the face. Ans.: $2,100.
31. What is the cost of a draft of $500 for 60 days at f %
premium, int. 6%? Ans.: $498.50.
32. I paid $343.22 for a 90-day draft at ^% discount, and int.
6%. Find the face. Ans.: $350,404-.
33. When exchange on New York is 98^, what is the cost of
a draft for $362 for 30 days, int. at 6%? Ans. : $354.58—.
34. What is the face of a draft payable 60 days after sight
that will cost $652,925, exchange ij%,int. 6%? Ans.:
$650.
35. The face of a draft for 30 days, exchange being 98I, and
interest 6%, was $1,588,595. Find the cost. Ans. : $1,560.
36. What will be the cost in Nashville of a sight draft on Col-
umbus for $1,000, the rate of exchange being ^% pre-
mium? Ans.: $1,005.
37. If exchange on Chicago is i\% premium, what will be the
cost in Memphis, Tenn., of a sight draft of $3,000?
Ans.: $3,037.50.
38. A merchant in Chicago bought a draft on Albany, New
York, for $5,000, payable 30 days after sight. Find the
cost if exchange was 1% premium. Ans. ; $4,978.75.
EXCHANGE.
39. What will be the cost in Lansing, Mich., of a draft for
$1,500 on Cleveland, O., payable 90 days after date, when
exchange is ^ % discount ? Ans. : $1,471,875.
40. How much will be realized from the sale of a draft for
$6,000 2X\fo discount ? Ans. : $5,985.
41. How much will be realized from the sale of a draft on
Cincinnati for $3,000, sold at \% premium? Ans.:
$3>oo3-75.
42. When exchange is looj, what will be the cost of a draft
for $5,000, purchased in St. Louis on Denver, to be paid
3 nios. after date .? Ans. : $4,928.75.
43. If exchange is 100^, what will a draft for $1,500 cost, pur-
chased in Detroit, Mich., on Columbus, payable in 2
mos. without grace ? Ans. : $1,488.75.
44. If exchange is \% premium, what will a draft for $1,500
cost, purchased in St. Paul, Minn., on Zanesville, O.,
payable in 4 mos. without grace .-* Ans. : $1,473.75.
45. If exchange is at yV% premium, what will a draft br
$5,000 on Memphis, Tenn., cost in New York, payable
2 mos. after date ? Ans. : $4,952.50.
46. How large a draft on N. Y. can be purchased for $5,000
when exchange is at i\% premium? Ans.: $4,926.11 — .
47. What will be the cost of a sight draft on N. Y. for $5,725,
when exchange is |^% premium? Ans. : $5,710.71-4-.
48. Find the face of a 30-day draft purchased for $1,500, if the
rate of exchange is ^% premium. Ans. : $1,506.40.
49. If I pay $1,200 for a draft payable in 2 mos. when the
premium on exchange is ^% and the rate of interest is
9% , what is the face of the draft ? Ans. : $1,213.04+.
50. How large a sight draft on St. Paul can be purchased in
N. Y. for $10,000 if exchange \% \% discount? Ans.:
$10,012.51+.
51. How large a draft can I buy on Cincinnati for $1,750 if
exchange is at ^% premium ? Ans. : $1,747.81+.
52. A commission merchant in Denver, Col., sold goods
amounting to $3,500 for a man in N. Y. He sent the
amount due by a draft payable in 30 da. after sight, ex-
change being | % premium. How large a draft did he
purchase ? Ans. : $3,5i4-93+'
42 INSURANCE.
53. Find the face of a draft ou I/ondon that can be bought in
N. Y. for $3,762.50 in currency when gold is at 105J and
exchange is at I4.87. Ans. : ^732 6s. 2.44-d.
54. When exchange is $4.86 for a pound sterling and gold is
at 107^, what will be the face of a draft that can be
bought in N. Y. on London for $2,984.38? Ans.: /571
4s. 6.64-d.
55. I wish to obtain a bill of exchange on Paris, at sight for
3,269 francs. What will it cost, exchange being at 5.15
francs to the dollar and gold at losf ? Ans.: $668.87+.
56. When exchange is at 5.19 francs to the dollar and gold at
106^, what must be paid in currency for a sight bill of
exchange on Paris for 8,950 francs? Ans.: $1,832.25 — .
57. Find the currency value of a draft on London for ;^895
los., when exchange is $4.87 for a pound sterling and
gold is at io6|. Ans. : $4,65o+.
58. When exchange is 5.20 francs for a dollar and gold is
worth 106^, what must I pay for a sight draft on Paris
for 5,725 francs? Ans.: $1,169,774-.
59. I purchased a sight draft on London for ^585 los. 5d. Find
the currency value of the draft, if exchange was at par
and gold 107J. Ans. : $3,059.05-!-.
60. Gold is quoted at 104J. Exchange is $4.88^. Find the
cost in currency of a sight draft on London for ;i^875
5s. 4d. Ans. : $4,484. II -|-
INSURANCE.
1. I insured | of a shop worth $3,600 and f of a store worth
$6,000. Find the rate of insurance if I paid $126, pay-
ing $1 for the policy. Ans. : \\fo.
2. It cost me $75 for insuring a store for f of its value at
ii%. What was the store worth ? Ans. : $10,000,
INSUJ^ANCE. 43
3. Find the cost of insuring f <^f ^ factory at f %^ which is
valued at $340,000. Ans. : 1 1,328.124-.
4. I paid $17.25 for insuring f of a building at i\'fo ; find the
value of the house. Ans. : $2,300.
5. I paid $39 for insuring a building worth $4,550 at i\%\
what fraction of the value was insured ? Ans. : f .
6. Find the cost of insuring | of a building worth $24,000
and f of another worth $36,000, the former at 2^%, the
latter at ij%. Ans. : $607.50.
7. A shipment of goods costing $1,275 is insured at f ^, the
policy costing $1.00 ; find the cost of insurance. Ans. :
$8.08^.
8. I paid $19.20 for insuring f of a barn worth $4,800. What
was the rate ? Ans. : f ^.
9. I insured a house at i\%\ reinsured | of it at 2%, and \
of it at 2\%\ what rate of insurance do I get on the
remainder? Ans.: t\%.
10. I took a risk of $45,000 ; reinsured at the same rate $1,000
each in five offices, and $5,000 in another. Find the rate
of insurance, my share being $262.50. Ans.: 2|%.
11. I took out a life policy at the age of 21 for $5,000. The
annual premium is $19.89 on $1,000. What will it cost
me to keep up my insurance if I live to be 75 yrs. old?
Ans. : $5,370.30.
12. I wish to secure an endowment policy for $1,000 payable
in 10 yrs., annual premium costs $104.58. Find the
amount of the 10 payments, allowing int. at 6%. Ans.:
$1,390.91+.
13. I received $118 for insuring a building at |%. Find the
value of the building. Ans. : $14,750.
14. I received $42.30 for insuring | of a house at t*^%l what is
the value of the house ? Ans. : $7,520.
15. My share of the premium was $197.13 after taking ^ of a
risk at 2j%, and reinsuring! of it at 2^%. Find the
amount of the risk. Ans. : $262,840.
16. Took a risk at if, reinsured I of it at the same rate, and
I of it at ij%. How large was the risk, my share of the
premium being $58. 1 1 ? Ans. : $19,370.
44 INSURANCE.
17. I insured property at 2^; reinsured $8,ocxd at i|%, and
$10,000 of it at 2\%. What was the amount insured,
my share of the premium being $207.50 ? Ans. : $28,000.
18. For how much must a ship worth $2,000 be insured, so
that the insurance will cover \ of the value and premium
at \\%} Ans.: $1,522,842.
19. I received $225 for insuring a store and contents for | of
their value at \\%. The stock was worth \ as much as
the store. Find the value of each. Ans. : Stock,
$6,666.661 ; store, $i3,333-33i.
20. I paid $325 for insuring my store for $16,250. What was
the rate of premium ? Ans. '.2%.
21. I paid $2,475 for insuring f of my property at \\%. Find
the amount of my property. Ans. : $297,000.
22. I insured my property for f of its value at 2 J %, paying
$1,657.50. What was the value of my property ? Ans.:
$88,400.
23. I paid $400 for having | of my property insured at 4^%.
Find the value of the property. Ans. : $13,333.33^.
24. My stock of goods is worth $30,000 ; insured it for | of its
value at f %. In a fire I saved $5,000 of goods. What
was my loss? Ans.: $25,168.75.
25. I paid $180 for insuring my stock for § of its value at 3%.
What is the value of the stock ? Ans. : $9,000.
26. Mr. Jones paid $652.50 for insuring a mill worth $43,500.
Find the rate. Ans.: i^^.
27. I paid $175 for insuring my house at ij%. It was de-
stroyed by fire. How much insurance did I procure ?
Ans. : $14,000.
28. What will be the annual premium on a life policy of
$5,000 at $21 10 per $r,ooo? Ans.: $105.50.
29. A person 33 years of age pays $123,90 annual premium on
a life insurance policy of $5,000. Find the rate. Ans.:
30. My building is worth $150,000 and is insured for \ of its
value in three companies ; the first takes a \ risk at |%,
the 2d a ^ risk at f %, and the 3d the remainder at f ^.
What is the premium? Ans. : $717.18.
TAXES. 45
My ^oods worth $6,000, and insured at 2,J%, were damaged
654%. What did the company have to pay above the
premium ? Ans. : $3,810.
32. I bought 1,500 bu. of wheat at $1.10 per bushel, and had it
insured at $1.20 per bushel at 2^%. It was all destroyed
by fire ; what is my gain ? Ans. : $105.
33. An insurance company took a risk on a vessel for $100,000
at 1%, but deeming the risk too great reinsured $60,000
at Ifc'y what was the amount received more than paid?
Ans. : $225.
34. The premium at 3% is $378 ; what is the value of the prop-
erty insured? Ans. : $12,600.
35. At what must property worth $1,950 be insured at 2j% so
as to include premium in case of loss ? Ans. : $2,000.
36. I had 9,700 bushels of wheat worth $1.20 per bushel ; I had
it insured at 3%, so as to cover premium and loss. For
what was it insured ? Ans. : $12,000.
37. For what sum must I have my property worth $2,600 in-
sured, premium at xV%> to cover property? Ans.:
$2,618.26+.
TAXES.
Find the tax to be raised in a township whose taxable
property is worth $486,250, the rate of taxation being 78
cts. on $100. Ans. : $3,792.75.
My property is assessed at $3,800. What is my whole tax
if the rate of taxation is xV(J% ^^^ ^ V^Y ^ poll-tax of
$1 ? Ans. : $30.64.
My whole tax is $53.46. I pay for 3 polls at $1.50 each. I
own $8,704 taxable property. Find the rate of taxation.
Ans. : 56^ cts. on $100.
My income is 16% of my capita. I am taxed 2}% of my
income and pay $26.04. Wlhat is my capital ? Ans. :
$6,510.
46 DUTIES OR CUSTOMS.
5. I sold my property for $7,599, whic'i was cost, and 1% be-
sides paid for tax. What was the cost ? Ans. : $7,450.
6. I pay a tax of $1.35 on $100 on my capital and I have left
$125,127.66. What was my capital and tax ? Ans.: Capi-
tal, $126,840 ; tax, $1,712.34.
7. Find the value of the taxable property in a village con-
taining 1,024 polls paying $1 each, that pays a tax of
$4,000, taxation being 2.4 mills on the dollar. Ans. :
$1,240,000.
8. A's real estate is assessed at $4,300, and personal property
at $1,940; pays for 2 polls at $1 ; is taxed $33.20. What
was the % of tax? Ans.: Y/c.
9. In a township whose valuation is $6,748,950, the rate of tax
is 3xV%I the collector is paid \\% for collecting. What
is the amount collected, and what are the collector's
fees? Ans.: Amount, $239,317.76; fees, $3,644.43+.
DUTIES OR CUSTOMS.
1. Find the duty on 3 boxes of tin weighing 11 1, 112 and
113 lbs., respectively, at 5 cts. a lb., tare 5^. Ans.:
$15.96.
2. What is the duty at 4% on 20 boxes, each containing 250
lbs. of tobacco costing 20 cts. a lb., tare (i\%'> Ans.:
$37-50.
3. I received 3,724 yds. of cloth invoiced at 23 cts. a yd. ; the
duty is 10 cts. a yd. and 1 1 % ad valorem, less 10% . What
is the total amount of duty? Ans. : $419 96 — .
4. Find the duty on 45 barrels of whisky, each containing 36
gal., invoiced at $1.25 per gal., at 40% ad valorem, al-
lowing 2% for leakage. Ans.: $793.80.
5. What is the duty on 12 98-lb. boxes of soap, tare 10%, at 5
cts. a lb. ? Ans. : $52.92.
DUTIES OR CUSTOMS. 47
6. What is the duty on 36 boxes of sugar, each weighing 668
lbs., at 2j cts. a lb., deducting \ of the entire weight for
tare? Ans. : IsiS-S^-
7. Find the duty on oilcloth 40 yds. long and 3I yd. wide,
worth 75 cts. a sq. yd., at 30% ad valorem. Ans.:
$35-07+.
8. What is the duty on 30 bags, each weighing 760 lbs., tare
12% , at $1.20 a cwt. .? Ans. : $240,764-.
9. What is the cost per gal. of Jamaica rum if I pay $631.43
for 1,680 gal., duty 15%, leakage 2%, charges $53.34?
Ans. : 30 cts.-f.
10. Find the invoice price of an amount of cloth after paying
30% duty and other charges $73.80, and cost in store
$7,389-03- Ans. : $5,627.10.
11. A wine merchant imported 60 casks of wine, 54 gal. each,
invoiced at $1.80 a gal., transportation 25 cents a gallon,
charges $8.50, leakage 5% and duty 20^. What was the
entire cost ? Ans. : $7,758.58.
12. I paid $184.80 duty on 50 bbls. of sugar, weighing 220 lbs.
each, gross tare 4%, invoiced at 5 cts. a pound. What
was the rate ? Ans. : 35%.
13. What is the duty at 15% on 540 bags of coffee, gross
weight 160 lbs. each, tare 3^%, invoiced at 9 cts. a pound?
Ans.: $1,125.57+.
14. What is the duty at 28% on 25 cases of cloth containing
24 pieces each, 45 yds. in a piece, and worth $1.13 a yard?
Ans.: $8,542.80.
15. What is the duty on 12 barrels of whisky of 42 gal. each,
invoiced at $1.30 per gallon at 31 J %, leakage 5%? Ans. :
$196.07-.
16. A imported 40 rolls of carpet, 160 yds. each, and paid
$1,024 tiuty at 20%. At what price per yd. was the carpet
invoiced ? Ans. : 80 cts.
17. What is the duty on 20 boxes of raisins of 25 lbs. each,
valued at 10 cts. a pound, allowing 15% for tare, when
the rate of duty is 6% ad valorem ? Ans. : $2.55.
18. What is the duty on 7 tons of steel of 2,240 lbs. each, in-
voiced at 17 cts. per lb. when the rate of duty is 20^ ad
valorem? Ans.: $533.12,
48 PROPORTION.
19. Find the duty on 20 hhds. molasses, each containing 63
gal., at 9 cts. per gal., allowing 5% for leakage. Ans. :
$107- 73-
20. What is the duty on 10 barrels of Havana tobacco, each
weighing 145 lbs. gross, tare 8%, at 6| cts. a pound?
Ans.: $90.04-1-.
21. When there is a duty on tea of 10 cts. a pound, what must
be paid on 45 chests of tea, each weighing 120 lbs., tare
10 %? Ans.: $486.
22. What is the duty on 210 bags of coffee, the gross weight
of each being 190 lbs., invoiced at 5 cts. a pound, the
tare being 5% and duty 25%? Ans. : $473.81+.
23. What is the duty at 40% ad valorem on 15 cases of broad-
cloth, each containing 25 pieces of 35 yds., invoiced at
$3.95 a yd. Ans. : $20,737.50.
24. The duty on 15 gross of bottle beer, allowing 10% break-
age, was $40.50 at 20% ad valorem. How much a dozen
were they invoiced at? Ans. : $1.25.
25. The duty on 100 pieces of silk of 18 yds. each was $337.50
at 25% ad valorem. What was the invoice price per yd.,
and what must I sell it per yd. to gain 20%? Ans. : In-
voiced at 75 cts. per yd. ; selling price $i.i2j.
26. Paid $806.12 duty on cloth at 35%. What were they in-
voiced at, and what did they cost in store? Ans.: In-
voiced at $2,303.17 ; cost $3,109.27-1-.
27. I pay a duty of $1,473.80 on goods valued at $3,684.50.
What is the rate of duty ? Ans. : 40%.
PROPORTION.
1. The first, third and fourth terms are 8.4, 9J and 5J. What i
is the second? Ans. : 4.95. \
2. The last three terms are 9^, \\ and 8^. What is the first j
term? Ans.: i|. 1
PROPORTION. 49
3. If I can build f rods of wall in f of a day, how much can
I build in -^-^ of a day ? Ans. : x% rd.
4. 35 men have flour for 24 days. If 14 leave, how long will
it feed the remainder ? Ans. : 40 days.
5. If the consequent is f and the ratio \, what is the ante-
cedent ? Ans. : aV*
6. If the antecedent is 6 and the ratio i|, what is the conse-
quent ? Ans. : 5.
7. What is the ratio of a pound troy to a pound avoirdupois?
Ans.: ill.
8. What is the difference between the compound ratios
9. What is the difference between the ratio 4f : 7J and the
inverse ratio ? Ans. : \\\\.
10. If the ratio is 2\ and the consequent is 6J, what is the
antecedent ? Ans. : 14^.
11. Find the inverse ratio of the two numbers ^\ and 2 J.
Ans.: f.
12. A certain number has been divided by one more than it-
self, giving a quotient \. What is the number? Ans. : \.
13. If 48 lbs. of salt water contain \\ lbs. of salt, how much
fresh water must be added to these 48 lbs. so that 40 lbs.
of the mixture shall contain \ lb. of salt ? Ans. : 72 lbs.
14. Divide the number 3I into two such parts that the first
shall equal the second plus jV Ans. : i|f and if ^.
15. A, B and C earned $3,456 ; B earned 3 times as much as C
and A 4 times as much as B. How much did each earn ?
Ans. : A, $2,592; B, $648; C, $216.
16. A and B have 2,255 l>u. of corn ; | of A's equals \ B's
amount. How many bushels has each? Ans. : A, 1,100;
B, 1,155.
17. The difference between two numbers is 120, and \ of the
first equals f of the second. What are the numbers ?
Ans. : 1,296 and 1,176.
18. The sum of two fractions is ly^. and | of the first equals
f of the gecoud, Find the fractioi^s, Ans. : \ and |.
50 PARTNERSHIP.
19. John has $637 less than James, and | of James' equals \\
times John's. How much has each ? Ans. : John, $728 ;
James, $1 365.
20. A and B have 13,650 sheep ; 5 times A's equals 8 times B's.
How many has each ? Ans. : A, 8,400 ; B, 5,250.
21. A bought a farm, store and a house for $28,100. The farm
cost three times as much as the house, plus $450 ; and
the store cost twice as much as the farm, minus $650.
What was the cost of each ? Ans. : Store, $16,450; farm,
$8,550; house, $2,700.
PARTNERSHIP.
1. A, B and C buy property for $2,500; A pays $500; B,
$1,200; C, $800; they rent it for $300. What is each
one's share of the rent? Ans.: A's, $60 ; B's, $144 ; C's,
$96.
2. X, Y and Z rent a farm for $1,200; X pastures 16 cows;
Y, 14 cows, and Z, 12 cows. How much should each
pay ? Ans. : X, $457} ; Y, $400 ; Z, $342!-.
3. A, B and C buy a store ; A puts in $18,000 ; B, $6,000 ; C,
$10,000 ; they lose 30% of their stock by fire and sell the
remainder at a gain of 50%. What is each one's share
of the gain ? Ans. : A's, $900 ; B's, $300 ; C's, $500.
4. What is the stock of each, when A, B and C gain $2,250;
A's gain is $800, B's gain is $1,000, and C's capital is
$3,000? Ans. : A's, $5,333^ \ B's, $6,666f.
5. Ray Jones willed his son $6,500; his wife, $8,000, and his
daughter, $5,500 ; his estate amounted to only $12,000.
What did each get? Ans.: S, $3,900; W, $4,800; D,
$3,300-
6. A, B and C buy a store for $16,000; A pays $5,000; B,
$6,500; C, $4,500; they pay $2,500 for clerks, $600 for
rent, then sold out for $23,000, What did each gain?
Ans.: A, $1,218.75; B, $1,584 37*; ^$1,096.87^.
PARTNERSHIP. 5t
7. X, Y and Z hire a pasture for $87.20 ; X puts in 3 cows for
16 weeks ; Y, 5 cows for 20 weeks ; and Z, 7 for 10 weeks.
How much does each pay, and what is the pasturage of
a cow per week? Ans. : X, $19.20; Y, $40; Z, $28; P,
40 cts. a week.
8. A, B and C, on closing business, paid $2,706. A had $4,200
invested ; B, $3,600 ; C, $4,500. What amount did each
pay ? Ans. : A, $924 ; B, $792 ; C, $990.
9. A, B and C do a piece of work for $1,600 ; A furnishes 7
men 30 days ; B, 5 men 40 days, and C, 6 men 32 days.
How much should each receive if they pay $95 for
clerks ? Ans. : A, $525 ; B, $500 ; C, $480.
10. X invested $675 ; B, $810 for the same time ; X's gain was
$125. What was the whole gain ? Ans. : $275.
11. A invested $2,500; two months afterward B joined him
with $3,000 ; in two yrs. they cleared $2,835. Divide
their gain. Ans. : A, $1,350; B, $1,485.
12. A, B and C invested $1,000 each ; A's money was in 10
mos. ; B's, 12 mos. ; C's, 14 mos. ; they sold for $2,730.
What did each lose .? Ans. : A, $75 ; B, $90 ; C, $105.
13. Divide 756 into two parts, which shall be to each other as
7.5 to |. Ans. : 720 and 36.
14. Divide 10.25 into two parts to each other as if to 2J.
Ans.: 4.1 and 6.15.
15 A, B and C bought a horse for $100, sold at a gain of 50%,
by which A gained $18, and B $19. How much did each
pay for the horse? Ans. : A, $36 ; B, $38 ; C, $26.
16. A pastures 8 horses 3 weeks 2 days ; B, 12 horses 4 weeks
I day. What part should each pay? Ans. : A, y^a ; B,
17. A company charter a boat for a picnic for $50 ; having but
210 to go, they receive on board another company of
140. What should the second company pay ? Ans. : $20.
18. A and B rent a lot for $50 ; on dividing, A's tract is 80
yds. long and 60 yds. wide ; B's, 64 rds. long and 50 rds.
wide. What should each pay ? Ans. : A, $30 ; B, $20.
52 EQUA TION OF PA YMENTS.
19. A, B and C gaiu $3,250; A puts in $2,500; B, $1,500; after
9 mos. they take in C with $5,000; 9 mos. after this they
quit. Divide their gaiu. Ans. : A, $1,250; B, $750; C,
$1,250.
20. X and Y hire a pasture for $275 ; X puts in 80 sheep and
Y 100 ; after 6 mos. they each sell h of their sheep, and
allow C to feed 50 sheep the rest of the yr. How much
should each pay? Ans.: A, $103.12^; B, $128.90!; C,
$42.96^.
21. A's stock is to B's as 4 to 5 ; after 3 mos. A withdraws ^
of his and B ^ of his. Divide $1,695 at the end of the
year. Ans. : A, $720 ; B, $975.
22. A, B and C's capital is as 2, ^, J ; after 4 mos. A takes out
J of his; after 9 mos. more their gain was $1,988. Di-
vide it. Ans. : A, $714 ; B, $728 ; C, $546.
23. A's capital is $4,200; B's $5,600; after 4 months how much
must A put in to entitle him to half the year's gain ?
Ans.: $2,100.
24. A furnishes 404 bus. of corn at 50 cts. per bu. ; B, 340 bus.
of wheat at $1.10 per bu. ; they gain $31.68. What did
each gaiu? Ans.: A, $ii.ii; B, $20.57.
25. A put in $7,000 for 6 mos. ; B put in $5,000 and received j^j-
of the profit. How long was his money invested ?
Ans. : 7 mos.
EQUATION OF PAYMENTS.
1. I wish to pay $600 in one payment, instead of paying $50
on the first day of each mo. of the yr. When should I
pay it ? Ans. : In 5f mos.
2. I owe $900, due in 12 morths; if I pay $300 now, when
shall I pay the balance ? Ans. : 18 mos.
3. Bought goods as follows : Jan. 15, $30 ; Jan. 27, $80 ; Feb.
8, $70; Feb. 24, $60. Find the equated time. Ans.;
Feb. 5.
TION OF PA YMENTS. 53
4. May I, I owe $300 ; July 12, $700 ; and Sept. 22, $Soo, When
may I pay them all together? Ans : Aug. i.
5. I exchanged three notes : one of $500 at 4 nios., $600 at 5
mos., and $400 at 7 mos,, for one of $1,500. How long
should the ii,5oo note run .? Ans. : 5 mos. 6 days.
6. I owe $900, due Jan. 12; $r,ooo, July 12; and $r,ico, Set t.
12. When can I pay them all together? Ans. : Junr 11.
7. A owes I500 due May 4, and $500 May 26. When sli u-d
both be paid? Ans.: May 15.
8. Suppose I300 is due in 14 days, and $6,000 in 35 days. At
what time should both be paid ? Ans. : In 34 days.
9. 1 bought a farm for $10,500, payable in 6 mos. ; I paid
$2,000 in 2 mos., and $4,500 in 4 mos. How much time
should I have on the remainder ? Ans : 11^ mos.
10. Bought a house for $ro,ooo, to be paid for as follows : \ in
6 mos., I in I yr. 6 mos., and the remainder in i\ yrs.
Find the average time of payment. Ans.: i yr. 9 mos.
18 days.
11. I paid $600 in 5 mos., $1,000 in 10 mos., $1,200 due in 7f
mos. What would have been the average time of pay-
ment? Ans.: 8 mos.
12. I sold $2,100 worth of goods Apr. i, to be paid as follows :
$300 in 4 mos., $800 in 5 mos., and $1,000 in 8 mos.
Find the equated time of payment. Ans. : 6f mos.
13. I bought $1,800 worth of wheat June i, to be paid for as
follows : $300 in 30 days, $600 in 60 days, and $900 in 90
days. What is the equated time of payment ? Ans. :
Aug. 10.
14. I owe $840 due Oct. 3 ; if I pay $400 July i, $200 Aug. i,
when should I pay the balance ? Ans. : Apr. 30, next
year.
15. I bought a house and lot for $12,000,^ in cash and the
balance in two equal payments at 3 and 6 mos. ; I pay
\ down and the balance in three equal payments at
equal intervals. What is the interval ? Ans. : 2 mos.
16. I exchanged three notes, $300 due in 10 days, $500 due in
25 days, $1,000 due in 40 days, for $600 cash and two
notes for $550 and $650 due at equal intervals. Find the
interval. Ans. : 30 days.
54 ALLIGATION.
17. I owe a certain sum, \ of which is due in 3 mos., ^ iu 6
mos., and the remainder in 8 mos. What is the average
time of payment? Ans. : 5I mos.
18. I lent A $400 for 6 mos. ; at another time $600 for 8 mos.
For how long a time must A lend me $900 to balance
the favor ? Ans. : 8 mos.
19. A owes $600, due in 6 mos. ; 4 mos. before it is due $200 is
paid, and 2 mos. before it is due $200 more is paid. How
long after the expiration of the 6 mos. may the remain-
ing $200 remain unpaid ? Ans. : 6 mos.
ALLIGATION.
1. I mix 3 lbs. of sugar at 10 cts., 5 lbs. at 8 cts., and 2 lbs. at
15 cts. What is the average price per pound? Ans.:
10 cts.
2. How much worsted goods at 10, 13 and 15 cts. a yard must
I sell that the average price may be 12 cts. a yard?
Ans. : 4 at 10 cts., 2 at 13 cts., and 2 at 15 cts.
3. A buys hogs at $5, $6, $7 and $ro a head ; how many of
each did he buy if the average price was $7.50 ? Ans. :
I at $5, 5 at $6, 5 at $7 and 5 at $10.
4. How many pounds of coflfee at 12, 15, 18 and 20 cts. a
pound must be sold that the average price per pound
may be 16 cts.? Ans. : i at 12, 2 at 15, i at 18 and i at
20 cts.
5. A merchant sold 25 yards of ribbon at 12 cts. a yard ; how
much must he sell at 8 and 15 cts., respectively, that
the average price maybe 13 cts.? Ans.: 25 yds. at 8
cts., 25 at 12, and 75 at 15 cts.
6. I buy corn at 60, 62 and 65 cts. a bushel ; how much did I
buy of each if I bought 70 bu. at 70 cts. a bu., and the
average price is 67 cts. ? Ans. : 1$ bu. of each,
ALLIGATION, 55
7. I have 6 gal, of rum 95% strong and some 90% strong;
how much water and how much of the 90% rum must
be mixed with the 6 gal. that the strength may be re-
duced to 80%? Ans. : 3 gal. at 90%, and i^ gal. water.
8. How much sugar at 8, 9, 12 and 15 cts. a pound must be
mixed so as to fill an order of 300 lbs. at 10 cts. ? Ans. :
150 at 8 cts., 60 at 9 cts., 30 at 12 cts., and 60 at 15 cts.
9. B hired 10 laborers for 5 weeks, consisting of men and
boys, men at $15 a week, and boys at $5 a week ; he paid
them all $450 ; how many were there of each ? Ans. : 4
men and 6 boys.
10. Sold 100 lbs. of coffee for $33 ; some sold at 30 cts., some
at 28 cts., and some at 35 cts. a pound; how many
pounds were there of each? Ans.: 12 at 30 cts., 20 at
28 cts., and 68 at 35 cts.
11. I buy geese at 85 cts., ducks at 30 cts., and chickens at 40
cts. each; in all, 80 fowls for $48; how many of each
were there ? Ans. : 40 geese, 20 ducks and 20 chickens.
12. What is the average price of 7 articles, 5 at $1 each, the
others at 2 cts. each ? Ans. : 72 cts. each.
13. A man mixed 4 gal. of whisky at 50 cts. a gal., 2 quarts of
V alcohol at 80 cts. a qt., and i gal. of water ; what was
the mixture worth per gal. ? Ans. : 50rx cts.
14. What relative number of sheep at $3, $5 and $10 a head
can be bought at an average value of $7 per head ? Ans. :
I at $3, I at I5 and 2 at $10.
15. I have a compound containing 15 lbs. of copper, whose
specific gravity is 7I; \ lb. of silver, specific gravity
\o\\ and 8 lbs. of iron, specific gravity 6|. What is the
specific gravity of the compound ? Ans. : 72^0 i»early.
s6 ARITHMETICAL PROGRESSION.
ARITHMETICAL PROGRESSION.
1. The first payment was 50 cts,, the 2d 53, the 3rd 56, and so
on. What was the 19th payment ? Ans. : $1.04.
2. Find the 20th term of a decreasing series whose first term
is 94, second 92, and so on. Ans. : 56.
3. First term 43, com. dif. y\ ; find the 37th term of an in-
creasing series. Ans. : 64.
4. If A makes $939 the first month, and each succeeding
month $80 less, find the profits in one year. Ans. : $5,988.
5. If 100 apples were placed two yds. apart in a straight line,
what distance must a person travel to gather them
singly into a basket placed in line and 2 yds. from the
first apple ? Ans. : i\\\ mi.
6. I sold 1,000 sheep at 10 cts. for the first, 20 for the second,
and 30 for the third, etc. What did I receive for the
sheep? Ans.: $50,050.
7. I employed a clerk on the following terms for 10 mos. :
$20 for the first mo.; $30 for the second, $40 for the
third, etc. What did I pay for the whole time ? Ans. :
$650.
8. A board 10 ft. long is 2J in. wide at the narrow end and
increases in width i^ in. for every foot in length. What
is the width of the wide end? Ans : 16 inches.
9. The first term is 4, the last term 49, the number of terms
10. What is the sum of the series ? Ans. : 265.
10. A buys a farm on monthly payments, to be paid in 3 yrs.
10 mos. The 5th payment was $21. the 20th $60. What
did he pay for the farm ? Ans. : $2,971.60.
GEOMETRICAL PROGRESSION. 57
GEOMETRICAIv PROGRESSION.
I. A travels 96 mi. the first day, and on each succeeding day
\ as far as on the preceding day ; how far did he go on
the 5th day ? Ans. : 30 mi. 3 fur.
(2. What is the 7th term of the series 128, 192, 288, etc.?
f Ans. : 1458.
•3. A hound and a fox are 20 rds. apart. The hound runs 10
rds. while the fox runs 9 rds. At this rate how far will
the hound run to catch the fox ? Ans. : 200 rds.
4. B engaged to work 20 da. for ^ of a cent for the first day,
I cent for the second, 2 cents for the third, and so on.
How much, at this rate, will he receive for the 20 days ?
Ans.: $5,242.87 J.
5. What is the last term in the series whose 3d term is 16 ;
and common ratio 6 ; number of terms 9 ? Ans. : 746,496.
6. Suppose the 33d term is 1,024, common ratio \ ; find the
40th term. Ans. : 136^^.
7. Find the sum of the infinite geometrical series of i, J, t,
etc. Ans. : 2.
8. Find the sum of the infinite geometrical series of i|, i, f,
etc. Ans. : 8^.
9. The first term is 8 ; fourth term 512. Find the common
ratio. Ans. : 4.
ID. Insert one geometric mean between 3 and 27. Ans. : 9.
II. Insert two geometric means between 4 and 32. Ans.: S
and 16.
5^ TIME.
TIME.
1. The time past noon is I of the time past midnight. What
is the hour ? Ans. : 8 o'clock p. m.
1. The time past noon is \ of the time from now to mid-
night. What is the hour? Ans. : 4 o'clock p. m.
3. What is the time of day if the time past noon is j\ of the
time past midnight ? Ans. : 10 o'clock p. m.
4. What is the time of day if the time past noon is x\- of the
time to midnight ? Ans. : 45 min. past 3 p. m.
5. \ of the time past noon equals ^^ of the time to mid-
night. What is the time ? Ans. : 4 o'clock p. m.
6. At what time between 7 and 8 o'clock are the hour and
minute hands together? Ans. . "^yx inin. after 7.
7. What is the time of day when f of the time past noon
equals 2*^9 of the time to 12 ? Ans. : 2\ p. m.
8. If I of the time past noon equals /^ of the time to mid-
night, what is the time? Ans.: i7y min. after 4 p. m.
9. What is the time of day when f of the time past noon
equals jVj of the time to the second midnight ? Ans. :
i|^ o'clock A. M.
ID. If ^ of the time past midnight equals \ of the time to
midnight, what is the hour? Ans.: 8 o'clock p. m.
11. If the time past noon increased by 90 min. equals j\ of
the time from noon to midnight, what is the time?
Ans. : 57tt ™i"- P^st 3 p. m.
12. When the hour hand is 22 min. ahead of the min. hand,
how far must the min. hand go to overtake the hour
hand ? Ans. : 24 min.
13. At what time between 9 and 10 will the hour hand be i
minute-space behind the minute hand ? Ans. : 9i\ min.
before lo o'clock.
APPLICATION OF SQUARE ROOT. 59
14. At what time between 10 and 11 o'clock are the hands of
a clock opposite ? Ans. : 2ij\ past 10.
15. At what time between 4 and 5 o'clock are the hour and
minute hands 10 minutes apart? Ans. : 32 j\ min. past
4 and \o\\ min. past 4.
i6. At what time between 8 and 9 is the minute hand midway
between twelve and the hour hand? When is the hour
hand as far behind the minute hand as it is past 6?
Ans. : 2o|f min. past 8 ; and 60 min. past 8, or 9 o'clock.
17. At what time between 5 and 6 o'clock is the hour hand
midway between 4 and the minute hand ? Ans. : 36
min. after 5.
18. The time past noon is y^ of the time to 4 o'clock P. M.
What is the time ? Ans. : i^ o'clock p. m.
APPLICATION OF SQUARE ROOT,
1. Find the side of a square field containing one acre. Ans. :
12.64+rds.
2. Find the side of a square field containing 10 acres. Ans. :
40 rds.
3. What will the lumber cost that will fence a square field,
5 rails high, containing 10 acres, with post and rail fence,
allowing 15 ft. to the panel, rails at $6 a hundred and
posts $40 a hundred ? Ans. : $123.20.
4. The entire surface of a cubical block is 216 sq. ft. What
is the side of one face? Ans. : 6 in.
5. How long must a tape-line be to wind spirally around a
cylinder that is 50 ft. long and 8 ft. in circumference, if
it pass once around in every 6 ft. of the cylinder's
length? Ans.: 83 J ft.
6o APPLICATION OF CUBE ROOT.
6. Two freight traius ^tart at the same point, one going due
south at the rate of 15 miles an hour, and the other due
east at the rate of 18 miles an hour. How far apart
were they at the end of 6 hrs. ? Ans. : i4o.58-t-niiles.
7. What is the distance around a rectangular field containing
20 acres whose length is twice its breadth ? Ans. : 240
rds.
8. The area of a rectangle is 5,408 sq. ft., and is composed of
two squares. What is the length of its sides ? Ans. :
52 ft. wide, 104 ft. long.
9. A room is 100 ft. long, 60 ft. wide and 26 ft. high. What
is the distance from a lower corner to the opposite up-
per corner ? Ans.: 119.48-)- ft.
10. Hypotenuse 50 ; the base and perpendicular equal. Find
them. Ans.: 35.35+.
APPLICATION OF CUBE ROOT.
1. A cubical box holds one bu. What is the inside measure*, ?
Ans.: i2.9-j-in.
2. The volume of a cube is 15! cu. ft. Find its surface in
sq. in. Ans. : 5,400 sq. in.
3. Find the difference between 6 cu. in. and a 6 in. cube.
Ans. : 210 cu. in.
4. What is the size of a cubical cistern which holds 1,500 gal,
of water? Ans. : 70.234-cu. in.
5. What are the dimensions of a cubical pile of wood whicn
contains 80 cords ? Ans. : 21.71-l-ft.
6. What are the dimensions of a cellar, from which 192 cubic
yds. of earth were removed, if the length is 4 times and
the width 6 times its depth ? Ans. : 6, 24 and 36 ft.
MEASUREMENTS. 6i
7. A stick of timber contains 13J cu. ft. Its length is 32
times its width or thickness. Find its dimensions.
Ans. : 24 ft. long and 9 in. square.
8. A cubical box has a capacity of 2,048 cu. ft. What are the
dimensions of 4 equal cubical boxes that can be placed
in it.? Ans.: 8 ft.
9. I have 8 boxes containing 729 cu. ft. each. What is the
side of a cubical box equal in capacity to the 8 ? Ans. :
18 ft.
10. I wish to make a wagon bed to hold 100 bu., the length
being 3 times the width and height. What will be the
dimensions 1 Ans. : 3.46-J-ft. high ; 10.38-f-length.
MEASUREMENTS.
1. What is a cylindrical stack of clover hay worth that is 12 ft.
in diameter and 10 ft. high at $15 a ton ? Ans. : $30.84-1-.
2. How much timothy hay will a mow hold that is 20 ft.
square and 15 ft. deep? Ans. : 13J tons.
3. How much clover hay in a mow that is 30 ft. long, 20
ft. wide and 20 ft. deep ? Ans : 2Iy\ tons.
4. I have 12 bins, each 10 by 5 and 8 ft. deep, full of wheat.
How many bu. of wheat have I .? Ans. : 3,840 bu.
5. How many gallons in a barrel whose capacity is 6.25 cu.
ft.? Ans.: 46.75-l-gal.
6. How many bu. of wheat in a box containing 750 cu. ft. ?
Ans. : 600 bu.
7. I have a wagon-bed that holds 135 bu. What are its di-
mensions if the length is six times its width and 9 times
its depth ? Ans. : 18 ft. long, 3 ft. wide and 2 ft. deep.
8. A cubical box holds 583.2 bu. What are its dimensions?
Ans. : 9 ft.
62 MEASUREMENTS.
9. How many bags holding i^ pk. eacli can be filled from a
bin of wheat which is 10 ft. long, 4 ft. wide and 8 ft.
deep ? Ans. : 768 bags.
10. What will it cost to build a stone wall 80 ft. long, 2\ ft.
thick and 10 ft. high at $1 a perch ? Ans. : $8o||.
11. I paid $254.54y^x fo^ the cellar wall of my house, 60 ft. by
45 ft. The wall was 8 ft. high and i\ ft. thick. What
did I pay a perch ? Ans. : $2.50.
12. What will a log cost that is 20 ft. long and average girt 60
in. at 2\ cts. a cu. ft. ? Ans. : 99.5+cts.
13. What is the number of feet of lumber in a stick of timber
20 ft. long, 8 in. wide and 4 in. thick ? Ans. : 53^^ ft.
14. How many feet in 12 boards 16 ft. long and 15 in. wide ?
Ans.: 240.
15. What is the largest cube that can be cut from a sphere 30
in. in diameter ? Ans.: 17.324-iii.
16. A globe 40 in. in diameter, the shell beirg i in. thick, is
filled with water. How many gallons are in it? Ans. :
124.37+gal.
17. What will it cost to guild a globe 60 in. in diameter at 2
cts. a square inch? Ans.: 1226.195+.
18. If it cost $1005.312 to guild a globe at 5c. a sq. in., what is
its diameter ? Ans. : 80 in.
19. I paid $226,195 to have a globe 60 in. in diameter gilded.
What was the price per sq. in. ? Ans. : 2 cts.
20. What will it cost to have a cube whose sides are 2 in.
plated with silver at 50 cts. per sq. in. ? Ans. : $12.
21. How many cubic ft. in 20 posts 12 ft. long, 6 in. square at
one end and 4 by 4 at the other? Ans. : 42f cu. ft.
22. How many cu. ft. in a log 40 ft. long, 3 ft. in diameter at
one end and 2 ft. at the other? Ans. : 198.968-I-.
23. A water tank in the shape of a. frustum of a cone is 15
ft. deep, the lower diameter is 16 ft. and the upper 12
ft. Find the contents. Ans. : 2,324.65-f-cu. ft.
24. How many cu. ft. in the frustum of a square pyramid of
stone 20 ft. high ; the side of the upper base is 8 in.
and thfe lower base 20 in ? Ans. : 28| cu. ft.
MEASUREMENTS, 63
25. The slant height of the frustum of a square pyramid is
10 ft. The side of the upper base is 20 in. and the
lower 30 in. Find the convex surface. Ans. : 83J sq. ft
26. I sold a block of marble 20 ft. long and 20 in. square at
each end at $2.25 per cu. ft. What did I receive for it ?
Ans.: $125.
27. The base of a square pyramid is 764 ft. on each side ; height
480 ft. What is the solidity ? Ans. : 93,391,360 cu. ft.
28. The slant height of a square pyramid is 8 ft. and the sides
of the base 5 ft. Find the entire surface. Ans. : 125
sq. ft.
29. If I receive $140.80 for painting an octagonal church spire
whose slant height is 80 ft. and the sides of its bases 8
ft., what do I receive a sq. ft. ? Ans. : ^\ cts.
30. What will it cost to paint a cone whose slant height is 60
ft. and the circumference of its base 40 ft., at 5 cts. a
square foot ? Ans. : |6o.
31. How many gallons will a cistern hold that is 20 ft. deep
and 30 ft. in diameter ? Ans. : 105,753! gal.
32. A log 50 ft. long and 2 ft. thick was sold at 20 cts. a cu. ft.
What did it cost ? Ans. : $31.41-!-.
33. I sold a log i\ ft. in diameter at 10 cents a cu. ft. and re-
ceived $3,927. What was its length ? Ans. : 8 ft.
34. A square stick of timber 60 ft. long at 20 cents a cu. ft.
cost $27. How many ft. of inch plank will it make, al-
lowing \ waste for sawing ? Ans. : 1,440 ft.
35. I paid $3.31^ for painting the sides and one end of a rect-
angular prison 6 ft. high and the sides 2 J ft. each. What
did I pay a square foot ? Ans. : 5 cts.
36. How large a square can be placed in a circle whose diame-
ter is 3 ft. ? Ans. : 25.455+in.
37. A circular island is 14 rds. in diameter. What is the value
of the largest inscribed square at $2 per sq. rd. ? Ans. :
$196.
38. The circumference of a circular pond is one mile. What
is its diameter ? Ans. : 1,680. 674-ft.
^4 MEASUREMENTS.
39. What is the area of a circular field inclosed by one mile
of fence ? Ans. : 50 acres 148 perches 188.39-l-sq. ft.
40. A circular fish pond 100 ft. in diameter was sold at 10 cts.
a sq. ft. What did it bring ? Ans. : $785.40.
41. A horse tied by a rope grazed over 7854 sq. ft. How long
was the rope ? Ans. : 50 ft.
42. Two boys in rowing across a stream 620 ft. wide go 800 ft.
How far did they drift ? Ans. : 505.57+ft.
43. A rope 40 ft. long tied to the top of a house reaches 10 ft.
in the street. How high is the house ? Ans. : 38,72-j-ft.
44. What will it cost to paint a steam boiler 30 ft. long and 5
ft. in diameter at 2 cts. a sq. ft., allowing 10 sq. ft. for
openings ? Ans. : $io.oi-|-.
45. A cistern holds 20 hhds. and is 5 ft. 10 in. in diameter.
What is its depth ? Ans. : 6 ft. 3.63-i-in.
46. If a pint of water will fill 15 cone-shaped glasses, how
many times will a gallon fill similar glasses of i^ times
the diameter at the top ? Ans. : 53J.
47. How many square inches on a school globe 15 in. in
diameter? Ans.: 706.86.
48. What is the diameter of a tin pan whose area is 196 sq. in. ?
Ans.: 15.79+in.
49. The radius of a circle is 11 ft. What is the area? Ans. :
380.133+sq. ft.
50. I paid $76.80 for the flooring of a two-story house 24 x 32
ft. What did I pay for every hundred ft. ? Ans. : $5.
51. What will be the cost of 9 boards 13 ft. long, 9 in. wide
and i\ in. thick at $1 a hundred ? Ans.: $1.31-!-.
52. The surface of a globe is 1520.5344 sq. ft. Find the diame-
ter. Ans.: 22 ft.
53. What is the surface of a globe whose circumference is
39.27 in.? Ans. : 490.875 sq. in.
54. The solidity of a sphere is 65.45 cu. in. Find the surface.
Ans.: 78.54 sq. in.
55. What is the solidity of a globe wh«se diameter is \\ ft. ?
Ans.: I cu. ft. 391.5 cu, in.
MISCELLANEOUS. 65
56. Over what area can a horse graze, tied by a rope 52 ft. long
to the top of a stake 20 ft. high ? Ans. : 26.58-j-sq. rds.
57. Find the curved surface of a right cone whose base is
4 ft. in diameter and slant height 5 ft. Ans. : 31.41-I-
sq. ft.
58. The sides of a triangle are 10, 10^ and 14^. What is the
area.? Ans. : 52.5.
59. The base of a triangle is 136, altitude 17. What is the
side of a square equal in area? Ans. : 34.
60. How much paper 2 ft. wide will it take to cover the walls
of a room 16 ft. long, 14 ft. wide and 8 ft. high ? Ans. :
80 yds.
61. My cistern is 5J ft. deep and 6 ft. in diameter at the top
and 6 ft. at the bottom. How many barrels will it hold ?
Ans.: 35.254-bbls.
Note.— The answers to a few of the above problems, such as finding
the capacity of wagon beds, etc., are only approximately correct.
MISCBLIvANEOUS.
1. A tree 100 ft. high was broken by the wind so that the
top reached the ground 30 ft. from the stump. How
high is the stump ? Ans. : 45^ ft.
2. What is the least number of squares of the greatest pos-
sible size contained in a field 40 by 30 rds, ? Ans. : 12.
3. If the diameter of a ball whose volume is 27 cu. in. is
3 in., what is the diameter of a ball whose volume is
343CU. in.? Ans.: 7 in.
4. A grocer at one straight cat took off a segment of cheese
which had \ of the circumference and weighed 3 lbs.
What is the weight of the whole cheese? Ans.: 33.02
+lbs.
66 MISCELLANEOUS.
5. If a pipe i^ in. in diameter fill a cistern in 5 hrs., in what
time will a pipe 3 in. in diameter fill the same cistern?
Ans. : i|^ hrs.
6. Three poles, each 50 ft. long, are tied together at the top
and stand 60 ft. apart at the base ; what is the distance
from the apex to the ground? Ans. : 38.73-}- f^-
7. The diagonal of a field in the shape of a parallelogram
containing 30 acres is 100 rds. Find the sides. Ans. :
80 and 60 rds.
8. The base of a triangle is 9 in. What will be the length
of a line drawn parallel with the base so as to divide it
into two equal parts ? Ans. : 6.36-l-in.
9. What integer multiplied by the next greater gives 1,332 ?
Ans.: 36.
10. What integer is that whose square root is 5 times its cube
root? Ans.: 15,625.
11. What is the side of a' square field whose diagonal is 10
rods longer than its side ? Ans. : 24.14-f-rds.
12. How much square edged inch lumber can be cut from a
log 32 in. in diameter and 20 ft. long ? Ans. : 980 ft.
13. The side of a square field containing 18 acres is 53.6-f-rds.
What is the side of a similar field that contains \ as
much ? Ans. : 30.9-{-rds.
14. What is the side of the largest cube that can be cut from
a globe 36 in. in diameter ? Ans. : 20-|-in.
15. How much wheat will a cubical box hold whose diagonal
is 12 ft. ? Ans. : 2664-bu.
16. The perpendicular and base of a right-angled triangle are
equal and its area is 8 acres. What is the hypotenuse ?
Ans.: 71.5+rd.
17. The base of a triangle is 136, the altitude 17. Find the
side of a square equal in area. Ans. : 34.
18. Two poles are of equal length. When one is placed up-
right and the other is leaning against it, their tops are
4 ft. asunder and their feet are 16 ft. apart. What is the
length of each ? Ans. : 34 ft.
MISCELLANEOUS. 67
19. A board \\ inches thick contains 49I sq. ft. What is the
side of the largest cubical box that can be made from
it? Ans. : 36 in.
20. How many acres in an equilateral triangle each side of
which is one furlong in length ? Ans. : 4. 334- A.
21. If Ihc diameter of the greater of two concentric circles be
30 ft,, and that of the smaller 20, what is the area of
the space between them? Ans. : 392.7-l-sq. ft.
22. The length of a field containing 4 A. is 12 rds, longer than
its side. What is the length and breadth? Ans.: 20
and 32 rd.
23. It is required to inclose a piece of ground with a fence 10
rails high, 2 panels to the rod, and to have just as many
acres inclosed as there are rails in the fence. How
many acres in the field, the field being square ? Ans.:
1,024,000 A.
24. How many square inches of leather will cover a ball 3J
in. in diameter ? Ans. : 38.4-l-sq. in.
25. A man was hired 50 days on condition that for every day
he worked he should receive 75c., and should pay 25c.
for every day he was idle. On settlement he received
$27.50 ; how many days was he idle ? Ans. : 10.
^6. Divide 120 apples among 3 boys, and as often as the first
shall receive 3, give the second 5, and the third 7 ; what
will be the share of each ? Ans. : 24, 40 and 56.
27. Three men bought a grindstone 30 in. in diameter, each
paying the same. They grind off their shares succes-
sively. Find the thickness of each man's share. No
aperture. Ans.: ist, 2.75+; 2d, 3.59-I- ; 3d, 8.65-f.
28. A circuit is 20 miles in circumference. A goes 2 miles an
hr., B 4, and C 6 ; they start at the same point ; how long
will it be before they meet ? AnS. : 10 hrs.
29. \ the number of dollars in a purse exceeds J by 20 ; what
does the purse contain ? Ans. : $240.
30. The head of a fish is 10 in. long, its tail is as long as its
head and \ the body, and the body as long as the head
and tail both. How long is the fish ? Ans. : 80 in.
68 MISCELLANEOUS.
31. A and B together can do a piece of work in 18 days. A
alone can do it in 30 days ; in what time could B do it
alone? Ans.: 45 days.
32. Suppose the radius of the earth is 4,000 miles; what
would a 20 lb. ball weigh 3 miles from the surface of
the earth .> Ans. : 19.97-hlbs.
33. In what time will a leaden ball drop from a steeple 484
feet high ? Ans. : 5J seconds.
34. A ball discharged directly upwards returns to the earth
in 12 seconds ; how high did it ascend ? Ans. : 576 ft.
35. A stone let fall reaches the bottom of a well in 2 seconds;
how deep is the well ? Ans. : 64 ft.
36. If a scaffold 20 ft. square holds 50 bu. of fruit, how many
bu. will one 30 ft. square hold ? Ans. : 112 J bu.
37. What is the diameter of each of the 3 largest equal cir-
cles that can be inscribed in a circular farm containing
500 acres? Ans.: 148.14-rds.
38. If cloth for a suit of clothes for a man weighing 125 lbs.
cost $10, what will it cost to make a suit for a man
weighing 216 lbs. ? Ans. : $14.40.
39. I am 45 yrs. of age. How many yrs. old would I be if I
had lived the same length of absolute time on the
planet Mercury? On Jupiter? Ans.: Mercury 186.8
yrs. old ; Jupiter .53 or a little past \ yr. old.
40. A and B shot by turns at a target ; A put 7 balls out of 12
in the center, and B 3 out of 4, and between them they
put in 32 balls. How many shots did each fire ? Ans. : 24.
41. From the middle of the side of a square lo-acre field a
line is run cutting off i|^ acres. What is the length of
the line ? Ans. : 36-f-rods.
42. A tube \ in. in diameter will empty a cistern in 50 min.
In what time will it empty it when another pipe \ of an
inch in diameter is running into it ? Ans. : 623-% min.
43. Three equal circles touch each other externally, thus in-
closing one acre. What is the diameter of each circle ?
Ans.: 63-f-rds.
MISCELLANEOUS. ' 69
44. What are the sides of a right-angled triangle having the
least hypotenuse in which, if a square be inscribed, its
side will be 12 ? Ans. : 24.
45. If the arch line of a sector measures 5 ft. and the radius
4 ft., what will be the area ? Ans. : 10 ft.
46. I bought a 6 per cent. $2,500 mortgage at 5 per cent, dis-
count, with two yrs. to run ; prove that I get 8|f per
cent, interest on the money invested, the mortgage be-
ing satisfied at maturity.
47. Required the number of acres in a field whose length is
to its breadth as 4:5, having a fence around it 7 rails
high, two panels to the rod, and just as many rails as
acres. Ans. : 508,032.
48. The perpendicular of a right-angled triangle is 36 ft., and
the sum of the other sides is 108 ft. Find them. Ans.:
Base, 48 ft. ; hypotenuse, 60 ft.
49. A square field has an area of 10,000 sq. yds. What is the
breadth of a walk around it, that the area of the walk
is Y^^ of the area of that part within the walks ? Ans. :
10 yds.
50. Two ladders are standing in a street with their bases 20
ft. apart, inclined toward each other, at an angle of 45
degrees until their tops intersect. What is their length ?
Ans.: 14.14-hft.
51. A cube of lead whose side was 4 inches was evenly plated
with 61 cu. in. of silver ; how thick was the plating ?
Ans. : \ inch.
52. A bicycle wheel makes 840J revolutions to the mile ; what
is the height of the wheel ? Ans. : 2 ft.
53. A tower is 195 ft. high and 10 ft. in diameter at the top.
To a man whose eye is 5 ft. above the center of the top
of the tower, what area of the street will be hid ? Ans. :
502,656 sq. ft.
54. How much inch rope will be required to go round a stove-
pipe I ft. in diameter so that the outer edges will meet ?
Ans. : 43.984-in.
55. Mt. St. Elias is 19,283 feet high. At what distance on the
Pacific Ocean may its top be seen ? Ans. : 169.9-l-niiles.
^6 MISCELLANEOUS.
56. A rectangular piece of ground containing \ an acre is 5
times as long as it is broad. What is the length and
breadth ? Ans. : 4 and 20 rods.
57. A had hired for a year at $168 and 5 cords of wood ; he left
in 7^ months and received $98 and the wood. What
was the wood worth per cord ? Ans. : $1.40.
58. How much gold 90^ pure must be mixed with 24 oz. 65^
pure to make the mixture 80% pure .? Ans. : 36 oz.
59. Yesterday at noon my longitude was 16° 18^ west. To-day
the sun came on the meridian at ii o'clock and 36 min.
What is my longitude ? Ans. : 10° 18^ west.
60. I have a mirror 12 by 36 in., and its frame of uniform
width contains 448 sq. in. How wide is the frame?
Ans. : 4 in.
61. A ladder placed 8 feet from a wall just reaches the top of
the building 40 ft. high. How far must it be placed
from the wall to reach a point 10 ft. from the top?
Ans.: 27.64-l-ft.
62. A room in the shape of a cube measures 20 ft. on each
side. How far is it from each upper corner to the cen-
ter of the floor ? Ans. : 24.49+ ft.
63. A sc[uare field is of such size that if silver dollars i^ in. in
diameter are laid around the boundary so they will touch
each other they will pay for the land at $40 per acre.
How many acres in the field ? Ans. : 27,878! acres.
64. A rifle ball fired perpendicular in the air returned to the
ground in 16 sec. How far did it go ? Ans. : 1,024 *t.
65. There is a park 16 rods square. I make a path around
the edge containing ^| of the area of the park. How
wide is the path ? Ans. : i rod.
66. A man weighs 160 lbs. av. What will he weigh troy?
Ans. : 194-f-lbs.
67. A fence 5 boards high, each board 6 in. wide, is built
around a lo-acre square field. What is the lumber
worth at $8 per M ? Ans. : $52.80.
68. A regular octagon has a perimeter 96 ft., and the distance
from the center to the middle of each side is 12 ft
Find the area. Ans : 576 fq. ft.
MISCELLANEOUS. 71
69. What is a field worth in the shape of a triangle and the
sides in proportion, as 6, 8 and 10, the shorter side be-
ing 12 rds., at $850 per acre ? Ans. : $510.
70. A boat can go 15 mi. per hr. down stream and 10 miles
per hr. up stream. How far can it go and return in
4 hours ? Ans. : 24 miles.
71. How much more water will a tile 6 in. in diameter dis-
charge per hr. than one 4 in. ? Ans. : i\ times.
72. A, B and C dine on 6 pies. A furnishes 4 and B 2. C pays
10 cents for his dinner. How shall A and B divide the
money ? Ans. : A gets 10 cts.
73. What is the diameter of a sphere whose volume is equal
to a cone whose base is i ft. in diameter and altitude 2
ft. ? Ans. : I ft.
74. How many bu. of coal will a cart hold that is 9J ft. long,
3 J ft. wide, 13 in. deep ? Ans. : 24-l-bu.
75. How long will it take $50 to amount to $72.50 at 8J%?
Ans. : 5 yrs. 3 mo. 16 da.
76. If the time past noon plus i^ hrs. is -f^ of the time from
noon to midnight, what is the hour ? Ans. : 3J o'clock
p. M.
77. If a cistern 5 ft. in diameter and 10 ft. deep holds 500 bbls.,
how many bbls. will a cistern 10 ft. in diameter and 20
ft. deep hold ? Ans. : 4,000 bbls.
78. How many feet of lumber in a stick of timber 18 in.
square at one end, 6 in. square at the other and 20 ft.
long ? Ans. : 260 ft.
79. How much lumber in a pole 20 ft. long and 10 and 5 in.
in diameter respectively ? Ans. : 7.7-l-sq. ft.
80. If a man 5 ft. high weigh 120 lbs., what will a man 6 ft.
high weigh ? Ans. : 207-l-lbs.
8r. If a piece of gold weigh 9 oz. in the air and 8 J oz. in the
water, what is its specific gravity ? Ans. : 18.
82. A cube has an area of 5,400 sq. in. What is its solid con-
tents? Ans.: 27,000 cu. in.
83. I can pasture 12 horses or 15 cows. How many horses can
I keep if I have 10 cows ? Ans. : 4.
72 MISCELLANEOUS.
84. A can do a piece of work in 80 days, B in 40 days ; both
together work 12 days, then B quits but returns in time
for them to complete the work in 40 days. When did
B return ? Ans. : End of 32d day.
85. The extreme point of a minute hand of a clock moves 30
in. in 12 minutes. How long is the hand ? Ans. : 23-|-iti.
86. A man hired for 80 days at $3 per day ; he spent $r every
day he was idle; at the end of that time he had $150.
How many days did he work? Ans. : 57^.
87. A cistern 5 ft. in diameter holds 100 bbls. of water. What
will one of the same depth and \2\ ft. in diameter hold?
Ans. : 625 bbls.
88. A pyramid is 10 ft. square at the base and 20 ft. high.
How far from the base must it be divided parallel to the
base to make two equal parts ? Ans. : 4.«2 — ft.
89. If a hay stack 20 ft. high contains 10 tons, what will a
similar one 10 ft. high contain ? Ans. : i^ tons.
90. Find the length of an hour hand of a clock, whose ex-
treme point moves 2 in. in 15 minutes. Ans. : i5-|-in.
91. Two men carry a hog weighing 200 lbs. with a stick 6 ft.
long. What weight does each sustain if it is 6 in. from
the center of the stick? Ans. : 83 J and ii6f lbs.
92. A, B and C buy a grindstone 3 ft. in diameter for $5.00. A
pays $2, B $1.75, C $1.25. How much must each grind
off to get his deserved share ? A grinds first, B second
and C last. Ans. : A, 4064-; B, 355+ ; C, 2544-sq. in.
93. How much water must be mixed with vinegar worth 40
cts. a gal. to make 50 gal. of the mixture worth 25 cts.
a gal. ? Ans. : i8| gal.
94. If a cu. ft. of iron was made into a bar \ in. square, what
would be its length ? Ans. : 2,304 ft.
95. Find the sides of a rectangular field containing 200 acres,
one side being 40 rods longer than the adjacent side.
Ans. : 160 and 200 rds.
96. Find the cost of a fence at $3 per rd. that will enclose a
square field of 20 acres. Ans. : $678.
97. How many sq. yds. of canvas will be required to make a
tent, diameter 24 ft. and height of the center pole 32
ft. ? Ans. : id2.84-sq. yds.
MISCELLANEOUS. 73
98. The diagonal of a rectangular field containing 7J acres is
50 rds. Find the sides. Ans. : 30 and 40 rds.
99. Three women own a ball of yarn 10 in. in diameter. Find
what each will wind off to share equally. Ans. : ist,
1.3-f-; 2d, 3.2-h; and 3d, 5.5+10.
100. A teacher hired on conditions if he had 40 pupils, he was
to get $40 per mo. ; if he had 28, he was to get $35 per
mo. It so happened he had 35 pupils. What should
he receive ? Ans. : $38.64x^5.
loi. How much water will a bucket hold whose upper diame-
ter is 13 in., its lower diameter 8^ in. and its height 8J
in.? Ans.: 3 gal. i qt. i— pt.
102. A has two horses and a cow. The first horse is worth
|6o. The first horse and cow together are worth f as
much as the second horse, and the second horse and
cow are worth twice as much as the first horse. What
is the value of each ? Ans. : Cow, $40 ; horse, $80.
103. Ten years ago I was \ as old as my father, but two years
hence I will be \ as old. What are our ages ? Ans. : 22
and 46 yrs.
104. Two men engaged to build a barn for $540. The first
worked | as many days as the second, plus 40, and re-
ceived $300. How many days did each work ? Ans. :
ist, ico; 2d, 80.
105. The head of a fish weighs one pound, the tail weighs as
much as the head, plus \ the body, and the body weighs
twice as much as the head and tail both. What is the
weight of the fish? Ans. : 12 lbs.
106. A pole 134. ft. long stands on a bluff; 16 times the length
in the ground plus 6 feet equals \ of the length in the
air increased by 80 ft. How much is in the air ? Ans. :
130 ft.
107. A pile of wheat in the corner of a rectangular room
forms a portion of a cone ; the pile is 6 ft. high and it
is 5 ft. from edge of the pile to corner of the room.
What is the wheat worth at $1 per bu. ? Ans. : $31.55+.
108. The amount of my money for 6 yrs. at 6% is $300 more
tha;; the amount of it for 3 yrs. at 10^, How mu^l?
^^yel? Ans.: |5,ooo, , . — .
74 MISCELLANEOUS.
109. A debt with interest at 6% was paid Aug. 18, 1893; if it
had been paid May 12, 1895, there would have been due
$26 more. What was the debt at first ? Ans. : $250.
no. The 3d term of a geometric series is 507 ; the first term
3. Find the ratio. Ans : 13.
111. It is 2 mins. after 2 o'clock p. m., 2^ 30^^ east long. What
is the time 31° 27' 30^^ west long. ? Ans. : 56 min. after
II A. M.
112. How many pens must I buy for $1 so that I may gain
20% by selling them 4 for i cent? Ans. : 480.
113. The present worth of a debt at 6% is $660, which is
$213.40 less than the debt. How long before the debt
is due ? Ans. : 5 yrs. 4 mos. 20 days.
114. At what time between 5 and 6 o'clock is the min. liand
14 mins. behind the hour hand? Ans. : 12 mins. after 5.
115. What number is that whose square is 22|% of the cube
of 8? Ans.: io|.
116. I saved $7.25 interest by paying off a note 20 days before
due. Find the face, int. 6^. Ans. : $2,000.
117. At his marriage B agrees that if, at his death, he leaves
only a daughter, his wife shall have \ of his mone}-,
and if he should leave only a son, she should have \ ;
he left a son and daughter. What did each one receive
if he left $6,591? Ans.: Son, $4563; widow, $1,521;
daughter, $507.
118. What is the greatest number that will divide 27, 48, 90,
and 174, and leave the same remainder? Ans. : 21.
119. A, B and C pasture an equal number of horses on a field,
of which A owns 9 acres, and B 15 acres ; if C pays $24
for his pasturage, how much should A and B receive?
Ans.: a, $3; B, $21.
120. A, in buying coffee, found, if he paid 11 cts. per pound,
he would lack 30 cts. of having money enough to pay
for it ; he bought at 10^ cts. and had 15 cts. left. How
many pounds did he buy ? Ans. : 90 lbs.
121. A bought at one time 5 pears and 6 peaches for 28 ct3.,
and at another time, 6 pears and 3 peaches for 21 cts.
What was the cost of each kind of fruit ? Ans. : Pears,
2 cts. ; peaches, 3 cts.
MISCELLANEOUS. 75
122. A company of 10 hire a team. Two fail to come but four
others join the company, thus reducing the estimated
expense to each by 50 cents. What does each pay and
what does the team cost? Ans. : $1.25 and $15.
123. If 40 cats kill 40 rats in 40 mins., how many cats can kill
10 rats in 10 mins. ? Ans. : 40.
124. The ages of A, B and C are to each other as 3, 4 and 5,
and their sum is 136 yrs. What is the age of each?
Ans. : a, 34 ; B, 45 J ; C, 56! .
125. A and B were partners ; A put in $4,500 and received | of
the profits. What was B's capital ? Ans. : $3,000.
126. What number multiplied by y\ of itself will give 1,188?
Ans.: 66.
127. A teacher hired on condition that if he had 20 pupils he
was to receive $20 per mo., and if he had 12 pupils he
was to receive $15 per mo. ; but he had 17 pupils. What
should he receive ? Ans. : $18.59!.
128. A piece of cheese weighs 4 lbs. in one side of a pair of
scales and 9 lbs. on the other side. What is the true
weight of the cheese ? Ans. : 6 lbs.
129. The interest on \ of A's plus f of B's money for a certain
time, at 2%, was to this sum as 9: 250, and this interest
for 25 times as long, at 10 times as great a % was $180.
What was their money, if A's money was to B's as 1:3?
Ans. : A, $200 ; B, $600.
130. What is the diameter of the largest circle that can be in-
scribed in an equilateral triangle whose sides are 15 ?
Ans.: 8.6+.
131. If the hands of a clock were 3 and 4 ins. long, how far
apart would the points be at 3 o'clock ? Ans. : 5 ins.
132. Find the side of a square lot equal in area to a circular
one 60 rds. in diameter. Ans. : 53.1-i-rds.
133. What is the diameter of a round field of such size that
every 6 ft. of fence is equal to \ acre ? Ans. : 7,260 ft.
134. The area of an equilateral triangle is 173.2 ft. What are
the sides? Ans.: i8.6i+ft.
135. The axes of an ellipse are as 2 : 3 and its area is 125 sq.
ft. Find the diameters. Ans. : 10 and 15 ft.
MISCELLANEOUS.
136. The strength of two men are as 3:4; where must a
weight be placed on a spike 3^ ft. long, so that they
may carry in proportion to their strength ? Ans. : \\
ft. from stronger man.
137. A newsboy buys papers at 20 cts. per dozen, and sells
them at a nickel apiece. Find his per cent, of profit.
Ans. : 200%.
138. What % of .005 is $100? Ans. : 2,000,000%.
139. A and B's hotel bill was $3 ; A pays \ more than B. What
did each pay ? Ans. : A, $1 f ; B, $if.
140. A board is 18 ft. long, 18 inches wide at one end and 6
ins. at the other. How far from the larger end must I
cut it across to divide it equally ? Ans. : 6.5-l-ft.
141. How much lumber in a board 12 ft. long and one inch
thick by 12 ins. wide at one end and 2 ins. square at
the other ? Ans. : 9I ft.
142. How many posts 7 ft. apart will it take to fence a lot
containing 70,756 sq. ft., the length of the fence being
4 times the width ? Ans.: 190.
143. What is the mean proportional of 9 and 16 ? Ans. : 12.
144. Find the side of the largest square that can be inscribed
in a right angled triangle whose base is 16 ft. and per-
pendicular 12 ft. Ans. : 6.8+ft.
145. What is the diameter of the largest cylinder that can be
cut out of a globe 30 ft. in diameter ? Ans. : 24.5-f-ft.
146. What is the solidity of a cubical box that will hold 625
lbs. of water ? Ans. : 10 cu. ft.
147. What is the diameter of the largest circle that can be
inscribed in a right angled triangle whose base is 8
and perpendicular 6 ft. ? Ans. : 4 ft.
148. f of A's money added to f of B's, which is 3 times | of
C's, being put on interest for 8 yrs. at 5% gives $i8oo
interest. How much money have they all ? Ans. :
$2,000.
149. A building whose height is 18 ft. to the square is 25 ft.
wide, and the rafters on one side are 15 ft. and on the
other 20 ft. What is the height of the house ? Ans. :
30 ft.
MISCELLANEOUS. 77
i;o. A piece of ground whose 3 sides are equal cost $375 at
the rate of $75 per acre. How many rods of fence are
required to inclose it ? Ans. : 120 rods.
151. What time between 5 and 6 o'clock will the hour hand be
midway between the minute hand and the figure 5?
Ans. : Half past 5.
152. How many acres in a rectangular field whose sides are as
2 to 3, if the number of acres in the field _just equals
the number of panels in the fence inclosing it, the
panels being 10 ft. long ? Ans. : 7,260.
153. I find my watch, which keeps correct time, is 3 hrs. slow.
How far and in what direction did I travel ? Ans. :
East 45°.
154. A street 200 feet wide has a wall on one side 100 ft. high
and 80 ft. high on the other side ; find the length of
the shortest line that will reach from the top of one
wall down to the middle of the street and then to the
top of the other wall. Ans. : 269-f-ft.
155- $i)4oo is left to two children, whose ages are 11 and 16. I
want to invest it at 10% so that each will have the same
when he is of age. How shall I divide it ? Ans. : $600
and $800.
156. A rectangular field contains lof acres and the sum of its
sides is 168 rds. Find the sides. Ans. : 36 and 48 rds.
157. Awheel 4 ft. in diameter stands one ft. in water ; what
fraction of the wheel is in the water ? Ans. : .195-I-.
158. If a man can plant a field 100 rds. in diameter in 4 days,
how long will it take him to plant one 200 rds. in
diameter .? Ans. : 16 da.
159. Two wheels, one 6 ft. in diameter and the other 4 ft., are
on an axle 12 ft. long, and are started to roll. How
large a circle will they inclose .? Ans. : 72 ft. diameter.
160. Find the diameter of the 3 largest circles that can be in-
scribed in a circle whose circumference is 128 ft.
Ans.: i8+ft.
16 r. A lot lies between two parallel roads \ mile apart ; it is
90 rds. on one road and 75 rds. on the other. What is
the lot worth at $80 an acre .? Ans. : $6,600.
78 MISCELLANEOUS.
162. I have a circular piece of land 5 rds. in diameter, from
which I take enough earth to fill a cone whose base is
10 ft. in diameter and 15 ft. deep. How much was the
lot lowered ? Ans. : .o734H-ft.
163. Find the solidity of an octahedron whose linear side is 6
in. Ans. : ioi.82-|-cu. in.
164. What debt can be discharged in 12 days by daily pay-
ments which are in geometrical progression, the sec-
ond payment being 3 cents and ratio being 8? Ans.:
$36,814,005.39.
165. The length of the hypotenuse is 10 ft, the sum of the
base and altitude 14 ft. What is the base and altitude ?
Ans. : Base, 6 ft. ; alt., 8 ft.
166. How much will I make by borrowing money at 5% to
pay a debt of $6,400, due in 8 mos., allowing the pres-
ent worth of this debt to be reckoned by deducting
5% per annum discount? Ans. : $7.11+.
167. B wishes to divide $290 between his two sons A and D,
whose ages are respectively 15 and 19 yrs., in such a
manner that the parts bearing simple interest at \o%
shall amount to such sums, when they are 21 yrs. of
age, that f of A's money shall be equal to f of D's.
Ans. : A's, $90 ; D's, $200.
168. B owns a piece of land 320 rds. long and 180 rds. wide,
and wishes to lay it off into the smallest practicable
number of square fields. What will be the number of
fields and what is their size ? Ans. : 144 fields 20 rds.
square.
169. How far will a heavy ball fall in 20 seconds ? Ans. :
6,400 ft.
170. What is the diameter of each of the four largest circles
that can be inscribed in a larger circle whose radius is
10 ft.? Ans.: 4.14-l-ft.
171. A body falls 904^^ ft. in 7^ seconds. How far does it fall
the first second ? Ans. : i6yV ft.
172. Find the difference between two numbers whose sum is
12 and their product 35 ? Ans. : 2.
173. The sum of two numbers is 16 and their difference is 2.
Find the numbers. Ans. : 7 and 9.
MISCELLANEOUS. 79
174. The diflference between two numbers is 3, and their prod-
uct 180. What 2re the numbers? Ans. : 12 and 15.
175. The sum of two numbers is 7 and the sum of their cubes
133. Find the numbers. Ans. : 2 and 5.
176. The diameter of each of four ec^ual circles that can be
inscribed in a larger circle is 4 ft. What is the
diameter of the larger circle ? Ans. : 19.31-j-ft.
177. The sum of the squares of two numbers is 41 and the
difference of their squares 9. What are the numbers?
Ans. : 4 and 5.
178. The sum of two numbers is 19 and the sum of their
squares 193. Find the numbers. Ans. : 7 and 12.
179. The difference of two numbers is 7 and the sum of their
squares 65. Find the numbers. Ans. : 8 and r.
180. Suppose there be a round pole 20 ft. high and i ft. in
diameter and a vine entwines itself around it just 12
times at equal distances from bottom to the top. What
is the length of the vine? Ans.: 42.79-f-ft.
181. A boy hired on conditions for 12 weeks, that he should
receive $12 and a coat. At the end of 7 weeks the part-
ies separated, and it was found that the boy was en-
titled to $5 and the coat. What was the value of the
coat? Ans.: $4.80.
182. A globe 6 in. in diameter weighs 25 lbs. What is the
weight of another of like metal 3 in. in diameter?
Ans.: 3.12-l-lbs.
183. The sides of two square pieces of ground are as 3 to 5,
and the sum of their areas is 30,600 square feet. What
is the side of each piece ? Ans. : 90 and 150 ft.
184. B gives $1,200 to C to be invested in trade for one year,
on condition that if C add $500 to it and act as mana-
ger he shall have | of the gain. What was C's time
worth? Ans.: $300.
185. A has 4 sons, whose ages differ from each other 4 yrs.
and the youngest is half as old as the oldest. Find
the age of each. Ans.: 12, 16, 20 and 24 yrs.
8o MISCELLANEOUS.
i86. A and B together have 60 sheep, and if you divide what
A has by what B has the quotient will be 3. Required
the number each has. Ans. : A, 45 ; B, 15.
187. A owns 720, B 336 and C 1,736 rods of land. They agree
to divide it into equal lots, fixing on the greatest num-
ber of rods for a lot that will allow each owner to lay
out all his land. How many sq. rods must there be in
a lot ? Ans. : 64.
188. It is required to find a sum of money of which, in the
space of 4 yrs., the true discount at simple interest is
$5 more at the rate of 6% than at 4% per annum.
Ans.: $89.90.
189. If a railroad carry 4,500 pounds 1,800 miles for $27, how
far can 3,000 pounds be carried for $11 ? Ans. : 1,100 mi.
190. An equilateral triangle whose sides are 8 is inscribed in
a circle. What is the circumference of the circle ?
Ans.: 2S.99-J-.
191. How many acres in a field in the shape of a parallelogram
whose diagonal is 100 rods and the difference of the
squares of the sides is 2,800 ? Ans. : 30 acres.
192. The difference in the sides of a grass plot is 9, and of
their squares 135. Find the sides. Ans. : 12 and 3.
193. The diameter of 3 equal circles touching each other is 10
ft. What is the inclosed space ? Ans. : 4.034-sq. ft.
194. The altitude of a field in the shape of an equilateral tri-
angle is 60 rds. What will it cost to fence the field at
80 cts. per rod.? Ans.: $i66.i7-f-.
195. How many acres in a square field whose diagonal is 24
rods longer than its side ? Ans. : 20.9-I-.
196. The area of a parallelogram is 140 square rods., and it is
inclosed with 48 rods of fence. What are its dimen-
sions ? Ans. : 14 and 10 rds.
197. A garden is 4 rods longer than it is wide and contains
140 square rods of ground. What are its dimensions ?
Ans.: 14 and 10 rds.
198. A parallelog^ram is 6 rods longer than it is wide, and its
diacjonal is 30 rds, Hqw many rods d-oes it contain?
Ans.: 432 rds,
MISCELLANEOUS. 8i
199. A gentleman told a lady that his age was 25, intimating
that he would be glad to know how much he was her
senior. The lady replied : " The square root of the
product of yours by mine is equal to 4 times the square
root of your own." What was the age of the lady?
Ans. : 16.
200. Says Charlotte to her brother, Mr. S. has lived as long as
both Jane and I together, and if his age be multiplied
by mine the product would be 420; but if my age and
hers be multiplied the product is only 224. What are
the ages of the young ladies? Ans.: Charlotte, 14;
Jane, 16.
201. Three men are to carry a stick of timber of iiniform size
10 ft. long, two at the spike and one at the end of the
stick. How far from the center of the stick must the
spike be placed so that each may carry equal weight ?
Ans. : 2J ft.
202. What is the diameter of each of 7 the largest circles that
can be inscribed in a larger one 15 ft. in diameter ?
Ans. : 5 ft.
203. A stick of timber 20 ft. long and of uniform size is to be
carried by 4 men and one boy, the boy equal to ^ of a
man, the men at the spike and the boy at the end.
How far from the center of the stick must the spike
be placed ? Ans. : i J^ ft.
204. If a board 18 in. wide at one end and 6 in. wide at the
other and 12 ft. long be divided into 3 equal pieces,
how far from the wide end must each division be made ?
Ans.: 2.6 and 5,7 ft.
205. A ball 10 in. in diameter is put into a cubical box, each
side of which is 10 in. What will be the diameter of
each of the four largest balls that can be placed in the
four corners ? Ans. : 2.68-f-in.
206. How many feet of lumber in a stick of timber 2 x 4 ft. at
one end and i x 6 at the other, and 12 ft. long ? Ans. : 80.
207. A piece of land is 17 rds. wide at one end and 7 rds. at
the other and 60 rds. long. How far from the larger
end must it be cut straight across so that the area of
the two parts shall be equal ? An^. : 24 Td3,
82 MISCELLANEOUS.
208. A stick of timber of uniform size and 20 ft. long is to be
carried by one man and 4 boys, the boys' strength each
being equal to | of a man. How far from the center
must a spike be placed so that each may carry the
same, the man being at the end and the boys at the
spike ? Ans. : 3^ ft,
209. What is the diameter of each of the four largest circles
that can be inscribed in an equilateral triangle whose
sides are 24 inches ? Ans. : 6.9-l-ft.
210. What will 10 yds. of cloth cost at liG-^f^- per yard?
Ans. : $10,001.
211. If a man weigh 300 lbs. on the earth, what will he weigh
on the moon ? Ans. : 50 lbs.
212. The hypotenuse is 74 ft. and the base and perpendicular
are equal. How long is the base ? Ans. : 52.34-ft.
213. What number divided by 6, 7, 8, 9, 10 and 12 will always
leave 5 for a remainder? Ans. : 2,525.
214. The sides of a field are as 3 : 4 and diagonal 60 rds. What
are the sides ? Ans. : 36 and 48 rds.
215. The area of a garden is 3 acres and its boundary 104 rds.
What are the sides ? Ans. : 40 and 1 2 rds.
216. If a log 2 ft. in diameter will make 300 ft. of lumber,
what will one of the same length and 4 ft. in diameter
make ? Ans. : 1,200 ft.
217. A stone fell into a cistern 10 ft. in diameter and the wa-
ter in the cistern rose 6 in. What is the content of
the stone ? Ans. : 39.27 cu. ft.
218. The solidity of a cone is 56 cu. ft., and the diameter of
the base 3 ft. Find the altitude of the cone. Ans.:
23.764-ft.
219. Find the solidity of a prolate spheroid whose polar
diameter is 20 and equatorial diameter 15 ft. Ans.:
2,8o6-j-cu. ft. approximately.
220. How many acres in an equilateral triangular field of such
size that the number of acres in the field will equal
the number of panels in the fence surrounding it, the
panels being straight and 12 ft. long? Ans.: 7,071-!-
MISCELLANEOUS. 83
221. A, B and C live at the corners of a triangular field; from
A to B is 100 rds. ; from B to C 80 rds., and from C to A
120 rds. They want to dig a well that shall be the
same distance from each. How far from each to the
well? Ans. : 60.52-f-rds.
222. What is the side of the largest square that can be in-
scribed in an equilateral triangle whose sides are 12
in.? Ans.: 5.564-in.
223. What is the side of the largest square that can be in-
scribed in a right angle triangle whose sides are 6, 8
and 10 in. ? Ans. : 3|4-i^«
224. What is the diameter of the largest circle that can be in-
scribed in a right angled triangle whose sides are 12,
16 and 20? Ans.: 8.
225. What is the diameter of the largest circle that can be in-
scribed in an isosceles triangle whose base is 9 ft. and
equal sides 20 ft. 6 in. ? Axs. : 7.24-ft.
226. At what figure must Tennessee 5's be bought to give the
buyer 5|§% on his investment? Ans.: 92^.
227. What is the area of the largest square that can be in-
scribed in a semi-circle, the diameter of the circle be-
ing 20 in. ? Ans. : 80 sq. in.
228. Two similar fields together contain 518 square rods.
What is the area of each if their like sides are as 5 to
7 ? Ans. : 175 and 343 sq. rds.
229. A wheel on a locomotive is 5 ft. in diameter, and a fly
rides on the rim of the wheel. How far does the fly
travel while the locomotive runs 10 miles ? Ans. : 15.9
-f-miles.
FRACTIONS.
FRACTIONS.
(i) To cut each piece once=50 cts.
To cut each piece twice=$1.00, Ans.
(2) i-i=jV; ^V=l; 1^=20; 20=iof less; f =80 less.
20—1=19 ; 19=1 of larger ; |=95 larger, Ans.
(3) |— f=i ; i=28 ; f =^252 larger, | of 252=224 smaller, Ans.
(4) \-\=-h\ 3rV=3; If =60, Ans.
(5) i+i==T\ ; ^=15 ; tV=3 ; i|=54, Ans.
(6) f=A; f=B; | of |=l.f C ; f4-f+H=H.
||=$770; 5V=$10; ||=$450 A.
I of $450=1180 B ; I of $180=$140 C, Ans.
(7) |=length; f-f =J ; |=6; |=1 8 ft. length.
I of 18=12 ft. breadth, Ans.
(8) 1 time A's— 120=^ B's ; 3 (A's— 120) or«3A's— 360=B's ;
also C's=2 B's or 2 (3A's— 360)=6A's— 720. lA's-}-3
A's— 360+6A's— 720=6450. 10 times A's=6450-f360-f
720=7530 A's=753; B's=(753— 120)X3=1899. 1899x2
=3798 C's, Ans.
(9) J-J=^, i=6; 1=36; i=36; |=180, Ans.
(10) 2 persons receive 15c each and one 9c ; 3 persons receive
39c, or 13c average price.
$4.68-^1 3c=36, Ans.
(11) f=$45; ^=$63; 45+4J=49J; 49J-h63=}^, Ans.
(12) 1+1=1 B ; 12X|=21 da. B ; i=21 ; f=28 da. A, Ans.
FRAtriONS. 83 i
i
(13) f=B; f=f ; -|=A; t^^+«=M; H=$5700.
ia=$3000 B.
-/^=$2700 A, Ans.
(14) l=A; i=|; 1=1; |=B; f of f =^ ; ^=f; |=V-;
-i^=C; f+f+i^=!l; f^=$540; i|=$240A.
|=$160 B ; x^2=$140 C, Ans.
(15) T3 \f^\^\ T3 T3 = r3 > 73=^1'^^^. J T I ^^l"'*^.
$1444|-f$1000=$2444|, Ans.
(16) i : I as 2 : 3 ; 2+3=5 ; f of 490=196 smaller.
f of 490=294 larger, Ans.
(17) \\A-h=\\\ If4-H=f!; !!=1357; H=649 smaller.
12=708 larger, Ans.
(18) 1-1=1; f=$36; f=$48. |+i=f;
6=$48 ; |=$40, Ans.
(19) i+!=M;lf-^34=2H<la.,ANS.
(20) tV-?V=^V; 11-^2^=24 da., Ans.
(21) ,^—}=f A; J^ of f=/o ; f+T%=M; f|-5-l=T'Tr of D's, Ans.
(22) 1=1 ; 3=1-1 ; I of 12=1, ANS.
(23) l=C; 1+1=1 B; f of |=V^ ; |+V=¥; ¥-^!=2|. Ans.
(24) 1=1; l=f; f+f=¥; |h-V=A,ans.
(25) i+i=2^o; lg-/^=U; M-/o=tV; tV=8; 1§=80, ans.
(26) I— f=i; 1=12; 1=30; f of 30=21 f yrs.
30— 21f=8f yrs., Ans.
(27) fX4=f; fX2=-V-; ¥— l=V-; -^-=100; f=90, Ans.
(28) if-A=TV ; f of ,7^=,?, ; T?^-A=iV ;
^^^=$2100 ; f f=$10,800, Ans.
(29) 1+1=0^ ; l=$21 ; |=$15 cost A.
I— 1=1 ; l=$15 ; f=$25 cost me, Ans.
86 FRACTIONS.
(30) |=B; |+1=|=A; 1+1=1; 1=54; |=24 A.
1=30 B, Ans.
(31) K?=f; ?-f=?; f=8ft.; |=18| ft, Ans.
(32) t^t^-|=tV ; tV=6 ; ie=60 B ; i of 60=18 A, AxNS.
(33) \-\=\ ; $6+$9=$15 ; i=$15 ; |=$120 B. .
\ of $I20=$105 ; $105— $6=$99 A, Ans.
(34) 1=1; 1=11; i§-H=TV; ^=2; if=30 B'sage.
11=32 A's age, Ans.
(35) f of 8=6f hrs., Ans.
(36) 10x5=50 days for 1 man.
50-i-12=4^ da. for 12 men.
6 — 4^=1 days saved, Ans.
(37) 1—1=!; !-|=i; i=$900; |=$4500,Ans.
(38) 1+7=8, the worth of both.
I of 8=6-1 ; 6f-T-7=|f, Ans.
(39) 1=1; 1=1; l+f=V-; ¥=102; |=48 smaller.
1=54 larger, Ans.
(40) i— J=l; 8+12=20; 1=20; |=80, Ans.
(41) 8+4=$12; $12-i-3=$4; $4x8=$32, Ans.
(42) fcxl2=9c; 10+9=19c cost.
icxl2=3c; 19+6=25c, Ans.
(43) iVof $1.00=10c; 2|-=-10=H,Ans.
(44) 10-4-3=3^0 ; 3J— J=2fc cost.
10-T-4=2ic ; 2f — 2^=Jc, Ans.
(45) 4 qt.=J bu.; I— J=J; |=6 bu. ; %=^ bu., Ans.
(46) 1=30; 1=50; i-f=|; f =6 ; 1=15.
iz—h-=^i:U\ iH-5-Tk=21f da., Ans.
(47) f+i=| ; 1+1=1 ; 4816-4-1=1806 ;
f of 1806=1204 smaller ; 4816—1204=3612 larger, Ans.
FRACTIONS. 87
(48) f+f+l=Y-; i-¥=TV, ans.
(49) 6Vx30=|t; ^oX3=j%; M-hA=T¥o.
il§-T¥(y=T¥o- ; t¥o^TV=l' ^a.; 30-17=13 da., Ans.
{50) tV+*=2¥; ^\— i=2¥ ; h of 2\=4V a in one da.
1 1 J T) . 1 1 5 C
T2 58 16-^) t 16 T8 ^•
?V4-iV+A=¥^^; f|-^/8=5J da., Ans.
(51) ^ of f=J^ ; J, of f=TV ; tV+tV=A ; ff^/3=5f da., Ans.
(52) tV-^V=3V ; 1 2^3'o=30 da., Ans.
(53) i^^-h=h\ ; A-4¥8=if 8 ; in-^if 8=81f da., Ans.
(54) A, \ acres in 1 da. ; B, f ; C, ^
f-4-f+i=if acres together in 1 da.
2^-5-ff=li da., Ans.
(55) l+l=H; !f-H=H; 34--h=30, ans.
(56) 2|=V-; -¥-+!=¥; ¥=76- |=20A; 24=56 B,Ans.
(57) t+l+f=|f; M=88; 11=42 A; f of 42=28 B.
f of 42=18 C, Ans.
(58) |=C,i=B,^%=A; f4-|+^=M; U=$440;
f fi=$200 C ; I of $200=$150 B ; ? of $150=$90, Ans.
(59) i4-?+i-=I ; 1=98 ; i=14 C ; 1=28 B ; f=5G A, Ans.
(60) I— 1=J; \—\=^-o\ $7+$3=$10; -i2,=$l0; j §=$75, Ans.
(61) 91-4-7=13; 91x7=637-4-13=49 larger; 91— 49=42 smaller,
Ans.
(62) \—h-='h ; il^x'3=15 da., Ans.
(63) 4-T-6=| ; A does f while B does f ; |=20; |=30 da., Ans.
(64) f of \ of |=i\ ; |=$t'o ; •l=$H- ; i\XlH=$||, Ans.
(65) |-i=l; f of^=i^; 1-1-1^=11; 11=18 24; 11=11.52, Ans.
(66) $12|-f$5^=$18i; $125|-$18i-=$107i- ; i of ^107if=$35| A.
$3o|-f-$5^=$41i, B ; $41i+$7i=$48^ C, Ans.
FRACTIONS.
{67) H?=-V-; 45+20=65; -y=6o; i=35,ANS.
(68) 1— i=| ; 1=100 ; 1=40 ; |=140. 40 and 140, Ans.
(69) l+J+J=M; if-i=H; il=5i; ii=36,ans.
(70) J=20 ; |=80c cost ; 94—80=14 ; 14-j-7=2c.
94-7-2=47, Ans.
(71) J+i+i=^; ^==118; H=$24,an8.
(72) 9|-4|=5; 5^2=2J; 2|+4|=6i; 6^X4=27^;
27J-r-2J=ll, Ans.
(73) -,% of t\=iVii ; iV(y=$40,500 ; ^^=$165,000 ; f of f=f ;
f of $165,000=$70,714f, Ans.
(74) I : ! : : 3 : 4=^ A, if B ; ^^ of $1520=$720 A.
jl of $lo20=$800 B, Ans.
(75) l=B; 1=1; 1=1 A; |4-f=V-; V-=153; |=72 B.
1=81 A, Ans.
(76) f=100; 1=140; 140+100=240;
240-T-18=13| ; one mile in 13J min., Ans.
(77) f =20 ; |=26| ; \ of 26f=6| ; f of 6|=4 hrs., Ans.
(78) One man can do ■^\^ in one day.
\ of 12=2| da. ; ^i^X V=Tk ; ifax3=f ^g.
!n-^T^iy=300, Ans.
(79) $2660xl|=$4560 ; \ of $4560=$2280.
$2280-i-2f=$840 ; $840-t-2=$420, Ans.
(80) 7,250-1,250=6000; |+|=-V ; ^=6,000;
§=3200 B ; ^ of 3200=2800; 2800+1250=4050 A, Ans.
(81) 7862X7^=58,965 ; ^ of t=f ; | of 58,965=39,310 ;
\ of i=TV ; i^ij of 39310=3931 ; 39310—3931=35379, Ans.
(82) 12+12=24; 1=24; 1=96 in., Ans.
(83) \-\=-\ ; § of (J+24)=|+16 ; (i+24)-(f+16)=^+$8.
848— $3=$ 10; i=$40; |=$360, Ans.
FRACTIONS. 89
(84) f-|=J; h-\=h\ 3+2=5; J,=5; ii=60 ;
I of 60=40 ; 404-3=43 gal. acid.
I of G0=15; 15-f-2=17 gal. acid, Ans.
(85) ^+(1 X|^f)~(J-^iV) + {f X|)=i Ans.
(86) $68+$I=$69 ; f=$69 ; f=$161 ; ^ of $I61=$80.50 ;
$80.50— $G9=$12.50, Ans.
(87) 1-1-24=1; f=|-h$32; f+|=V-; $5 12-$32=$510 ;
-y-=$510; |=$240; 240+32=$272 B's.
$542— $272=$270 A's, Ans.
(88) 1=1+8; 1=1+12; 148-12=136; f+f=-V-.
-V-=136; 1=64 A; |=72; 72+12=84 B, Ans.
(89) $1.0.^fj=$l01; $101X10=$1010, Ans.
(90) I : f : : f : f =|f ; A : B as 63 : 64 ; | of 63=42 ;
% of 64=48 ; 48+42=90 ; M of 180=84 ;
1=84 ; 1=126 A; f f of 180=96 ; 3=96 ; f=128 B, Ans.
(91) f=C, f=B, i+$12=A ; $645— $12=$633.
1+1+^=2 0; ^-|=$G.33; i|=$379.80 C.
J of $379.80=$ 1 89.90 B ; (J of $189.90) +$12=$75.30 A, Ans.
(92) \=i times; f=16 times; 16+1=17; $170^1 7=$10 pig;
$10xl6=$160 horse, Ans.
(93) J=3; 1=9; 6=9; 1=1J; i of 50=10 ; 10x1^=15, Ans.
(94) $1.00.o-2^=$6; $6X100=$600, Ans.
(95) 20+20=40; ^=40 yrs. ; |=S0 C ; 80— 20=60 B, Ans.
(96) 10X2=20; 35— 20=15 yrs., Ans.
(97) ^ij=wliat thev both do in oue hr.
f+f=I; 1=20; 1=3^; t|-=-J,=35 hrs. B.
1=35 ; |=46f hrs., A, Ans.
(98) |+J=|; 1-1=1; 1=20; |=26|, Ans.
(99) ^=1; 1=1; f-!=l; 1=8; |=40b.
4=48 A, Ans.
90 FRACTIONS.
(loo) lf-A=^; iof (t\4-65)={H+iB ; (r\+65)-(H+J-B
=(i^T+-¥-); {i'i+¥)=(|-l0);-«^4-l0=H^; f|=33,ANs.
(loi) |=5Vj of (/r+l35) ; f=$33 ; y\ of $33=$6 spent, Ans.
(102) fof 5^=v-; ^of ^^=3^^; ^v=¥-; fl=^F;
i|i=99 fur. ; 99-i-8=12| mi., Ans.
(103) f+l=l; ^of |=J; iof f=^; JXJ=^; i=4;
|=$36 ; f of $36=$24, Ans.
(104) |-J=|A; 1+100=1; |=$100, Ans.
(105) 1=7^ rds.; |=10 rds. ; 12-10=2; 100H-r22=600, Ans.
(106) tV+A=M; M^2=tV_^; A-iVd=rk.
^|^==$3500; if ^=$60,000, Ans.
(107) 10+14=24 years; f— J=|; |=24; |=36 father's age 10
yrs. ago; 36+10=46; 46—1-1=32; 32—2=30; 30-4-2=
15; 15+2=17. 15 and 17 yrs., Ans.
(108) f=what he had at first.
1+1=1; f of (|-$i6)=,4-v-.
(|-$16)-(M-V-)=/o— V-.
T%+I=M; M— ¥=so; Y-+-V=H^.
\%-=^^-\^\ i§=$52, Ans.
(109) !+}=!; f=$40; 1=32 men.
32X.20=$6.40; f=$').40; -|=$8.
$40— $8=$32; $32-t-32=$1.00.
$40-^$1.00=40 men, Ans.
(no) |+f=|§; f§-f!=jV. $15-$13=$2.
tV=I2; fg=$80,ANS.
(111) f-J=J^; 6+10=16. x\=16 ; i|=240.
f of 240=96 A ; J=80 B ; 80+96=176.
240—176=54 C, Ans.
(112) 2X4=8; 20—8=12; J=12; |=36, A.
\ of 36=12 ; 12+2=14 B. Ans.
FRACTIONS.
(113)
22+13=35; K^- of 35=55 A.
tV of 55=5; 5—2=3; j=3; |=21 B, Ans.
(:i4) i=l'i; 1=42 sum.
J=4; 1=8; 42—8=34; 34-7-2=17 smaller.
42— 1 7=25 larger, Ans.
(115) g=4; §=36 ; 75-j-l^=50 ; 50—30=14 ; 11-^-2=7 the small-
er. 50-7=43, the larger, Ans.
(i:6) i=16; 1=80 sum. 80x4=320.
480—320=100 ; 1C0-t-4=40 diff.
80-f 40=120; 120-j-2=60, the larger.
80—40=40 ; 40-r-2=20, the smaller, Ans.
(117) Sl.O.ofa— ^.O0.oo%¥=^l; $1X4=$4 gain, Ans.
(r iS) Goes one mile in f of an hr.
Comes one mile in ^ of an hr.
f+J=l; 7^-H=13^ mi, Ans.
(119) f=larger; f of (|-287)=^ of (|+287);
1=451 larger, Ans.
(120) 1—1=1 ; \ of 1=2^ ; |-^V=H cost.
Tff — T0=T%> To ^^ T0=lt7; TIT — 2^7=1^^ 5 J-nh — M=^f»
Ans.
(121) i~v=2V; ^Vof io=3|.
A=3i; f 5=70 gal., Ans.
(i22) f=smaller; 12^ times f=V-, the larger.
|4-5jO=54__i2J, number to be divided.
i=T¥8 ; 1=11 smaller.
12J-tf=llf i larger, Ans.
(123) f=watch; 1 (|_[48-5])=48-f.
|=$30 watch ; $48— $30=$18 chain, Ans.
(124) J of $30=$10 gain ; $10-t-125=8c S. P.
=1; 1=8; f=ec C. P., Ans.
92 PERCENTAGE.
(125) I of $l=.66f ; i=.66| ; 1=^-; |
3 of 130-= Y- ; -'V^tV ; H=$20. ?
$20X10=$200, Ans. j
(126) 20X4=80 ; 804-20=100 yrs. sum of all their ages.
|4-^=y- . .i_o=ioo ; 1=90 sum of A and C. '<
\ of 90=10 C ; 80—10=70 B, Ans. ;
(127) 1=3; f=12; if 8=12, one will equal \\\ 90x1^=135; i
\ of 135=671, Ans. ' I
PBRCBNTAGB.
(1) f+i=!; f=$84; f=$70; $100-$70=$30.
$30-r-$70=42f%,ANS.
(2) $72— $6=$66, cost of f ; \=\ of $66=$22.
|=$88, cost of lot. $100— $88=$12.
$12-j-$88=13tV%, Ans.
(3) \ of ^1U=$2; $10— $2=$8 cost; $12— $8=$4 ; $4-t-$8=
50%, Ans.
(4) $440H-(100%+10%)=$100cost.
25% of $400=$100; $400— $100=$300, Ans.
(5) 125%=A; 125%-i-2=62i%B; 100%— 62i%=37^%;
37^% =$225; 100% =$600, Ans.
(6) $300-M25%=$240; $300-^75% =$400.
$400-j-$240=$640 C. P.; $300x2=$600 S. P.
$640— $600=$40 loss; $40-j-$640=6J%, Ans.
(7) 100%4.20%=]20%; 100%— 20%=80%;120%— 80%=40%;
40%=$250; 100%=$625; 80% =$500, Ans.
PERCENTAGE.
(8) '%-''\ ; 1=1 cost of 1st ; f =cost of 2d.
^h% of 1=1; f+f=-V- S. P. of 1st.
lox- of f=^«o ; H-^u=f§ s. p. of 2d.
Y.+ 9 9^i_y.. -y^9^$597; fS=4270; -|=$240, Ans.
(9) 1=^, 1=1; |-f=i gain. i=^6f%,ANS.
(10) ^=?; |=V; -V— 7=f; f=42f%,ANS.
(11) f of $300=$450 ; $450-^3SJ%=$1350.
^=$1350; f=$2700, Ans.
(12) 23^ oiZ'^^%^^%\ 8J%=$3350.50; 100^=$40206, Ans**
(13) J of i of G0=5; 75% of 33|%=25%.
25% =5; 100%=20, Ans.
(14) ^^% of -I of 100==26t; 5% of 10 times 25%=12J%.
12J%=26|; 100%=213^, Ans.
(15) 8^f^ of i==jVo ; ^Vo=$80; f§fi=$l882TV, Ans.
(16) \ of $3003=$1000; $1000^-62^% =$1600, Ans.
(17) 37^% of i of 20% of 480=9.
i of I of 50% of 324=36 ; 36—9=27, Ans.
(18) $21-^(100%— 12|%)=$24 cost; $24xll2J%=$27, Ans.
(19) 100%=labor; 30D%=material.
100^^+4% =104%; 300%— 15% =285%.
28o % 4-104 % =389 % ; 389 % =$2334 ; 400 % =$2400, Anx-.
(20) 100%=labor; 300%=material; 400%=both.
100% +4% =104%; 5% of 300%=15%; 300%— 15% =285% ;
28o%+104%=389%; 400%— 389%=11%.
11%=:$36; 100%=$600; 300% =$1800, Ans.
(21) $141.90-^(100%— 12^%)=$161.25.
$161.25-j-(100^-|-7i%)=$150, Ans.
(22) 75%— G0%=15%; 15%=$1.00; 100%=$6t.
60% of $6f=$4, Ans.
9A PERCENTAGE.
(23) 50^ of $425=$212.50. j
30% of $425=1127.50; $425— $127.50=$297.50. \
20% of $297.50=$59.50 ; $297.50— $59.50=$238. '
$238-$212=$25.50, Ans. \
{24) 30% of $60=$18; $60— $18=$42; 16f% of $42=$7. '
$42— $7=$35 cost ; 5% of $60=$3 ; $60+$3=$63. '
$63— $35=$28, Ans. \
(25) Jof$725.16=$241.72; $725.16— $241.72=$483.44. j
5% of $483.44=$24.17 ; $483.44— $24.17=$459.27, Ans.
(26) f=|; 1=1; |-f=i; *=12J%, Ans.
(27) 140% : 160% : : 36 in : W=41f in., Ans.
(28) 100%+40%=140%; 10% of 140%= 14%; 140%— 145^=m
126%; 20% of 126%=.252; 126%— .252=1.008.
1.008— 100%=.008; .008^100=f%, Ans.
(29) 30c-i-150%=20c price of mixture.
40c— 20c=20c; 20c-t-40c=50%,Ans.
(30) 20%=30%; 1%=1J%; 100%=150%.
100%4-30%=]30%; 150%— 130%=20%,Ans.
(31) 100%— 20%=80%; 1=80%; f=106f%;
106f %— 100%=6|%, Ans.
(32) 66f%of 240=160; 100%— ll^%=88f%.
88|%=160; 100%=180; 20%=180; 100%=900, ANi;.
(33) t=!; f=f; |-|=i; i=20^ioss.
(34) $300-=-120%=$250costof 1st
$300-T-75%=$400 cost of 2nd.
$400+$250=$650 cost of both.
$300X2=$600 S. P. of both.
$650— $600=$50 loss, Ans.
(35) 100%-40%=60%; 60%=$30; 100%=$50,
50% of $50=$25; $50-|-$25=4/6.
$76— $30=$45, Ans.
PERCENTAGE. 95
(36) 100^—37^^=62^;^; G2J%=$60; 100% =$96.
$96-=-(100%+20%)=$80; $96— $80=$16, Ans.
(37) 8^=15%; 1%=U%; 100f^=187|%; 100%+15%=115%;
187|%— 115%=72^%, Ans.
(38) 5%=J^; -|§-2^n=H; 50cXl33J=66tc.
66ic^H=.70i?c. Ans.
(39) 100-j-.005=2,000,000j^, Ans.
(40) ioo%4-io%=iiof, crii; io%=tV;
tV-H=tV; tV=20; ii=220%.
220%— 100^=120%, Ans.
(41) §=l; 1=1; f-l=J; i=i2i%.
(42) 100%— 20%=80%; 80%=f ; |— f=l.
iof f=i; i=15%; 1=60%.
100%— 60% =40%, Ans.
(43) 20% of $180=$36 ; $180-f $36=$216.
100%— 10% =90%; $2I6-i-90%=$240, Ans.
(44) 12%— 10%=2%; 2%=$150; 1 00% =$7500 C.
60% of $7500=$4500 ; $7500-|-$4500=$12000 B.
. 17500+$! 2000=$19500; 100%— 35%=65%;
65%=$19500; 100%=$30000; 35% of $30000=$ 10500 A,
Ans.
(45) 100%— 10%=90%; 90%=$18; 100%=$20.
$20— $12=$8 ; $8-r-10=80c ; $12-t-80c=15 lbs., Ans.
(46) 100%— 25%=75%; 100%+25%=125%; 125%— 75%=50%.
50%-^75%=66|%, Ans.
(47) 20% of $4=.80; $4-|-.80=$4.80
100%— 20% =80%; 80% =$4.80; 100%=$6, Ans.
(48) $12550— $400=$12 150; 125%+100%=225%.
225%=$12150; 100 % =$5400 B.
125% of $5400=$6750 ; $6750+$400=$7150 A, ANS.
96 PERCENTAGE.
(49) ■!4-|=l; |=$810; |=$450; |=$360.
$360-4-(100%+33J%)==$270 C. P. of 1st
$4o0-r-(100%— lli%)=$506.25 C. P. of 2nd.
$o06.25+$270=$776.25.
$810— $776.25=$33.75, Ans.
(50) 74 X 5=370 lbs. ; 370 X .45=$166.50.
2% of $166.50=13.33 ; $166.50— $3.33=$163.17 j
$163.17 X12J% =$20.12+, Ans.
(51) 80%— 25%=55%; 100%— 55%=45%;
45%=66f%; 100fo=US^S%.
100-f-66f %=166f%; 16^fc—US^\fc=mffo, Ans.
(52) 100%-j-(100%— 25%)=133J%; 100%^(100%4-25%)=80%
133J%+80%=213J%; 213^%— 200%=13J% loss.
13J%=$30; 100% =$225 S. P.
$225x80%=$180 1st.
$225-7-(100%— 25%)=$300 2nd, Ans.
(53) 6cXl50=$9.00; $9x 110% =$9.90 ;
100%— 5% =95%; 6cX95%=5.7c.
5.7c X 100 lbs.=$5.70; $9.90— $5.70=$4.20 ;
$4.20-^-50 lbs.=8f c, Ans.
(54) 100%=cost; ^of 100%=50%; 50%Xl25%=62J%;
f of 100%=40%; 40%X112^%=45%;
50%4-40%=90%; 100%— 90%=10%;
J of 10%=5%; 62J%+45%-h5%=112J%;
$1125-?-112^%=$1000, Ans.
(55) 100%— 15%=85%; 5% of 85% =.0425
85%— .0425=.8075
100%— 5%=95%; 15%of 95%=.1425 ^
95%— .1425—8075
.8075— .8075=0, Ans.
(56) 30%of $850=$255; $S50— $255=$595.
2i%.of $595=$14.87^ ; $595— $14.87J=$580.12^, Ans.
PERCENTAGE, 97
(57) 40%=60%; 100%=150^; 100^+150%=250^.
250% =4655; 100^=1862; 150 % =2793, Ans.
(58) 100%— 24^=76%; 76%=$760; 100 % =$1000, Ans.
(59) 100%— 12^%=87^%; $1.60x87^% =$1.40.
$1.40-T-(100%— 30%)=$2.00, Ans.
(60) $72X125%=$90; $90-f-(100%-10%)=$100, Ans.
(61) $480 XI 12^% =$540; 1^%=$540; 100% =$36,000, Ans.
(62) $120 -^ (100% — 8%) = $130^f ; $130|f X (100% — 10%) =
$1172%, Ans.
(63) $105-f-(100%+25%)=$84.
$10o-f-(100%— 2o%)=$140; $140+$84=$224 C. P.
$105X2=$210; $224— $210=$14 loss, Ans.
(64) 75% of $600=$450; 3J%=$450; 100% =$1350.
^=$1350 ; |=$2700, Ans.
(65) 25% of i=jV; tV=$350; if =$4200, Ans.
(66) 100%— 20%=80%; 6%of 80%=.04; 80%— 4%=76%.
(100% 4-15%)— 76% =.39; .39-5-76 %=51t'V%, Ans.
(67) 10%of 125%=12J%; 125%— 12J%=112^%.
112^%- 100%=12i%; 12|%=$4684; 100% =$37,472, Ans.
(68) 100%-Hl20%=83J%; 100%-r-125%=80%; 83J% — 80%=
3J%.
3| % =$60 ; 100 % =$1800 ; $1800 X 83J % =$1500, Ans.
(69) 100%-^(100% + 25%)=80%; 100%-=-(100%— 25%)=133J%.
(133^%-f 80%) — (100%X2) = 13J%; 13J%=$60; 100%=
$450.
$450X80% =$360 1st; $450-t-75%=$600 2d, Ans.
(70) $120X(100%— 25%)=$90; $90xl33J%=$120; $120— $120
=0, Ans.
(71) (100%+20%) — (100%— 20%)=40%; 40%=$90; 100%=
$225, Ans.
qS percentage.
(72) J of $1200=$600 ; $600xllo%=$690; $90 gain.
$600-4-1 5/=4000 yds.; 17^^X4000 yds.=$700; $100 gain.
$100-f-$90=$190, Ans.
(73) |of 100^=60fc; 60%X130%=78%; |of 100%=40%.
40fcX{l00%—5fc)=SS%; 38%-f78%==116%; 116%— 100/^
=16%
16 % =$720 ; 100 % =$4,500, Ans.
(74) 30%=x%'V; T^^of |=Agaiii.
5%=Tf (7 ; T^TT of l=Tf^ loss.
t5=t\\', T\\—ih=j^j> net gain.
in=l4500; ji^=$4o; ifo==$405, Ans.
(75) $240X125%=$300; $300-4-(100%— 2o%)=$400, Ans.
(76) 100%=rice; 160%=tea; 240%=coffee; 300%=sugar.
100 % +1 60 % +240 % +300 % =800 % ; 800 % =$240.
100%=$30rice; 160%=$48tea; 240%=$72 coffee; 300%
=$90 sugar, Ans.
(77) ^of 100%=50%; 50%X120%=60%; 50%x90%=45%.
(60%+45%)— 100%=5%; $100^5% =$2000, Ans.
(78) 100%-38%=62%; 25% of 62%= 15|%; 62%+15|% =
100%— 77i%=22^%; 22J%=9A; 100% =40 A, Ans.
(79) i of 100%=50%; 50%X120%=60%; 60%x(100%— 12i%)
=43|%.
60% +433% =1031%; 103f%— 100%=3|%.
3|%=$30; 1C0%=$800; $800-j-300=$25, ANS.
(80) 100%-r-(100%+20%)=83J%; K0%-^{100%— 20%)=125%.
125 % +83^ % =208^ % ; 208 J % —200 % =8^ % .
8J%=$50; 100%=$600; $G00x83J%=$500 Ist.
$600-^80 % =$750 2d, Ans.
(81) 100%— 10% = 90%; 8<^xl30%=10.4<^j 10.4<?-^90%=11^)^
Ans.
PERCENTAGE. 99
(82) $2.50X46=$115; $115x125 ^=$143.75.
46—6=40 gal. ; $143.75-^40=$3.59|, Ans.
(84) 2|%=^V;H+3V=H,ans.
(85) 10% of 50^=5/' ; 50^4-5^=55^.
25% of 50^=12|c ; 55c4-12Jc=67K Ans.
(86) 10% of {100%4-33J%)=13J%; 133J%— 13J%=120%.
120%— 100%=20%, Ans.
(87) (100%+20%)-7-(100%-15%)=:141tV%.
141xV%— 100%=41t\%, Ans.
(88) I60Z.— 12oz.=4 oz. ; 4-7-16=25%, Ans.
(89) $238-j-(100%— 20%)=$297.50 2d.
$297.50H-(100%+40%)=$212.50 1st, AnS.
(90) By spending 50% of his money for 12 days he has re-
maining ToVi ; tA¥=$i ; lMI=$i»024, ans.
(91) $2,400-5-120% =$2,000 gain 2d yr,
$2,000-r44|% =$4,500 gain 1st yr., AnS.
(92) 268.8 cu. in.— 231 cu. in.=37.8 cu. in.
37.8 4 37.8 1
=16— % gain; =14 — % loss.
231 11 268.8 16
4 1 53
16— %— 14— %=2 — % gain, Ans.
11 16 176
(93) 100%— (6%+30%)=64%; 40% of 30%=12%; 30%— 12%
=18%.
64%4-18%=82%; 100%-hl4%=114%; 114%— 82%=32%.
32 % -7-64 % =50 % , Ans.
(94) 100%=C; 133J%=B; 133J%— 100%=33J%.
33|%=$100 ; 100% =$300 C; 4% of $300=$12, AnS.
(95) 100%— 25%=75%; 25%-^75%=33J%, Ans.
100 PERCENTAGE.
(96) 100^+8^=108%; 108%X112J%=12H%.
Vl\\% X (100% — 4%)=116.64% ; $1,166.^0-^-116.64% =
$1,000, Ans.
(97) 100%— 18tV%= 81^9^%; 75% of (81x^i%+ $G5)=61/r% +
$48|.
(8lT«T%+$65)-(61^x%+^8f)=20A/«+ll6l ; $16J+$10=
$26^.
100%— 20i53.%=79x\%; 79T«r%=$26J; 100% =$33, Ans.
(98) 100%=larger.
75% of 287=215i; 16§% of 287=47|; 75%— 16f%=58J%.
215i+47|=263jV ; ^'^\%=1^2>^r^ 100%=451, Ans.
(99) 6%=$15; 100%=$300; $300h-$2.50=120, Ans.
(100) $.193X10X100=$193, cost.
10% of 100=10; 100—10=90 yds.
$.238X10X90=$210.60 selling price.
$210.60— $193=$17.60 gain.
$17.60-r-$193=9jV3% gain, Ans.
(loi) 100%=B; 150%=A; 100%-T-150%=66f %, Ans.
(102) 40% of $100=$40; $100+$40=$140 S. P.
100 % —12^ % =87^ % of asking price.
$140-T-87^%=$160, Ans.
(103) \ of 100=40; 10% of 40=4; f of 100=57f.
4-5-57^=7%, Ans.
(104) 36 in.— 35 in.=l in.; 1 in.-r-35=2f %.
40%+2f%=42f%; 42f%=$330; 100% =$770, Ans.
(105) 100%4-12^%=112^%; 112^%— 90%=22^%.
$18+$20=$38; 22^%=$38; 100%=$168|. Ans.
(106) $24~-(100%— 25%)=$32cost; $34— $32=$2.
$2-^$32=6i% gain, Ans.
(107) 100 %=eacli investment.
100%4-25%=125% A; ^ of 125%=62^% B.
I00%— 62J%=37*%; 37^%=$225; 100% =$600, Ans.
INTEREST.
(io8) 10% of 120=12; 8+12=20; 5^=20; 100^=400, Ans.
(109) $25-j-(100%— 16f %)=$30 1st.
$30— $25=$5; 16%=$o; 100%=$31.25 2nd, Ans.
(no) i%=$5; 100^=14000 cost.
$6— $5=$1 gain ; $l-r-$4000=5V%, Ans.
(111) 160H-140=lf yds., Ans.
(112) $3h-150 <fo =$2 ; $4— $2=$2 ; $2-r-$4=50 % , Ans.
(113) 100%— 50%=50%; 6—1=5; 50-^-5=10%, Ans.
(114) 100%=costof each; 100% +20% =120% rice; 100 fc +10 fc
=110 fc coffee.
100%— 8%=92%; 120%+110%+92%=322%.
322% =$3,864; 100% =$1,200, Ans.
INTEREST.
(1) $2,442.04X$1.61051=$3,932.9298 am't.
The sum of the compound am'ts for 4, 3, 2, 1 and 0 yrs.s
$6.1051.
$3,932.9298-j-6.1051=$644.204, Ans.
(2) 365 da.-4-73=5 ; $1.00+.10=$1.10; v^no=1.924%, Ans.
(3) f mill=.24; 100% =$1,080, Ans.
(4) Am't of $1 at 12% for 6 mo.=$1.0609; $1.0609— 3>^ int.=
$1.0309.
Am't of $1.0309 at 12% for 6 mo.— 3^=$1.06368181.
Clearing .06368181 on each $1; $2,450.85 -r- .06368181=
$38,485.87, Ans.
INTEREST.
(5) $750h-4=$187.50. By multiplying $187.50 by the am't of
$1 at simple int. for 4, 9, 12 and 20 mo. we have $190,625,
$194,531, $196,875 and $203,125, which, added together
make $785,156, Ans.
(6) 4J% of $180 for 8 mo.=$5.40 ; $1804-$5.40=$185.40.
$185.40— $156=$29.40 gain ; $29.40-7-$156=18^i%, Ans.
(7) The am't of the present worths of $250 for \, \\, 2^, Z\
and 4^, and the remainder in 5 yrs. is $3413.08+, Ans.
(8) The sum of the present worths of $200 for 1, 2, 3, 4 and 5
mo.=$978.15, Ans.
(9) Am't of $300 at 6% for 1 yr. 10 mo.=$333.
$1,500— $333=$1,167 ; 1 yr. 10 mo.=22 mo. ; 22—6=16 mo.
Pres. worth of $1,167 for 16 mo. at 6% =$1,080.56, Ans.
(10) The compound am't of $1 for 1 yr .=$1.1 2550881.
$1.12550881— $1=12.550881%, Ans.
(11) '$100 at 2% a mo. for 33 da.=$2.20 ; $2.20xll=$24.20.
$100+|24.20=$124.20 ; $124.20— $106=$18.20, Ans.
(12) $3,325 at 1% for 10 mo. 24 da.=$29.925.
$119.70-T-$29.925=4%, Ans.
(13) 1.00-T-6%=l6f yrs., Ans.
(14) $6,000 at 1% for 1 mo.=$5; $45-4-$5=9%, Ans.
(15) $1 at 1% a mo. for 68 da.=.02x^j ; $17-r-.02T\=|750, An&
(16) 2.00-7-30 yrs.=6f %, Ans.
(17) 100%— 40^=60%; 100%-T-60%=$lf.
$lf at 5% semi-annually=16§%, Ans.
(18) $4.00— $1.00=$3.00 ; $3.00-4-24=1 2 J %, Ans.
(19) Am't of $1 for 1 yr. 8 mo. 5 da.=$1.084yV
$819.45-T-$1.0843V=$755.93, Ans.
(20) $1.00-j-8=12J yrs., Ans.
INTEREST. 103
(21) 24-3=5; f of $2,640=11,584; $l,584-r-2=$792 A's int.
$1 at 6% for 5 yrs. 6 mo.=.33; $792-r-.33=$2,400 A.
f of $2,400=$1,600 B, Ans.
(22) $1,480.78— $1,374.50=$106.28 int.
106.28
10% of $1,374.50=$137.45. yr.=9 mo. 8 da., Ans.
137.45
(23) 6% of $175.12 for 1 yr.=$10.5072.
6.43
yr.=7 mo. 10 da., Ans.
10.5072
(24) 12%of $3,642.08=$437.0496; $4,007.54— $3,642.08=^365.46 ;
365.46
yr.=10 mo. 1 da., Ans.
437.0496
(25) $100 at 2% for 63 da.=$4.20; $1004-$4.20=$104.20.
.18235=int. for given time; $4.20-7-.18235=233i/3-%, Ans.
(26) $1 at 6% for 93 da.=.0155 ; $1— .0155=.9845.
$1,000-^.9845=$!, 015.74, Ans.
(27) 20% of $100 for 63 da.=$3.50; $100-1-$3.50=$103.50.
1% of $103.50 for 63 da.=.181125; $3.50-j-181125=19jV7%»
Ans.
(28) 1% of $200 for 2 yrs.=$4; $48h-$4=12%, Ans.
(29) 6% of $1 for 2 yrs.=.12 ; $48h-.12=$400, Ans.
(30) 6% of $1 for 6 mo. 12 da.=.032; $640-f-.032=$20,000.
i=$20,000 ; f=$100,000, Ans.
(31) Compound int. of $400 for 2 yrs.=$66.56.
Annual int. of $400 for 2 yrs.=$66.56.
$66.56— $66.56=0, Ans.
(32) Compound int. for 3 yrs. at 6 % =$38.20-1'.
Annual int. for 3 yrs. at 6%=$38.16,
$38.20— $38.16=4^, An§,
104 INTEREST.
(33) Compound am't of $200 at 8% for 2 yrs.=$33.28.
Simple int. of $200 for 2 yrs. at 8% =$32.00.
^3.28— $32=$ 1.28, Ans.
(34) 37— 18=19 yrs.
The sum of the compound amounts from one to 19 yrs.
inclusive=$35.784-.
$25,000-j-$35.78+=$698.74— , Ans.
(35) f of A's=|of B's; f=|; |4-f=V-; ^=$3,213.
f =$1,512 B ; f=$l,704 A's ; 8% of $1 for 3 yrs. 9 mo.=.30 ;
|1,704^.30=$5,680 A's ; $l,512-j-.30=$5,040 B's, Ans.
(36) Am't of $1 for 2 yrs. at 5% =$1.10 ; $4,950h-$1.10=$4,500.
I of f=/:,; |+A=ff ; $4,500-4-ff=$4,375 farm.
1=3?; f=/r; A of $4,375=$l,666f house, Ans.
^37) $1 at 8% for 6 yrs.=.48 ; $960-t-.48=$2,000.
|-H=f; $2,000 X|=$3,000B.
\ of $3,000=$1,500 ; $l,500-r-3=$500 ; §=$500 ; |=$750 h ,
Aks.
(38) Amount at simple int. of $1 for 6 yrs. at 4% =$1.24.
$744-T-$1.21=$600.
1+1=1; 1=1600; |=$360A.
f of $360=$240, which is as 2 : 3.
Then §=$240 ; |=$360, Ans.
.975
(39) $13X6%=.78; =1 yr. 3 mo., Ans.
.78
(40) 2mo.=J^yr.; i=$3.25; f=$19.50; $19.50-t-$325=6^, Ans.
(41) $68— $87=$1; 5%— 4%=1%; $1.00-?-l%=$100 difference.
$68+$67=$135; 5%+4%=9%; $13o-r-9% =$1,500 am't.
$1,500— $100=$1, 400; $l,400-r-2=$700 ; $7004-$! 00=$800.
$700 and $800, Ans.
(42) $1 at 5% for 9 mo.=.0375 ; $1 for 15 mo. at 4% =.05.
.05— .0375=.0125; $150-^.0125=$12,000, Ans.
(43) $1.00-7-16 yrs.=6}f,, Ans.
INTEREST, 105
(44) $612— $558=$54 ; 4^ yrs.— 3 yrs.=lj yrs.
$54-j-l| yrs.=$36 int. for one year; 3 yrs.=$108.
$558— $108=$450 prin.; $36-r-$450=8%, Ans.
(45) l=prin.; f-!=f; f=$120; f =$200 prin.
f of $200=$80, Ans.
{46) 5=prin.; f-i=|; |=$120 ; f=$150, Ans.
(47) |=int. for 5 yrs. ; \ of f=i int. for 1 yr. ; ^=12^%, Ans.
(48) $LOO=prin.; $1 at 3^% for 8 yrs.=.28; |of.28=.04; .04-7-
$1.00=2T> Ans.
(49) For 1 yr. it is yV o f 1=25 ; 2?=*% . Ans.
(50) $1 at 11 % for 9 yrs.=.99 ; $l-h.99=$1.99 ; $597-f-$1.99=|300.
$363— $300=$363 ; $300 at 11% for 1 yr.=$33.
$363h-$33=11 yrs., Ans.
(51) .23X365=$9.125; $9.125-f-$l,460=6i%, Ans.
(52) t of $723.16^ = $451.978 J; 1\% of $723.16^ = $54.2373| ;
451.978J
=8 yrs. 4 mo., Ans.
54.23731
(53) $345— $790=$55 ; 19— 8=11 mo.; $55-t-11=$5.
$5X12=$60 int. for 1 yr.; $5x9=$45.
$ 45— $45=$800 ; $60-j-$800=7^ % , Ans.
(54) ($139X600)— ($600xl39)=0, Ans.
(55) ^i-f=f; f=$640; |=$560, Ans.
(56) $4— $1=$3; $3H-20yrs.=15%, ANS*
TOO STOCKS AND BONDS.
STOCKS AND BONDS.
(1) $100X32=$3200; $3200X(100%— 15i%)=$2712, Ans.
(2) 18x$o00=$9000; 100^— 28% =72^;
102%—72fc=S0fc loss; $9000x30% =$2700, Ans.
(3) 100%-4i%=95^%; $4775^95^% =$5000;
$5000-r-$100=50, Ans.
(4) 6%^75%=8%; 100%4-8%=108%;
$16200-M08%=$15000; $16200— $15000=$1200;
$1200X75%=$900, Ans.
(5) 6%-j-90%=6|%,ANS.
(6) 7%=8%; 100%=ll4f%,ANS.
(7) 8%=6%; 100^=75%, Ans.
S%
(8) $2000h =$32500. Ans.
130%
(9) $120x$10=$1200; $1200x(f%4-U5&)=$23. Ans.
(10) (100%4-2%)-i-(100%4-20%)=8o%; 1005&— 85%=155^.An&
(11) 6%-r^7J%=16%, A_N3.
(12) 4%+5%=9%gain; 9%=$4o0; 100%=$o000;
$o000-i-$50=100, Ans.
(13) $6894-j-(95i%4-|%)=$7200,ANS.
(14) 100%— 25%=75% cost;
100%+20%=120% S. P.; 120%— 75%=45%;
45%-i-75%=60%, Ans.
STOCKS AXD BONDS. 107
100%— 30^=70%.
I realize 4^+4% or 8^ on each share per annum.
8%-j-70%=llf%,ANS.
(16) $250x$100=$25000; $25000x0% =$1500;
$2-5000x70% =$17500; $17500x(8%-T-120%)=$1166f ;
$1500— $1166f=$333^, Ans.
(17) A\% of $100=^.50; $100— $4.50=$95.50;
$4775-=-$95.50=50, Ans.
{18) $100x50=$o000; J% of $5000=$25.
$2348.20-i-($5000— $25)=47i%, Ans.
(19) 6%-T-90%=6t%.
15%-j-6§%=2,K
100%x2i=225%,ANS.
(20) 115%X8%=9.2%; 9.2%-^90%=10|^, Ans.
(21) 6% of $50=$3; $3.00-7-8% =$37.50, Ans.
(22) $500X1H=$456.52^\, Ans.
(23) 8%=5%; 100%=62^%, Ans.
(24) $3XI0-r-5«5=$35625, Ans.
(25) (6%-r-107%)Xl50%=8^\%, Ans.
(26) (6%-^104%)Xl2y%=7||%, Ans.
(27) 105%X8%=8.4%; &%=&A%\ 100%=140,Ans
(28) 5% of $9500=^75.
^75XJ^^=$273.125, Ans.
(29) $8500X1 15% =$9775, Ans.
(30) $21300-T-106.5% =$20000; $20000x 109% =$21800;
$21800— $21300=$500, Ans.
(31) $1.-T-105% =$.95^=953^ cents, AnSw
(32) $800X110J%=$881, Ans.
7o8 STOCKS AND BONDS.
(33) Int. on $1. at If % for 4 intervals=$.065-^ \
1513.50 -^$.065— =17900, Ans.
^%
(34) $1000-5 ^=$16153.84^, Ans.
105%
(35) 100%4-4%=104%; hfo of 104%=5.2^.
104%-f5.2%=109.2%.
$12012-5-109.2 % =$11,000.
$ll,000-r-$100=110 shares, Ans.
r
{36) ($4982-^106 f^)X4%=$188, Ans.
(37) 7%-=-70=10%,Ans.
(38) {ioofc-m-imro+kfc)=Hfc;
9i%=$925; 100%=$10,000;
$lO,000-r-$100=100, Ans.
(39) $1921^{Tf^xll3%)=$40120, Ans.
{40) $100x25=$2500; 5% of $2500=$ 125;
$125-r-$2.50=50 per yr. ; 10 nio.=| yr.
50-4-1=60 lamps, Ans.
(41) 25X$1000=$25000; $25000X(114^%+J%)=$28593.75, AnS.
(42) $2d734.37^4-$15.62^=$25750 ;
j\fc=$lo.(j2}^; 100%=$25000.
$25750-r-$25000=103%, Ans.
(43) $3220;.VTiiiXl05%)=$283.50, Ans.
(44) r25x$100=$12500; $12o00x {G8^%+Jf.)=$8593.75. Ans.
(45) $3000x (108^%-f J%)=$8670, Ans.
(46) $100X55=$5500; $5500x28|%=$1581.25 ;
$l581.2o-f-$13.75=$l,595, Ans.
(47) $100 X 50=$5000 ; $5000 X 108}=$5412.50 ;
$5418.75— $5412.50=$125 ;
$6.25-r^5000=.00 Y25=lfc , Ans.
STOCKS AND BONDS. 109
(48) 35X$100=$3500; ($3500x108-1)— ($3500 X86^)=$761.25,
Ans,
(49) ia5x$100=$13500; $13500x (100%— 15 J ^)=$1 1407.50,
Ans.
(50) $3V90-T-(100%— 5J%)=$4000; $4000-f-$100=40, Ans.
(51) 5% of [$4196.25-T-(93%+J%)]=$225, Ans.
(52) 6% of ($1299-^37i%)=$209.23+, Ans.
(53) $4,696.95-r-(45%+i%)=$10380;
$622.80-i-$10380=6%, Ans.
(54) 6% of ($5000-f-75%)=$400;
bfo of ($5000-j-60%)=$416§;
$416§— $100=$16|.
5% at 60 ; $16f better, Ans.
(55) $11212.50-4-112J%=$10000;
6% of $10000X106|%=$641.25, Ans.
/ 6/. \ / h%
(56) — Xl08|%)=l+%; 6%at90,ANS.
\90%/ \95%
(57) =zUfo\ 6% at 90, Ans.
90^ 125%
1% 6%
(58) X =N. Y. 7'sy\'V%,ANS.
105% 98%
(59) 7%=15%; 100%=214f%, Ans-
(60) 6%-T-90%==6f%;
225X6|%=15%, Ans.
(61) 6% of $5000=$300 ;
$5000x115
5% of =$273.8C- f ;
105
$300— $273.804-=$2fi.20 loss, Ans.
(62) $1.00-^125=.80, Ans.
1 lo STOCKS AND BONDS,
(64) 108X7^=7.56%; 7.56^-6 % =126, Ans.
(65) =^h; jfj=$o; Iff orl00%=$1615,ANS.
(66) $1500-T-6 % =$25000 ;
$25000X(96|%4-J%)=$24,250, Ans.
(67) $10200^-30% =$34000. $34000x6% =$2040, Ans.
(68) 10%-j-125%=8%,ANS.
(69) $1.00-^150%=66f%,ANS.
(70) 6fc=7j%fe; 100%=121f, Ans.
(71) lO^of $50=$5; 9%=$5; 100%=$55f, Ans.
(72) $420-^-105% =$400.
$400 X 125 % =$500, Ans.
(73) 6% of $200=$12.
$I2-r-$150=.08=8%, Ans.
(74) $29,840-r-93i%=$32,000: 6% of $32,000=^1^20,
$29,840— $240=$29, 600.
$1920-4-$29,600=6^f %, Ans,
(75) $8475-T-113%=$750r,
5% of $7500=$375.
$375X110%
=$206.25, ans.
2
(76) 5% of ($7540-^104 %)=$362.50.
J of ($362.50X128%)=$232, Ans.
(77) '^Mo-^lOifc^li^fcANS.
(78) 6%=8%; 100%=133^%,Ans.
(79) $276-T-115%=$240; $240x2=$480.
$480-T-$9600=.05=5%, Ans.
STOCKS AND BONDS.
(80) $8500X115%=$9775, Ans.
(81) $26,250-^106^%=$24,647ff.
$24,647ff X 109 ^ =$26,866}f
$26,866^1— $26,250=$616}f, Ans.
(82) $8000X110^% =$8810, Ans.
(83) $2240-7-1 12% =$2000 face of stocks.
$2000X{100%— 20%)=$1600, Ans.
(84) 100%-T-125%=80%; 100%— 80%=20%, Ans.
(85) 6% of {$6840-r-95%)=$432, Ans.
(86) $1 1212.25^112 J % =$10000; 6% of $10000=$600.
$600xl06f %=$641.25, Ans.
(87) $300.87^^(20 %4-f%)=$1458ff, Ans.
(88) .075 of l.-f.015=.076125; .025% of .076125=.001903125.
.001903125-i-1.015=.001875=j%%, Ans.
(89) 60 % of 55 % =33 % ; 7 % H-33 % =21/^ % , Ans.
(90) $2700-f-(100^,— 25%)=$3600; $3600X8%=$288.
10%
$288-? =$2764.80, Ans.
100%— 4%
(91) 100%— 15%=85%; 85% X 115% =.9775.
100 % —97.75 % =2\ % , Ans.
(92) 105%^(100%-10%)=W-; -W-^102=}||.
$33-v-102%=$32x6y; %Z2^j—%li=%2l^^.
Hf-ifl=r¥3; t¥3=$21^; if f=$148.50, Ans.
(93) 100%— 94%=6%; 6%=$666; 100%=$11100.
$11100-=-$50=222, Ans.
(94) 72 X $1000=$72000 ; $72000 X 106^ % -^($500x 102 %)=150,
Ans.
(95) 4% =$300; 100% =$7500; $7500x92% =$6900, Ans.
(96) 6 % =$180 ; 100 % =$3000 ; $3000 X 102 % =$3060, Ans.
112 STOCKS AND BONDS.
(97) =U. S. 4fs/^\^,ANS.
106% 99f%
(98) $75 X 92 % =$69 ; $69 X 18=$1242, Ans.
(99) $100X15=$1500; $1500Xll8%=$1770, Ans.
(100) $100X9=$900; $900x85=$765.
$100 X 8=$800 ; $800 X 98=$784.
$784— $765=$19, Ans.
(loi) $100X23=$2300; $2300x102% =$2346, Ans.
(102) $50X18=$900; J%+|%=|%; |% of $900=$11.25, Ans.
(103) $10X120=$1200; l\%-\-l%=l\\%\ Ifi^ of $1200=$23,
Ans.
(104) 82%-65%=17%; 17%+5^%=22|% gain.
22J%=$1125; 100% =$5000.
$5000-^$ 100=50 shares, Ans.
(105) 21% =$945; 100% =$42000; $42000-t-$100=420 shares
86 J % —73 % =13 J % ; 13^ % of $42000=$556o.
$5565+$945=$6510 gain, Ans.
(106) $9040-T-113% =$8000 stock.
5J% of $8000=$440.
113%— lll|-%=li% loss.
1^% of $8000=$120.
$440— $120=1320, Ans.
DISCOUNT. 113
DISCOUNT.
(i) 4% of $1 for 4 yrs.=.16 ; 6% of $1 for 4 yrs,=.24
$25-T-(iyi-xV'V)=$449.50, Ans.
(2) Amt. of $1 at 4^% for 8 mos.=$1.03.
$156-^$1.03=$151.45+.
$180-4-$i5i .45+=$28.55— .
$28.55 r-$151.45-h=123VV^% nearly, Ans.
20 Hi
(3) — =1; %-%=\\ i=iH%; — =lyr.
22^ 20
1X360=200 days, Ans.
(4) 1% a month=10% per annum.
Bank discount of $1 for 6 mos. 3 da. at 10%=|.
$1— $.0508J=$.9491|.
$4800-^$.9491§=$5057.06+, Ans.
(5) $1804-$13.90=$193.90.
Bank dis. on $1 at 6% for 6 mo. 3 da.=.0305; $1— .0305=
.9695.
$193.90-T-.9695=$200, Ans.
(6) Simple int. on $1 for 3 yr. 4 nio.=.08^.
True discount=.07x% ; .08|— .07x33=.00ff=|f% rate.
$65— 160=$5; $5-^.00ff=$780, Ans.
(7) 8% of $1 for 1 yr.=.08 ; I wish to receive 9^.
Then f must be what is left after discount is taken out ;
|-|=i=lH cts.
— = time which equals to 1 yr, 4 ©o, 20 da., Ans.
8 ^ ^
114 DISCOUNT.
(8) $405— $30=$375.
1 % of $375 for 10 mo. 20 da.=$3^.
$30-4-$3|=9%, Ans.
(9) \ of $3275.60=$1637.80.
Int. on $1637.80 for 63 da.=$2.866.
$1637.80— $2,866=$! 635.03.
$1637.804-$1635.03=$3272.83+, Ans.
(lo) 31 gal. 2 qt.X 50=1575 gal.
1575 X $2.40=13780.
Int. on $3780 for 93 da. at 7^%=$73.24— .
$3780— $73.24— =$3706.76, Ans.
(ri) $1 at 8% for 100 days=.02f ; $l-|-.02f=$1.02g.
$999H-$1.02f=$977.27+, Ans.
(12) Am't of $1 for 183 da.=$1.0305.
$185.49-T-$1.0305=$180, Ans.
(13) 1% of $326.40 for 7 yr. 9 mo. 10 da.=$25.386f.
$114.24-f-$25.386|=4^%, Ans.
(14) $340— $336.43=$3.57.
6% of $340 for 1 yr.=$20.40.
3.57
X 360=63 da. ; 63—3=60, Ans.
20.40
$45
(15) 2 yrs.=24 mo. ; $45-f-24= ;
24
$45
24—10=14 mo.; — X 14=$26i, Ans.
24
(16) 1% of $396 for 60 da.=.66.
$3.96-^.66=6%, Ans.
(17) Am't of $1 at 9% for 10 mo. 20 da.=$1.08.
$105-f-] .08=$375 ; $405— $3.75=$30, Ans.
(18) 8% of $750 for one yr.=$60.
8.50
X360=5l da. ; 51—3=48, Ans.
60.00
DISCOUNT, xt^
(19) Am't of $1 at 6% for 4 yrs. 8 mo. 10 da — $1.28^.
$l-v-$L28i=.78yV^ ; $1— .78yV9=-21fii.
$169^.21f|i=$769 ; $769— $169=$eO0, Ans.
(20) $2366.80-|-$33.20=$2400 ;
6% of $2400 for 1 yr.=$144.
33.20
X360=83 da.; 83—3=80=2 mo. 20 da., Ans.
144
(21) $245— $105=$140 ; 8% of $140 for 1 yr.=$11.20.
105
=9 yr. 4 mo. 15 da., Ans.
11.20
(22) $800— $792=$8 ; 1% of $800 for 45 da.=$l.
8-7-1=8%, Ans.
(23) 6% of $1 for 63 da.=$.O105 ; $1— $.0105=$.9895
$1385.30-j-$.9895=$1400.
11400— 11385.30=$14.70, Ans.
(24) 1% of $2600 for 63 da.=$4|^ ; $27.30-^$4|^=6%, Ans.
(25) 6% of $1 for 63 da.=.0105; $72.66-7-.0105=$6920, Ans.
(26) From Feb. 19, 1892, to Jan. 1st, 1893,=10 mos. 12 da.
Amt. of $1 at 8% for 10 mo. 12 da.=$1.06||.
From Oct. 12, 1892, to Jan. 1, 1893,=2 mos. 20 da.
6% of $1.06ii for 2 mo. 20 da.=.0142x\.
$1.06^4 -.0142x25=$1.0551^.
$105.51J-=-$1.0551i=$100, Ans.
(27) 10;^ on $1 for 6 mo. 3 da.=.0508J.
$1— .0508^=. 9491§.
$l500-7-.9491 §=$1580.33, Ans.
(j8) Am't of $500 at 6% for 3 yrs.=$590.
Am't of $1 at 8% for 3 yrs.=$1.24.
$590-r-$1.24=$475.81— P. W.
$590— $475.81— =$114.194-Dis., Ans.
(29) Am't of $300 at 8% for 2 yrs.=$348.
Pres. worth of $348 for 2 yrs.=$310.71.
$348— $310.71=$37.29, Ans.
ii6 DISCOUNT.
(30) Am't of $1 for 5 mo. at \^Jo=%\M\ ;
$3G8.75-^|1.04i=$354 P. W.
$368.75— $354=$14.75 Dis., Ans.
(31) Am't of $1 at 10% for 4 mo.=$1.03^ ;
$775-T-$1.03^=$750, Ans.
132) Am'tof $1 at6% for8mo.=$1.04;
$260h-1.04=$250, Ans.
(33) 5% of $2480=1124 ; $2480— $124=$2356.
Am't of $2356 at 10% for 4 mo.=$2434.534-.
$2480— $2434.53=$45.47, Ans.
(34) xk— T77=tV7^; $2.45h-xV7%=$535, Ans.
(35) Am't of $1 for 10 mo. at 12%=|1.10 ; $1221-r-$1.10=$1110.
$1122— $1110=$12, Ans.
(36) Am't of $1 at 8% for 9 mo.=$1.06.
$840.40-r-$1.06=$792.83, Ans.
(37) Int. on $1 at 1^% a mo. for 33 da.=.0165.
$1— .0165=.9835; $1650-f-.9835=$1677.68, Ans.
(38) Int. on $1 for 43 da. at 8%=$.009f.
$1— .009f=.990f.
$2072.60-r-.990f=$2092.60— Ans.
(39) 20% of $100 for 63 da.=$3.50.
Int. on any sum for 63 da. at l%=y^oW
$3.50^-3-2%V^of $103.50=19/<f^%, Ans.
(40) Am't of $1 at 25% for 1 yr.=$1.25
$1^$1.25=.80; $1.00— .80=.20=20%, Ans.
(41) $10296 -f-3=$3432 ; the am't of the present worths of $3432
for 1, 2 and 3 yrs.=$8620
$8620— $8000=$620, Ans.
(42) Int. on $1 at 6% for 33 da.=.0055.
$1— .0055=.9945 ; $400h-.9945=$402.21, Ans.
(43) rf 7ir=bank discount ; y^^=true discount.
$3.60^3a^G^%=$1060, Ans.
EXCHANGE. 117
EXCHANGE.
(i) 6% ou $1 for 8? -ia-^-OlOS.
L (1.+^%)— .0i05=.9945.
\ $5680X.9945.-=|5648.76, Ans.
(2) $l+|%=$1.00f ; int. on $1 for 33 da.=.0055.
$1.003— .0055=$! .002.
I $1575X$1.002=$1578.15, Ans.
(3) %\\-\\%=%\S)\\\ $1 at 6% for 63 da— .0105.
$2625X ($1.01J— .0105) =$2636.81+, Ans.
(4) Int. on $1 for 33 da. at 6% =.0055.
$500 X ($1.01— .0055) =$502.25, Ans.
(5) Int. on $1 for 33 da. at 6% =.0055.
$502.25-r-($1.01— .0055)=$500, Ans.
(6) Int. on $1 at 8% for 63 da.=.01f.
$798.80-i ($1.01^— .01|)=$800, Ans.
(7) Int. on $1 at 6% for 33 da.=.0055.
$352.62-7-1^1— m ^ +.0055] ) =$360, Ans.
(8) $1 at 6^ for 93 da =.0155.
$4800 X (l.Olf— .0155)=$4791.60, Ans.
(9) Int. on $1 at 6% for 63 da.=.0105.
$1— (.02J+.0105)=.9645.
$512.36-T-.9645=$531.218+.
(10) Int. on $1 for 63 da. at 6% =.0055.
$5400 X ($1.005— .0055)=$5397.30, Ans.
1 18 EXCHANGE.
(II) Int. on $1 for 33 da. at 6 ^=.0055.
$1324.74-=- ($1.01f— .0055)=$1309.03, Ans.
(i2) $5075— $5000=475.
$75 -^ $5000=1^ % , Ans.
(13) $890xl01i%=$901.12^, Ans.
(14) $1800X99% =$1782, Ans.
(15) Int. on $1 at 7% for 63 eLd..:=S)\^q^.
$1400X (102^%— .01xV^)=$1420.18^, AlfS.
(16) Int. on $1 for 93 da. at 10%=.025|.
$2400X (103%— .025f)=$2410, Ans.
(17) Int. on $1 for 63 da. at 6% =.0105.
$1650X(.98^— .0105)=$1607.92o, Ans.
(18) $7900 ^101^% =$7783.25, Ans.
(19) $5000-5- .98|=$5076.14, Ans..
(20) Int. on $1 for 63 da. at 6% =.0105.
$1000^(103%— .0105)=$980.87, Ans.
(21) i"87x$4.82xl06%=$444.50+,ANS.
(22) $2000-^■($4.85xl06%)=/389 7d.4-, Ans.
(23) $1505.40X(1.00— 1%)=$1501.64— , Ans.
(24) Int. on $1 for 63 da. at 6% =.0105.
$12692.50X (100|%— .0105)=$12654.42+, Ans.
(25) $2000^1.00f=$l987.58— , Ans.
(26) $4681.25^(100%— li-%)=$4740.51-, Ans.
(27) Int. on $1 for 21 da. at 6% =.003^.
(I.OO4-.OO5— .003^)=1.001^.
$5264.15-J- 1.001 ^=$5256.27—, Ans.
(28) Int. on $1 for 24 da. at 6% =.004.
1.00-(^%-f-.004)=.9872i.
^6836.75 -^.9872f =$6925.04, Ans.
EXCHANGE. 119
(29) Int. on $1 for 63 da. at 6% =.01 05.
].01|— .0105=$1.0045.
$850X1. 0045=$853.82o, Ans.
'(30) Int. on $1 for 33 da. at 7%=.006iV
$2128.525^- (1.02— .006j\)=$2100, Ans.
(31) Int. on $1 for 63 da. at 6% =.0105.
$oOOX (1.00|— .0105)=$498.50, Ans.
(32) Int. for 93 da. at 6% =.01 55.
$343.22h-[1.00— (J-|-.0155)]=$350.404-, Ans.
(33) Int. on $1 for 33 da. at 6% =.0055.
$362x (.98^— .0055) =$354.58—, Ans.
(34) Int. on $1 for 63 da. at 6% =.0105.
$652.925h- (1.01^— .0105)=$650, Ans.
(35) Int. on $1 for 33 da. at 6% =.0055.
$1588.595 X (.98|—.0055)=$1560, Ans.
{36) $1000x100^% =$1005, Ans.
(37) $3000x1011% =$3037.50, Ans.
(38) Int. on $1 for 33 da. at 6%=.0055.
\ $5000 X (1 .00^— .0055) =$4978.75, Ans.
(39) Int. on $1 for 93 da. at 6%— 0155.
$1500X (.991— .0155)=$1471.875, Ans.
(40) $5000X991% =$5985, Ans.
(41) $3000 X100J% =$3003.75, Ans.
(42) Int. on $1 for 93 da. at 6% =.0155.
$5000x (l.OOJ— .0155)=$4928.75, Ans.
(43) Int. on $1 for 2 mo. at 6% =.01.
$1500x(1.00J— .01)=$1488.75, Ans.
(44) Int. on $1 foi 4 mon. at 0%— 02.
$1500X (1.00i% — 02)=$1473.75, Ans.
12Q EXCHANGE.
(45) Int. on $1 for 63 da. at 6% =.0105.
$5000 X (l.OOyV— .0105)=$4952.50, Ans.
(46) $5000 -f- 101^% =$4926.11—, Ans.
(47) $5725-^ 100 J^ =$5710.71+, Ans.
(48) Int. on $1 for 33 da. at 6% =.0055.
$1500-^(100^%— .0055)=$1506.40, Ans.
(49) Int. on $1 at 9% for 63 da.=.015|.
$1200 -J- (100|— .Olof )=$1213.04+.
{50) $10000-^(100%— i%)=$10012.514-, Ans.
(51) $1750^100J=$1747.81+, Ans.
(52) Int. on $1 at 6% for 33 da.=.0055.
$3500-^ (100J%— .0055)=$3514.934-, Ans.
(53) ($3762.50^-105^) H-$4.87=/732 6s. 2.4d.4-, Ans.
(54) ($2984.38^107^) -^-$4.86=^571 4s. 6.6d.-|-, Ans.
(55) (3269-^5.15) X105|=$668.87-|-, Ans.
(56). (8950-j-5.19)Xl06J=$1832.25— Ans.
(57) (/895 10s.-f-4.87)Xl06f=$4650-f-, Ans.
(58) (5725^5.20) Xl06i=$]169.77-f-, Ans.
(59) (^585 10s. 5d.^$4.86)Xl07^=$3059.05+, Ans.
(60) (/875 5s. 4d.-f-$4,885)Xl04|=$4484.1lH-, Ans.
INSURANCE, 121
INSURANCE.
(i) f of $36004-f of $6000=$7500. \
($126— $1) -4-$7500=lf ^ , Ans. 1
(2) 1J%=$75; 100%=$6000. \
|=$6000 ; |=$10000, Ans. \
(3) I of $340000=1212500. \
1% of $212500=$1328.12-f, Ans. * • ]
(4) 1J%=$17.25; 100%=$1380. \
|=$1380 ; |=$2300, Ans. \
(5) 11 ^=$39; 100^=$3250. \
lfM=f, Ans. '
(6) 2i% of f of $24000=$337.50. ;
1^% of f of $36000=$270. j
$337.504-$270=$607.50, Ans. I
(7) f % of $1275=$7.08; $7.08J+$1=$8.08J, Ans. \
(8) f of $4800=13200. \
$19.20^$3200=f%, Ans. \
(9) 2%of |=t%; 2l%oi\^Wo- \
iV%-iV=t\%,AnS. \
(lo) $5000+$5000=$10000.
|0Mfl=2. i=$262.50; f=$1181.25. 1
$1181.25^$45000=2f^, Ans. \
Ii2 INSURANCE.
(ii) $19.95x5=$99.45 annual payment. \
($99.45X75— 2 1)=$5370.30, Ans. i
(12) $104.58X10==$1045.80. \
Premium is paid at the beginning of each yr. and draws j
interest for 10, 9, etc., yrs.=55 yrs.
Annual int. on $104.58 at 6% for 55 yrs.=$345.11.
$1045.80-f$345.11==$1390.91-h, Ans. '
(13) $118-^1% =$14750, Ans. "^
(14) $42.30-5-^9^% =$4700.
|=$4700; |=$7520, Ans. '
(15) |=$197.13; |=$328.55; 2J%-2}%=J%; '■
J % =$328. 55; 100% =$131420. i
^ J=f 131420 ; §=$262840, Ans. ^
(16) J of l|%=f %; 1\% of J=J%. \
l|/«-(i%+l%)=T'o%; t\%=^8.11; 100%=$19370, Ans. \
(17) (1|% of $8000+2J% of $10000)+$^07.50=$560. \
2 fc =$560 ; 100 % =$28000, Ans. \
(18) f of $2000=$1500; $1500^(100%— U%)=$1522.84, Ans. •
(19) 1J%=$225; 100% =$15000. j
f =$15000 ; f =$20000 ; ^+l=i ; '
§=$20000 ; ^=$6666.66§ ; ' ^
|=$13333.33i, Ans. \
(20) $325-;- $16250=2%, Ans. J
(21) li%=$2475; 1000% =$198000. j
§=$198000; |=$297000, Ans.
(22) 2J%=$1657.50; 100%=$66300. ;
f =$66300; f=$88400, Ans.
(23) 4J%=$400; 100%=$8888|. ■
§=$8888| ; f=$13333.33A, Ans. i
(24) f % of I of $30000=$168.75. :
$30000— ($5000— $168.75)=$25168.75, Ans. « .^
INSURANCE. ii3
(25) 3%=$180; 100^=16000.
§=$6000 ; I =$9000, Ans.
(26) $652.50-^$43500=l^%, Ans.
(27) 1^%=$175; 100%=$14000, Ans.
(28) $21.10X5=$! 05. 50, Ans.
(29) $123.90^$o000=2|ff^, Ans. ,
(30) f of $1 50000=$1 1 2500.
|%of ^of $112500=$135.
1% of t of $112500=$210.93.
$112500— ($28125+$22500)=$61875.
1% of $31875=$371.25.
$135+$210.934-$371.25=$717.18, An3.
(31) 1\% of $6000=$135 prem.
65|% of $6000=$3945.
$3947— $135=$3810, Ans.
(32) $L10Xl500=$1650cost.
$1.20X1500=$1800.
(2^% of $lS00)+$1650=$169d.
$1800— $1695=$105, Ans.
(33) 1% of $100000=$750.
IK i% of $60000=$525.
I^P $750— $525=$225, Ans.
(34) 3%=$378; 100% =$12600, Ans.
(35) $1950^(100%— 2^%)=$2000, Ans.
(36) 9700X$1.20=$11640.
$11640^(100%— 3%)=$1200, An3.
(37) $2600^(100%— xV%)=$2618.26-f-, Ans.
124 TAXES.
TAXES.
(1) $486250X.00^^V=$3792.75, Ans.
(2) $3800X.00xVV==$29.64; $29.64+$l=$30.64, Ans.
(3) $1.50X3=$4.50; $53.46— $4.50=$48.96.
$48.96 -^$8704=53^c. on $100, Ans.
(4) 2J^=$26.04; 100%=$104i.o0 income.
16%=$1041.60; 100% =$6510, Ans.
(5) $7592-^(100%4-2%)=$7450, Ans.
(6) $1.35=1.35% on the dollar.
$125127.66 -f- (100 % —1 .35 % )=$126840 cap.
1.35% of $126840=$1712.34 tax, Ans.
(7) 1024X$1=$1024.
$4000— $1024=$2976.
$2976 -T- 2.4 mills=$1240000, Ans.
(8) $4300+$1940=$6240.
$33.20— $2=$31.20.
$31.20-^$6240=|% , Ans.
(9) 3x%% of $6748950=$242962.20 amount.
\\% of $242962.20=$3644.434- fees, Ans.
DUTIES OR CUSTOMS. 7^5
DUTIES OR CUSTOMS.
(1) 1114-1124-113=336 lbs.; 6% of 336=16.8.
(336—16.8) X $.05=$15.96, Ans.
(2) 250 lbs. X 20=5000 lbs. ; ^\% of 5000 lbs.=312.5 lbs.
(6000— 312.5) X|.20=$9375 ; 4^ of $9375=137.50, AnS'
(3) 3724 yds. Xl0c.=$372.40.
11% on 3724x23c.=$94.217.
$372.40+$94.217=$466.617.
$466.617X{100^— 10%)=$419.96— , Ans.
(4) 45X36X$1.25=$2025.
2% of $2025=$40.50; $2025— $40.50=$1984.50.
40^ of $1984.50=1793.80, Ans.
(5) 98X12=1176; 10% of 1176=117.6.
(1176—117.6) X $.05=$52.92, Ans.
(6) 668X36=24048; ^ of 24048=3435.42+.
(24048—3435.42+) X |.02^=$515.31+, Ans.
(7) 30% of (40X3|X.75)=$35.07+, Ans.
(8) 760 lbs. X 30=22800 lbs. ; 12% of 22800 lbs.=2736 n>«\
22800 lbs.— 2736 lbs.=20064 lbs.
(20064 lbs.-5-100)X$1.20=$240.76+, Ans.
(9) $631.43— $53.84=$578.09.
2% of 1680 lbs.=33.4; 1680—33.4=1646.6.
$578.09-v-(1646.6Xll5%)=30+cts.,ANS.
(10) $7389.03— $73.80=$7315.23.
$7315.23-^130%=$5627.10, Ans.
Ti^ DUTIES OR CUSTOMS.
(11) 60X54X$1.80=$5832.
60X54X$.25=$810.
5% of $5832=$291.60.
20% of ($5832— $291. 60)=$1108.08.
$5832+$810+$1108.08+$8.50=$7758.58, Ans.
(12) 50X220=11000 lbs.; 4% of 11000=440 lbs.
(11000— 440) X$.05=$528.
$l84.80-^$528=35%, Ans.
(13) 540X160 lbs.=86400 lbs.
3* % of 86400=3024 ; 86400—3024=83376 lbs.
83376 X$.09=$7503.84; 15% of $7503.84=$1125.57J. A.ns.
(14) 28% of (25X24X45X$1.13)=$8542.80, Ans.
(15) 12x42x$1.30=$655.20.
5% of $655.20=$32.76.
%^% of ($655.20— $32.76)=$196.07—, Ans.
(16) 40X160=6400 yds.
20%=$1024; 100%=$5120.
|5120-^6400=80c., Ans.
(17) 20X25X.10=$50.
15% of $50=$7.50.
6% of ($50— $7.50)=$2.55, ANS.
(18) 2240X7X$.17X20%=$533.12,AN&
(19) 20X63=1260 gal.
oyo of 1260=63 gal.
(1260— 63) X$.09=$l 07.73, Ans.
(20) 10X145=1450 lbs. ; 8% of 1450=116 lbs
(1450— 116) x.06|=$90.04-f, Ans.
(21) 45X120=5400 lbs.
10% of 5400=540 lbs. ; 5400— 540-=4860.
4860X$.10=$486, Ans.
PROPORTION. 12"
(22) 210X190=39900 lbs.
5% of 39900=1995; 39900—1995=37905 lbs.
25% of (37905 X$.05)=$473.81+, Ans.
(23) 40% of (15X25X35X$3.95)=$20737.50, Ans.
(24) 20%=$40.50; 100%=$202.50.
$202.50 ^ (100 % —10 % )=$225.
15X12=180 doz.; $225-^180=$1.25, Ans..
(25) 25% =$337.50; 100 % =$1350 ;
$1350 -^ 100 Xl8=75c. invoiced.
.75X125% X120%=$1.12^ S. P., Ans.
(26) 35%=$806.12; 100%=$2303.17+invoiced;
$2303.17+ X 135% r-=$3.\09.274-cost, Ano.
(27) $1473.80^$3684.50=40%, Ans.
PROPORTION.
(1) 8.4 : 4.95 : : 9i : 5|, Ans.
(2) lJ:9i::H:8iANS.
(3) f:T'i::|:^,ANS.
(4) (35—14) : 35 : : 24 : 40, Ans.
(5) fXj=^V,ANS.
(6) 6-^1^=5, Ans.
(7) 7000:5760 ::l:iH» Ans.
(8) (3X5:4X9)— (1X2:6X7)=!^, Ans.
(9) (7i-4f)-(4|^7i)=Ht^. Ans.
(10) 2Jx6^=14f, Ans.
12J
PROPORTION.
(11) 2J-5-6i=^c, Ans.
(12) ^=ratio; divisor 5 times the dividend.
Then there are 4 parts excess.
Then 4 : 1 : : 1 : J, AnS.
(13) 1 : 1| : : 40 : 120 ; 120—48=72 lbs., Ans.
(14) i of (3i-TV)=lM.
3|-lM=lt^, Ans.
(15) Their money is as 1, 3 and 12 ;
1+34-12=16.
xV of $3456=$216 C ; i\=$648 B ; if=$2592 A, Aks.
(16) |=f; f=ff ; 204-21=41.
If of 2255=1100 A ; f f=1155 B, Ans.
(17) l=f; f=lf ; ff-!f=i\.
^\=120; 11=1176;
f 1=1296, Ans.
(18) |=t;f=V-; V4I«=¥:
-¥=itV; 1=1;
¥=l. ••• f and f , Ans.
(19) l=H;l=¥-;-V— f=f.
|==$637; f =$728 John.
i/-=$1365 James, Ans.
{20) 5+8=
(21) The cost of the house, farm and store are to each other
as 1, 3 and 6.
1+3+6=10.
$450+$650=$1100.
$28100— $1100=$2700C.
tV of $27000=$270-. .'.us-.' ,
(t^^ of $27000) +$-l50=$8550 farri ;
(^ of $27000) +$650=$16450 store, Ans.
PARTNERSHIP. 129
PARTNERSHIP.
I
I
(1) 2^ of $300=$G0 A; if of $300==$144 B; ^V of $300=$96 C,
Ans.
(2) 16+14-4-12=42 ; if of $1200=$457f X.
If of $1200=^100 Y; || of $1200=$342f Z, Ans.
(3) $18000+$60004-$10000=$34000.
$34000 X (1 00 % —30 % ) =$23800.
$23800 X 1 50 ^^ =$35700 ; $35700— $34000=$1700.
if of $17uO=$900 A; /j of $1700=$300 B; || of $1700=
$500 C, Ans.
(4) $2250— ($800+$1000)=$450 C's gain.
$450^$3000=15% gain; 15%=$800; 100%=$5333J A's;
lo%=$1000; 100 % =$66661 B's, Ans.
(5) $6500+$8000+$5500=$20000.
2V(y of $12000=$3900 sons ; ^^ of $12000=$4800 wife ;
2V0 of $12000=13300 daughters, Ans.
(6) $5000+$6500+$4500+$2500+$600=$19100.
$23000— $19100=13900.
x^o of $3900=11218.75 A ; y^V of $3900=$1584.37| B ;
^^ of $3900=$1096.87| C, Ans.
(7)3X16=48 ^Vj of $87.20=$19.20 X
5X20=100 if I of $87.20=140 Y
7X10= 70 -gVV of $87.20=$28
— $87.20-^218=40^ per week, Ans.
(8) $4200-i-$3600+$4500=$12300.
iVa^ of $2706=$924 A ; -j^Jv of $2706=$792 B ;
xVj of $2706=$990 C, Ans.
I10 PARTNERSHIP.
(9) 7X30=210 $1600— $95=$1 505.
5X40=200 \\\ of $1505=1525 A ;
6X32=192 \%\ of $1505=$500 B ;
\%\ of $1505=$480 C, Ans.
oOi^
(10) $125-f-$625=18if%.
$810Xl8if%=$150; $125+$150=$275, Ans.
(11) $2500X24=$60000
$3000X22=$66000
$126000
tY^ of $2835=$1350 A ; -^^^ of $2835=$1485 B, Ans.
(12) $3000— $2730=$270.
10+12+14=36; \% of $270=$75 A;
\\ of $270=$90 B ; If of $270=$105 C, Ans.
(13) 7.5+1=7.875.
7 5 #
_— of 756=720 ; of 756=36, Ans.
7.875 7.875
If
(14) lt+2i=4J ; - of 10.25=4.1 ;
4^
— of 10.25=6.15, Ans.
4i
(15) $100X150% =$150; 50=gam.
$50— ($18+$19)=$13 C's gain.
50%=$18; 100%=$36A; 50%=$19; 100%=$38B.
50% =$13; 100 % =$26 C, Ans.
(16) 8X23=184 iM=A^A
12X29=348 IM=T3V B, Ans.
532
(17) 210+140=350; ||^ of $50=$20, Ans.
(18) 80X60=4800 ^-^ of $50=$30 A
64X50=3200 ff of $50=$20 B, Ans.
8000
PARTNERSHIP. 131
(19)
12500 X18=$45000
lYr of $325C=$1250 A
^^
$1500x18=127000
1V7 of $3250=$750 B
h
$5000 X 9=$45000
x^rV of $3250=11250 A, Ans.
1 $117000
(20)
80X6=480
720+9004-300=1920.
40X6=240
■j-V2<V of $275=$103.12| A
^^i~^ of $275=$128.90| B
720 A
100X6=600
i^i^ of $275=$42.96i C,
Ans.
50X6=300
900 B
50X6=300 C
(21)
4X3=12
36+48|=84f
fof 4xy=24
36A
36
of $1695=$720 A
84f
5X3=15
m
1 of 5X9=33|
48|B
48|
of $1695=$975 B, Ans.
84|
■m
Capital is as 6, 4 and 3
9
H
6X4=24
t:\V of $1988=$714 A
A
3X9=27
x\\ of $1988=$728 B
■
51 A
f j\ of $1988=$546 C,
Ans.
■
4X13=52 B
■
3X13=39 C
P
142
I
(23) $5600X12=$67200
$4200X12=$50400
$16800
$16800-^(12— 4)=$2100,
Ans.
EQUATION OF PAYMENTS.
(24) 404 X 50c.=$202
340X $1.10=1374
$576
f ^f of $31.68=$11.11 A
lif of |31.68=$20.57 B, Ans.
(25) $7000X6=142000.
\\—^T=^ix ; $42000-^T«x=$77000.
($77000— $42000) -v-|5000=7 mo., Ans.
EQUATION OF PAYMENTS.
(1) ll-f-104-9, etc. to 1 mo.=66 mos.
$50 paid the first of each mo. is $3300 for 1 ma
$3300-j-$600=5f mo., Ans.
600 2
(2) $900— $300=$600. =-;
900 3
2 3
-=12. -=18 mo., Ans.
3 3
(3) 30 X 0= 0
80X12= 960
70X24=1680
60X40=2400
240 )5040(21 da.=Feb. 5th, Ans.
(4) $300X 0= 0
$700 X 72 X 50400
$800X144=115200
1800 ) 165600(92 da.=Aug. 1st, Ans.
EQUA TION OF PA YMENTS. 133
(5) $500x4=2000
$600X5=3000
$400X7=2800
1500 ) 7800(5 mo. 6 da., Ans.
(6) $ 900 X 12= 10800
$1000X193=193000
$1100X255=280500
3000 )484300 (161.4+ or 162 da.=June llth, AnS.
(7) $500 X 4= 2000
$500X26=13000
1000 ) 15000(15 da.=May 15th, Ans.
(8) $ 300X14= 4200
$6000X35=210000
6300 ) 214200 (34 da., Ans.
(9) $2000X4= 8000 $10500 X6=$63000
$4500X2= 9000 6500 17000
$6500 17000 4000 )46000(11| mo., Ans.
(10) iof$10000=$2500
|of$10000=$2000
$2500 X 6^ 15000
$2000X18= 36000
$5500X30=165000
10000 )216000(21f mo.=l yr. 9 mo. 18 da., Ans.
(II) $ 600X 5 = 3000
$1000X10 =10000
$1200 X 7|= 9400
2800 ) 22400 (8 mo., Ans.
134
EQ UA TION OF PA YMENTS.
(12) $ 300x4= 1200
% 800X5= 4000
$1000X8= 8000
2100 ) 13200 (6f mo. , Ans.
(13) $300x30= 9000
$600x60= 36000
$900X90= 81000
1800
(14) $840 X 0= 0
$400X94=37600
$200X63=12600
) 126000(70 da.=Aug. 10th, Ans.
$840— ($400+$200)=$240
50200
(15) J of $12000=$4000
\ of $8000=$2000
\ of $8000=$4000
50200 ^$240=209 da.
209 da. after Oct. 3rd is Apr. 30tli
next yr., Ans.
$12000— $4000=$8000
$8000— $2000=16000
$4000X3=$12000
$4000X6=$24000
$36000-5-6000=6.
6^3=
$36000
=2 mo., Ans.
(16)
$ 300X10= 3000
$ 500X25=12500
$1000X40=40000
$600x0= 0
$550X1= 550
$650X2=1300
1850)55500(30 da.,
, Ans.
1850
(17)
1 3
-X3=-
4 4
1
-X6=3
2
1
-X8=2
4
1 )5|(5| mo., Ans.
ALLIGA TION.
353
(18) $400X6=2400
$600X8=4800
7200 7200h-900=8 mo., Ans.
(19) $200x4= 800
$200x2= 400
1200 1200^200=6 mo., Ans.
ALLIGATION.
(I)
(3)
(5)
3X10= 30
5X 8= 40
2X15= 30
10 )100(10cts.,ANS.
7^
5
2^
1
6
H
5
7
\
5
10
—
2|
5
(2)
(4)
12
16
Ans.
12
4
1
15
1
2
18
2
1
20
4
1
Ans.
Ans.
Note. — A simple solution for problems of alligation med-
ial is to write the differences conversely opposite the
31
numbers compared, as, |3
4
17
which shows that for every
3 at 3 cts., 1 at 7 cts. must be taken.
13
1X25
1X25
(6)
6 3X25 Ans.
67
3X5=15
3X5=15
3X5=15
14X^
14=5
(0
Ans.
136
ALLIGATION.
(7)
(9)
80
Ans.
$450^5=190
$90-^10=19
4(
Ans.
(II) $48-^60=80^^^.
(12)
(13)
30
50
10
1
40
40
8
1
80
—
2
85
5
1
4
(8)
10
8
9
12
15
2
1
2
5
150 at 8^
60 " ^f
30 " 12^
60 " 15^, Ans.
(lO) ,
33
1533
28
30
35
-r-
5
3
2
100=33 cts.
5 ^V of 100=20
3
X of 100=12
17
— II of 100=68
25 Ans.
of 80=20 chickens.
of 80=20 ducks.
I of 80=40 geese, Ans.
$1X5=$5; $5-f $.04=15.04 ; $5.04^7=72 cts., Ans.
(14)
(15)
4 gal. of whiskey=$2.00
\ " " alcohol= .80
1 " " water= 0
h\ $2.80
$2.80-^5^— 50|a cts.
Ans.
15^ 7f=1.935
" 10^= .024
6^=1.163
Ans.
\
8
23|
3.122
23i^- 3,122=7/^r-, Ans.
ARITHMETICAL PROGRESSION. 137
ARITHMETICAL PROGRESSION.
(i) 3X(19— l)-f50=$1.04, Ans.
(2) 2X(20— 1)=38;94— 38=56, Ans.
(3) tVX(37—1)=21; 21+43=64, Ans.
(4) 180X11=1880; $939— $880=$59.
$939+159=1998; $998Xl2=$11976.
$11976-^2=$5988, Ans.
(5) First term 4 ; com. diff. 4 ; uumb. terms 100. (100— 1)X4
=396 ; 4+396=400 last term.
(400+4) X 100
=20200 yds.=llfi mi., Ans.
2
(6) (1000—1) X 10=9990 ; 9990+10=10000 last term.
\ ($100.00 +$.10) X1000=$50050, Ans.
(7) (10— 1)X10=$90; 90+20=110;
\ (1 1 0+20) X 10=$650, Ans.
(8) (10— 1)X 1^=13.5; 13.5+2.5=16 in., AiiS.
(9) (4+49) X 10
-=265, Ans.
(10) 3 yrs. 10 mos.=46 mos.
60—21=39; 20—5=15.
39^15=21 com. diff.
(5-l)X2f=10|.
21— 10f=10| first payment.
(46—1) x2f =$108 ; $108+$10.60=$118.60 last payment
J (10.60+118.60) X 46=12971.60, Ans,
138 GEOMETRICAL PROGRESSION.
'3
i
1
GEOMETRICAL PROGRESSION. \
(1) (I) ^ X 9(.>=30| mi., Axs.
(2) 192 -^128=1 J ratio;
(li) «X 128=1408, Ans.
20
(3) ^5=ratio; =200 rds., Ans.
(1— r%)
(4) C2)t=^<>-'>=524288.
I X 524288=262 144 last term. -
(262144X2)— i=o24287i.
524287^^ (2— l)=o24287^ cts.=$5242.87J, Ans.
(5) 9thterm=7th; (6)^=46656.
16x46656=746496, Ass.
(6) (I) -X 1024=13611, Ans.
(7) iH-a— J)=2,Ans.
(8) |-^a-f)=8i.Ai^
(9) 512^8=64. ^^^^^4, Ans.
(10) 27X3=81. \/8l=9, or *-i/27T3=3; 3X3=9, Axs.
(11) 32-5-4=8. ^^^§=2.
4X2=8;
8X2=16. 8 and 16, Ans.
TIME, 139
TIME,
(1) 1=1 ; l=H ; !^-f^M ; 12^^=8 o'clock p. m., ans.
(2) i=|; 1=1; #4-1=1; 12^1=4 o'clock P.M., Ans.
(3) A=H;H=W;W-M=fl;i2-fl=i0o'ciockA.M.,ANs.
(4) A=H; ii=W; ¥f-f-M=W.
12-4-^5^6=40 min. past 3 p. m., Axs.
(5) l=A; i=i; i+f=!; i2^f=8.
12 — 8=4 o'clock P. M., Ans.
(6) If— t'i=H; 3o-f-i|=38T2x min. after 7, Ans.
(7) 1=2%; 'h^h\ fH-i=5=lf
12-^||=9f ; 12— 9f=2i o'clock P. M., Ans.
(8) I=/t; 1=1; l+f=¥; i2-^V=~f-
12 — 7f=4f or 17} min. after 4 p. M., Ans.
(9) l=A*5;l=H; M+H=f|.
36^ff=22f ; 36— 22|=13J or \\ o'clock a. m., Ans.
(10) i=J; |=J; \-^\=\\ 12^1=8 p. M., ANS.
(11) ^ of 12=ff hr.— 90 min.=3|| hrs.
3|^ lirs.=57^ min. past 3 p. m., Ans.
(12) if— x^^H; 22-^H=-24min.,ANS.
(13) 46 min. to gain.
46xft=^^i^ iiiiii-
60— o0x23-=9y^ min. before 10, Ans.
(14) 1 |_J^=^i. From 12 to 4=20 min.
20-5-1^^=213^ min. past 10, Ans.
lik APPLICATION OF SQUARE ROOT.
(i5> Minute hand must gain 10 and 30 min.
10xH=10ti niin. past 4.
30xH=32A iiiin- past 4, Ans.
{i6i The hour-hand is 40 minutes + a certain distance (or 1
space) from 12. The minute-hand is ^ as far or 20 min.
-\-\ space. The minute-hand moves 12 spaces to 1 of
the hour-hand. 20 min.-|-^ space equals 12 spaces, or
20 minutes=ll^ spaces. 20-^llJ=l|| or 1 space. 12
spaces=l||Xl2=20|f min., Ans.
(3) The hour-hand is 10 min.-f-l space from 6. The minute-
hand is (10 min.+l space) X 2=20 minutes-f-2 spaces or
50 minutes-|-2 spaces from 12. 50 min.4-2 spaces=12
spaces; 50 min.=10 spaces; 1 space=5 min. 5x12=
60 min. past 8 or 9 o'clock, Ans.
(17, 12—2=10. 30-^10=3 min.
Min. hand travels 12 times as fast as hour-hand. 3x12=
36 min., Ans.
(i8i H+^=!f ; 4-^-ff=2|; 4-2t=U p. m., Ans.
APPUCATION OF SQUARE ROOT.
(1) lA=160rds. \/l60=12.64-f-rds., Ans.
(2) v/lOx 160=40 rds., Ans.
(3) \/lOAX 160=40 rds. to the side.
40X16^=660 ft; 660-5-15=44.
44X4X140=170.40.
44X4X5
X $6=$52.80.
100
$70.404-$52.80=$1 23.20, Ans.
APPLICATION OF CUBE ROOT. 141
(4) v/2l6T6=6 in., Ans.
(5) Each round will be the hypotenuse of a right-angled
triangle whose sides are 8 ft. and G ft. \/8^-f-6^=10«
o0h-6=8J rounds; 10x8i=83J ft., Ans.
(6) 15X6=90; 18x6=108.
v/(90) 24- (108) 2=140.58+mi., Ans.
(7) 20X160=3200.
n/3200T2=40. 40X2=80.
(40X2) +(80X2) =240 rds., Ans.
(8) 5408^2=2704. \/2704=52 ft. width.
52X2=104 ft. length, Ans.
(9) \/(100) 2 4-(60) ^+(26) 2=119.48+ft., An&
(10) y/\ of (50)2=35.35+, AnS.
APPUCATION OF CUBE ROOT.
(1) '^2150.4=12.9+in., ANS.
(2) 1728xl5|='27000 cu. in,
\^27000=30 in.
30X30X6=5400 sq. in., ANS
(3) (1 6) 3—6=210 cu. in., Ans.
(4) \^'^23lXl500=70.23+cu. Jn. , hiA^.
(5) ^80Xl28=21.71+ft., Ans.
142 MEASUREMENTS.
(6) 192X27=5184.
1X4X6=24. 5184-^24=216.
^2l6=6 ft. depth ; 6x4=24 width ; 6x6=36 length, Ans.
(7) 13^=¥;¥-32=f|.
^^=1; fX 1=1 ft.=9 in. square.
\ X 32=24 ft. length, Ans.
(8) ^2048^4=8 ft, Ans.
(9) ^729X8=18 ft., Ans.
(lo) 2150.4X100=215040.
215040^3=71680..
^^^7l680=41.534-in.=3.464-ft. height and width.
3.464-X3=10.88-i-ft. length, Ans.
MEASUREMENTS.
(1) (6)2X3.1416X10=1130.976 cu. ft.
(1 130.976 -f- 550) X 115=130.844-. Ans.
(2) 20X20X15=6000; 6000 -f- 450=1 3^ T., Awa
(3) 30x20x20^550=21y\T, Ans.
(4) 10X5X8X12=4800 cu. ft.
4800X.8=3840bu.,ANS.
(5) 1728X6.25=10799.8 cu. in.
10799.8^231=46.75-r-gai., ans.
(6) 750-HlJ=600 bu., Ans.
MEASUREMENTS, 143
(7) 135 X. 8=108 cu. ft.
1X6X9=54. 108^54=2 ft. depth.
2 X 9=18 ft. length. 18 -^ 6=3 ft. width, Ans.
(8) ^583.2 H-. 8=9 ft, AnS.
(9) 10X4 X8X. 8=256 bu.
lbu.-^l^pk.=3;
256X3=768 bags, Ans.
(10) (80x2JXlO)-f-24|=80|^P.
80|§x$l.=$80|f,ANS.
(11) (45X2) + (60X2)=210.
$254.54y«x-^ (210X8X 1 J-4-24|)=:|2.50, Ans.
(12) (60-^3.1416) 2 X.7854X20X2J cts.=99.5-4- cts., Ans.
(13) 8 in.=| ft. 20Xf X4=53J ft, Ans.
(14) 16XUXl2=240ft, Ans.
(15) (30)2=900. n/900h- 3=17.32+ in., Ans.
Or side : diameter of cube : : 1 : \/3.
.-. 30-^-^/3=17.32+ in., Ans.
(16) [(40—2) 3 X .5236] ^231=124.37+ gal., Ans.
(17) (60) 2 X 3.1416 X. 02=1226.195+, Ans.
(18) 3.1416X5 cts.=$.15708.
11005.312^ $.15708=6400.
n/6400=80 in., Ans.
(19) $226.195^ [(60) 2 x3.1416]=2 cts., Ans.
(20) (2) 2 X 6 X .50=112, Ans.
(21) >/(4)2x(6)2=24; 24+36+16=76.
TV\X4x20=42f cu. ft, Ans.
(22) (3) 2 X. 7854=7.0686.
(2) 2 X. 7854=3. 1416.
\/7.0686 X 3.1416=4.7124.
(4.7124+3.1416+7.0686) X^ of 40^198,968+, An^
144 MEASUREMENTS.
(23) (16) 2 X. 7854=201.064-.
(12) 2 X. 7854=113.09+.
\/201.06X 113.09=150.78.
(201.06-1-113.094-150.78) Xi of 15=2324.65+ cu. ft.. ANa
24) (8) 2=64 ; (20) 2=400 ; \/64 X 400=160 mean base.
64+400+160=624; fffX J of 20=28f cu. ft, Ans.
(25) \oi (20+30)=25; 25-^12=2xV ft
10x2iVX4=83^ sq. ft, Ans.
(26) 20^12=lf ft; (1§)2x20x|2.25=$125,Ans.
(27) (764) 2 xi of 480=98391360 cu. ft, Ans.
(28) 8h-2=4; 4x5x5=100; 5x5=25.
100+25=125 sq. ft, Ans.
(29) \ of 8X80=320; 320x8=2560 sq. ft
$140.80-^2560=5^ cts., Ans.
60X40
(30) X.05=$60, Ans.
2
(31) (30) 2 X. 7854x20X1728-^231=1057531 gal., Ans.
(32) (2)2X.7854X50X.20=$31.41+, Ans.
(33) (2^) 2 X. 7854=4.90875.
$3.927 H- (4.90875X1 X.10)=8 ft, Ans.
(34) $27^(60X.20)=2.25.
v/2!25=1.5 ft.=18 in. square.
\ of 18=2 ; 18—2=16 plank.
16X60X1^ ft wide=1440 sq. ft, Ans.
(35) 6X2^X4=60.
(2J)2=6^; $3.31i-f-(60+6J)=5 cts., Ans.
(36) 3 X 12=36 ; V (36) 2 -- 2=25.45+ in., Ans.
(37) (14)2=196; (\/l96— 2)2=98; 98x$2=196, Ans.
(38) 6280^3.1416=1680.67+ ft, Ans,
MEASUREMENTS. 145
(39) 5280^3.1416=1680.674- ft.
(1680.67) 2 X .7854=50 A. 148 P. 188.39+ sq. ft., Ans.
(40) (100) 2 X .7854X .10=$785.40, Ans.
(41) 78544-.7854=10000; v/iOOOO=100.
100 H- 2=50 ft., Ans.
(42) n/(800) 2 — (620) 2=505.57+ ft, Ans.
(43) \/(40) 2— (10)2=38.72+ ft, Ans.
(44) 52x.7854x2=39.27sq. ft.
6X3.1416X30=471.24.
(471.24+39.27—10) X$.02=$10.01+, AnS.
(45) 20X63X231=291060 cu. in.
291060H-[(70)2X.7854]=75.63+ in.
75.63-7-12=6 ft 3.63+ in., Ans.
(46) Capacities are as 12 : (IJ)^
12
= =1; 16X^=6^
6§x8=53^, Ans.
(47) (15) 2 X 3.141 6=706.86, Ans.
(48) >/l96Tj854=15.79+ in., Ans.
(49) (11) 2 X 3.1416=380.133+ sq. ft., Ans.
(50) 24X32X2=1536; 1536-hl00=15.36.
$76.80-5-15.36=15, Ans.
(51) 9xl3x|Xli=131+fl.; 131-v-100=1.31+.
1.31+X|1=|1.31+, Ans.
(52) \/l520.5344 -^ 3.1416=22 ft., Ans.
(53) 39.27-4-3.1416=12.5.
39.27X12.5=490.875 sq. in., Ans.
(54) ^65.45-f-.5236=5.
(5)2X3.1416=78.54 sq. in., Ans,
146 MISCELLANEOUS.
(55) (U) 3 X. 5236=1 cu. ft. 391.5 cu. in., Ans.
(56) \/(62)'-^— (20)2=48 ft.
(48)2x3.1416=7238.2464 sq. ft.=26.584- P., Ans.
(57) 3.1416X4X2^=31.416— , Ans.
(58) 10+10^+14^=35; 35-j-2=17.5.
17.5—10=7.5; 17.5—10.5=7; 17.5—14.5=3.
\/l7.5X 7.5X7X3=52.5, Ans.
,5^ Ji5flZ=34,ANS. \
(60) 16X8X2=256 \
14X8X2=224 ' '
2)480(240 ; 240-^3=80 yds., AnS. ;
(61) (6) 2 X.7854X 5^X1728=256505.35+. \
256505.354-+(31iX231)=35.25+, Ans. '
MISCELLANEOUS.
(1) (100)2— (30)2=9100; 9100-v-(100x2)=45J, Ans. I
(2) 10=G. C. D.; 40x30=1200 rds. '
1200-i-(10) 2=12, Ans. j
(3) 27 : 343 : : (3) : ^K343=7, Ans. |
(4) Let l=diameter of cheese. 1
(1) 2 X .7854=. 7854 area of whole cheese. \
The square of the sq. rt. of \ of 1=.5, area of largest in- \
scribed square. \
.7854 — .5=. 2854+ area of segments. '
3X 4=12 lbs., four segments ; .2854 : .7854 : : 12 : 38.02+ lbs., j
Ans. i
MISCELLANEOUS. I47
(5) (3)^:(H)' : : 5 : H hr., Ans.
(6) n/(60)2— (30)2=51.96+ alt. of triangle.
f of 51.964-=34.64+ distance from corner of triangle to
the center.
n/(51.964-) 2— (34.64+) '^=38.73+ ft, Ans.
(7) 30X160X2=9600; 9600+ (100)^=19600.
■v/l9600=140 sum of sides; (100)2— (4800x2) =400.
^400=20 diff. of sides; 140—20=120; 120-^2=60 width ;
60+20=80 length, Ans.
(8) 1 : ^ : : (9)2 : 40.5; >/40r5=6.36+ in., Ans.
(9) 36=G. C. D.; 1332^36=37; 37—1=36, Ans.
(10) (5)3=125; (125)2=15625, Ans.
(11) 102=100; \/l00x2=14.14+; 14.14+10=24.14, Ans.
(12) 32—4=28; (28) 2 xf 1=980 ft, Ans.
(13) 18X160=2880; \ of 2880=960; v/960=30.9+ rds., Ans.
(14) \/(36)2-r-3=20.7+in., Ans.
(15) v/(12)2-H3=6.9+; [ (6.9) 3x1728] -^2150.4=266+ bu., Ans.
(16) %/8X 160X2=35.7+ rds., Ans.
(17) V\ of 136X17=34, Ans. .
(18) (16) 2+(4) 2=272; 272-r-(4x2)=34 ft, Ans.
(19) 49^X144=7146; (1^)^X2=1; 7146— |=7141J.
\/7l41iT6+l^=36 in., Ans.
(20) 1 fur.=40 rds.; v/(40) 2— (20)^=34.6+ alt of A.
34.6+ X 20=692+ sq. rds.; 692+ -^160=4.32+ A., ANS.
(21) [ (30)2X.7854]— [(20)2X.7854]=392.7+ sq. ft, Ans.
(22) A=length; A— 12=width.
(A— 12) X A=4 X 160 sq. rds.
\/A2—12A+36=v/ 640+36.
... A— 6=26 ; A=32 ; 32—12=20, Ans.
1 48 MISCELLANEO US:.
{23) 20 raUs per rd. 4 sides=8Q.
(rds.)2
(80)2=No A's .
160
(80)2xl60---1024000, Ans.
(24) (3^)2X3.1416=38.44-, Ans.
(25) 50x. 75=137.50; $37.50— $27.50=$10.
.754-.25=$l ; 110-^11=10 da., Ans.
(26) 3+5+7=15; 120-1-15=8.
8X3=24;
8X5=40;
8X7=56, Ans.
(27^ (30) 2 X. 7854=706.86+; f of 706.86+=471.24+.
^47 1 .24 -r- .7854=24.49+ ; 30—24.49=5.51+.
J of 5.51=2.75+ 1st.
J of 471.24=235.62; v/235.62-^. 7854=17.31+.
J of C24.49— 17.31)=3.59+ 2d.
\ of 17.31=8.65+ 3d, Ans.
(28) 2=G. C. D. of 2, 4 and 6 ; 20-^2=10 hrs., Ans.
(29) J-J=tV; tV=$20; H=$240, Ans.
(30) 10X2=20; 20+10=30 in. ; 30+10=40 in. tail and head.
40X2=80 in., Ans.
(31) rV—3V=?V; 11-^45=45 days, Ans.
(32) (4000+3)2 : (4000)2 : : 20 : 19.97+, Ans.
(33) v/484-^16=5j^ sec, Ans.
(34) J of 12=6; (6)2x16=576 ft., Ans.
(35) (2)2x16=64 ft., Ans.
(36) (20)2 : (30)2 : : 50 : 112^ bu., Ans.
<33l 500X160^.7854=319.1+ diameter.
Let l=:radius of small circle.
\/(2) 2 -(1)2=1.732+; I of 1.732+=1.1546+.
1.1546+1=2.1546; 319.1+ -5-2.1546=148.1+ rds., Ans.
MISCELLANEOUS. 149 \
(38) \^125=5; ^216=6; (5)2 : (6)2 : : $10 : $14.40, Ans.
(39) 87.96 : 365.25 : : 45 yrs. : 186.8 yrs. Mercury ;
30636.82 : 365.25 : : 45 yrs. : .53-f or a little over \ yr. old,
Jupiter. Ans.
(40) A hits xV and B f of the time ; TV4-|=Tf •
32H-f|=:24, Ans.
(41) 1^X160=300; 300X2=600; 600-^20=30.
\/i30)2+(20)2=36+ rds., Ans.
(42) (|)^-(J)^=t¥i; (I)^=t¥t; ih ' A : : so : 62^*^ min., Ans.
(43) Ivet l=radius ; n/(2) 2— (1)2=1.7324- alt. of triangle..
] .732X1=1.732 area of triangle.
(2) 2 X. 7854=3. 14 16 area of circle.
J of 3.1416=1.5708+ area of sectors.
1.732— 1.5708=.161-f- inclosed space.
.161 : 160 rds. : : (1)^ : 993.788+.
>/993.788+=31.5+ radius; 31.5X2=63+ rds., Ans.
(44) \/(12) 2x4=24, Ans.
(45) 5X4=20; 20-^2=10 sq. ft, Ans.
(46) $2500X(100— 5)=$2375.
$2500 X 6 % X 2=$300 ; $2500+$300=$2800.
$2800— $2375=1425 int. for 2 yrs. ; $425h- 2=$212.50 for 1 yr.
$212.50-^$2375=8if %, Ans.
(47) 16^^(2x7x2x9)=xV8; tVtX4=xV8; tV8X5=xVf;
*XrV8=/oV6; 43560^7^^=508032, Ans.
S2_p2 (108)2— (36)2
(48) =base or =48 base;
2S 2X108
108—48=60 ft. hypotenuse, Ans.
(49) If4-A=!§; ioooo-i-ft=640o.
v/10000— \/6400=20 ; 20-5-2=10 yds., Ans.
(50) \/(10)2+(10) 2=14.14+ ft., Ans.
I50 MISCELLANEOUS.
(51) (4)3=64 cu. in.; 64+61=125; ^125=5; 5—4=1;
l-j-2=^ in., Ans.
(52) 5280 ft. ^840^=6.2832 ft. cir. of wheel.
6.2832^3.1416=2 ft, Ans.
(53) 5 : (195+5) : : 5 : 200 radius hid.
(200X2) 2 X. 7854=502656 sq. ft, Ans.
(54) (12+2) X 3.1416=43.98+, Ans.
(55) 3957.5 miles radius of the earth at that point ;
3.65+ miles height of Mt vSt Blias ;
v/3957.5X3.65x2=169.9+ miles, Ans.
(56) \ A=80 sq. rds.
80-5-5xl=l«; \/l6=4 width; 4x5=20 length, Ans.
(57) (168^12)-(98--7J)=if ; HX7J=$7.
$7-T-5=$1.40, Ans.
^^^^ ^^Igolioll^ 1=24; H=36oz., Ans.
(59) 24 min.=6°; 16° 18^— 6°=10° 18^ W., Ans.
(60) 880-^4=220; 432^4=108.
220—108=112 ; (12) 2=144.
\/l44+112=16 ; 16—12=4 in., Ans.
(61) \/(40) 2+ (8)2=40.7+ length of the ladder.
\/(40.7+) 2— (40— 10) 2=27.64+ ft., Ans.
(62) \/(20) 2x2=28+ ft; 28+^2=14+.
V (20) 2 + (14+) 2=24.49+ ft, Ans.
(63) 40X^=60 in.=5 ft; 5-f4=|; (|)2=ff.
43560 -^ff =278781 A, Ans.
(64) (16-^2)2=64; 64X16=1024 ft, Ans.
(65) 16X16=256; i| of 256=60; \/256— 60=14
16—14=2; 2-^2=1 rd., Ans.
(66) 5760 : 7000 : : 160 : 194+, Ans.
MISCELLANEOUS. 151
(67) \/lOx 160=40 ; 40X16J=660 ft.
660 X ^ X 5 X 4=6600 sq. ft.
(6600 -r- 1000) X $8=152.80, Ans.
(68) 96-h8=12; (12-4-2) X 12x8=576 sq. ft, Ans.
(69) 6, 8 and 10 are in proportion as 1, 1^ and If.
12xli=16; 12xli=20; 12, 16 and 20=sides.
(12+16-f20)-;-2=24.
>/24x 12X8X4=96 rds.
(96^160) X$850=$510, Ans.
(70) yij-f-i^(r=i hr. to go 1 mi. and return.
4-Hj=24 miles, Ans.
(71) (6) 2-4-(4) 2=2J times, Ans.
(72) 4-j-2=6; 6-T-3=2 each. A furnishes the pies for C and
gets the 10 cts., Ans.
(73) (1) ^ X .7854 X I of 2=.5236 solidity of cone.
^.5236-7-.5236=l ft., Ans.
(74) 9Jx3Jx1tVX1728=62244cu. in.
62244-7-2150.42=24+ bu., Ans.
(75) $72.50— 150=$22.50.
8J% of 150 for 1 yr.=$4.25.
22.50
=5 yrs. 3 mo. 16 da., Ans.
4.25
(76) il+A=H; -H of 12=17; 17-12=5.
5— l^=3J p. M., Ans.
(77) (5)2 : (10)2 ::500: 2000.
2000 X (20-j-10)=4000, AnS.
(78) (6)2=36; (18)2=324; \/36x 324=108.
(36-1-1084-324) xi of 20=3120 cu. f .
3120-^12=260 ft., Ans.
152 MISCELLANEOUS.
(79) (5) 2 X. 7854=19.635.
(10) 2 X. 7854=78.54.
n/19.635X 78.54=39.27.
(19.635+39.27+78.54) X(i of 20X12)H-144=7.7+ ft, Ans.
(So) (5)3 : (6)3 : : 120 : 207+ lbs., Ans.
(Si) 9-8^=^; 9-^|=18, Ans.
(82) \/5400-j-6=30 side of cube.
(30) 3=27000 cu. in., Ans.
(83) 15-^12=1^; 15—10=5; 5-^-1^=4, Ans.
(84) (8VX40)+(^VXl2)=n; f^-n=lf.
16-51^=8 da.; 40— 8=32dday, Ans.
(85) 60h-12=5; 30x5=150 in.; 150^3.1416=47.7+.
47.7-7-2=23.8+ in., Ans.
(86) 80X|3=$240; $240— $150=|90.
$90-^(3+l)=22J da. ; 80— 22^=57J da., Ans.
(87) (5)2 : (12^)2 : : 100 : 625, Ans.
(88) (10) 2 X J of 20=666f ; 666f -^2=333J.
^(20)3 : 666f \\ {x^ \ 333^=15.8+.
20— 15.8+=4.2— , Ans.
(89) (20)3 . (10)3 :: 10:1 J, Ans.
(90) 60-5-15=4; 2X4=8; ^-^=8; if =96 in.
96^-3.1416=30+ ; 30+^-2=15+ in., Ans.
(91) 6^2=3; 3—^=2^; 6— 2J=3J.
Z\
3J+2J=6; —of 200=1161.
6
2J
— of 200=83^ Ans-.
6
MISCELLANEOUS.
153
(92) 3ft.=36in.; (36) 2 x. 7854=1016.8784 sq. in.
A I, B 2V and C i ; f of 1016.8784=406.75 sq. in. A's ;
■/o of 1016.8784=355.907 sq. in. B's ;
\ of 1016.8784=254.219 sq. in. C's, Ans.
J8^°To find what part of diameter each grinds off, see
rule to find diameter of circle.
(93) 50 X. 25=112.50 ; $12.50-7-.40=31^ gal.
50— 3U=18f gal., Ans.
(94) iXj=TV; 1728-^{TVXl2)=2304ft.,ANS.
(95) 200X160=32000 rds.
40-1-2=20; (20)2=400; \/32000-f-400=180.
180—20=160 rds. shorter sides ;
160+40=200 rds. longer side, Ans.
(96) 20X160=3200; n/3200=56.5-!-.
56.5X4X$3=$678, Ans.
(97) N/(32)2-f (12) 2=34.1+ ft. slant height
24X3.1416=75.3984 cir.
'75.3984X34.1
-i-9=142.8+sq. yds., AnS.
\ 2
(98) 7JX 160=1200; (50)2=2500; 1200X2=2400.
\/2500+2400=70 sum of sides.
\/(50) 2— 2400=10 diff. of sides.
(70— 10)-T-2=30 shorter side ; 30+10=40 longer, Ans.
(99) (10)3 X. 5236=523.6 cu. in. solidity.
523.6-1-3=174.3+ ; 523.6—174.53=349.07.
\K349.07-;-. 5236=8.7; 10—8.7=1.3+ 1st.
349.07—174.53+ =174.54.
^174.54-7-.5236=5.5+ in. 3d.
8.7—5.5=3.2+ in. 2d, Ans.
154 MISCELLANEOUS.
(loo) 40 for $40=$1.00 each.
28 " $35= 1.25 "
12 .25
40—35=5=1^2 of extra scholar.
y\ of .25=.10xV.
$1.00H-.10x52=$1.10xV
35X$1.10y\=$38.64372, Ans.
(loi) (13) 2 X .7854=132.735+.
(8 J) 2 X. 7854=56.74+.
\/l32.735 X 56.74=86.78+.
132.73+56.74+86.78+=276.25+.
276.25+ X (J of 8|)-^231=3 gal. 1 qt. 1— pt., Ans.
(102) $60X2=1120; $120+$60=$180.
1+4=1 ; f =$180 ; 1=180 2d horse.
$120— $80=$40 cow, Ans.
(103) 10X3=30; 30—10=20; 2X2=4; 4—2=2.
20+2=22 yrs. son's age.
^=22 ; 1=44 ; 44+2=46 father's age, Ans.
(104) $540— $300=$240 ; $300— $240=|60.
1-1+40=60; i=20; |=80 days 2d.
f of 80=60 ; 60+40=100 days 1st, Ans.
(T05) By the reading of the problem we can see that the head
and tail together weigh 4 lbs.
4X2=8 lbs. body; 8+4=12 lbs., Ans.
(106) ^=16 times+6 ; 1=48 times+18.
(134+80)— 18=196 ; 196-4- (48+1) =4 ft.
134—4=130 ft., Ans.
(107) 5X2=10; (10) 2 X. 7854=78.54
78.54X {\ of 6) X 1728-7-4=67858.56 cu. in.
67858.56-5-2150.4=31.55+ bu.
31.55+X$1=431.55+, Ans.
MISCELLANEOUS. 155
(108) Am't of $1 at 6% for 6 yrs.=$1.36
" " " 10% •' 3 " =11.30
.06
$300h-.03=$5000, Ans.
(109) 1859 5 12 Int. on $1 for 1 yr. 8 mo. 24 da. is .10? ;
1857 8 18 $26-^.1 Of =$250, Ans.
1 8 21
(no) 507-^3=169; \/Wt
1=13, Ans.
0 / //
(III) 31 27 30
2 30
hr. min.
14 2
2 6
15)31 30
11 56 Ans.
2 hr.6 min.
(112) $1+.20=$1.20; 120 cts.X 4=480, Ans.
(113) 6% of $660 for 1 yr.=$39.60.
$213.40-r-$39.60=5xV yr.=5 yr. 4 mo. 20 da., AnS.
(114) The minute-hand moves 60 min. while the b'^ur-hand
moves 5 minutes and gains 55 minutes.
60-T-55=ljV min. to gain 1 min.
25—14=11 min. to be gained.
l^ij-X 11=12 min. past 5, Ans.
(115) (8)3=512; v/512X.22|=10f, Ans.
(116) Int. on $1 for 23 da.=. 003625.
$7.25-T-.003625=$2000, Ans.
(117) Wife receives 3 times as much as daughter, son 3 times
as much as wife.
fX 3=1 son; f =wife ; i=daughter.
9-1-14- J==-\3; 1^3=16591; 1=1507 daughter.
f=$1521 wife ; |=$4563 son, Ans.
T56 MISCELLANEOUS.
(ii8) 48—27=21; 484-21=69; 90—69=21.
90+(2lX3)=153 ; 174—153=21, Ans.
(119)* 9+15=24; M-2'i==iV
■i^ of $24=16 ; if of $24=$15 ; 64-15=$21 B.
$24— $21=«:$3 A, Ans.
(I20) $.11— $.10^=^ct.; 30+15=45; 45-r-J=90 lbs., AnS.
(i2i) 5 pears + 6 peaclies=:28 cts.
6 " +3 " =21 "
And 12 pears + 6 peaches=42 cts.
5 « +6 " =28 "
7 pears=
14 cts.
1 " =
2 «
1 peach=
3 « Ans.
(122) 10 at 50^=$5.00.
$5-=-4=$1.25 each pays.
$1.25X (10— 2+4)=$15, Ans.
(123) 40 : ;^ : : 40 : 10=40, Ans.
40:10
(124) 3+4+5=12; 136-4-12=11^.
11^X3=34 yr. A; 11JX4=45J yr. B.
llJX5=56f yr. CANS.
(125) |=$4500; |=$7500.
$7500—14500=13000, Ans.
(126) t\=1188; ^1=4556; n/4556=66, Ans.
(127) 20 pupils for $20=$1.00 each
12 " " $15=$1.25 "
8 .25
20—17=3.
I of .25=.09|.
($1.00+.09f)Xl7=$18.59f, Ans.
(128) v/9x4=6, Ans.
MISCELLANEOUS. 157
(129) 250 X. 02=5; 9-J-5=lfyrs.
A's is to B's as 1 to 3 or I and f.
\oi\=\\ t of 3=2.
2% of i for If yrs.=.018 ;
2% of 2 for If yrs.=.072 ;
.018-f .072=.09 sum of interests.
.09X25X10=22.50.
($180-5-22.50) X 100=$800.
I of $800=1200 A's ;
I of $800=$600 B's, Ans.
(130) >/(15) 2 --(7^)2=12.94-; i of 12.9-h=4.3-}-.
4.3-fX 2=8.6+, Ans.
(131) \/(3)2 4-(4)2=5 in., Ans.
(132) v/ (60) 2x^7854=53.1+ rds., Ans.
(J33) \ A=21780 sq. ft. ; 21780-^3=7260 ft, Ans.
(134) 173.2X2=346.4.
\/340=18.61+, Ans.
(135) 2+3=5; 125-i-5=25; \/25=5.
5X2=10.
5X3=15, Ans.
(136) 3+4=7 ; f of Z\—\\ ft. from strong man, Ans.
(137) 12X5^=.60; .60— .20=40^.
(40xl00)-r-20=200%, Ans. .
(138) 100-^1^ of .005=2000000, Ans.
(139) 1+1=1; $3-H=$lf B; $3-$lf=$lf A. Ans.
(140) (18) 2+(6) 2=360; 360-r-2=180.
v/l80=13.4; 13.4—6=7.4.
18X12=216; 18—6=12; 216-^-12=18.
\/l8x 7.4=11.5+; 18— 11.5+=6.5 ft., AnS.
(141) 12X12=144; (12+2)-r-2=7 ; 144x7=1008.
(144x2)^-2=144; 10—2=5; J of 144X5=240,
(1008+144+240)-r-144=9f ft., An^,
i.,S MISCELLANEOUS.
(142) v/7075t)-T-4=133 width ; 1^3x4=532 length.
(133+532) X 2=1330; l330-r-7=190, Ans.
(143) \/9x 16=12, Ans.
(144) (12xl6)-7-(12+16)=6.84-, Ans.
(145) (30)2=900; N/f of 900=24.54- , Ans.
(146) 625-7-62.5=10 cu. ft., Ans.
(147) 8-T-(8— 6)=4, Ans.
(148) $1 at5% for8yrs.=.40; ,
$800-T-.40=$2000, Ans.
(149) 25+20+15=60; 60-7-2=30 half sum.
\/30X5XlOX 15=150 area of triangle.
(150X2) -7-25=12 ft. ; 12+i8=30 ft. height of house, Ans'.
(150) $375-7-175=5 A. ^ . .; .
5X160=800 sq. rds.
\/800X2=40 rds. 1 side.
40X3=120 rds., Ans.
(151) The hour-hand moves a certain distance from 5. The
minute-hand must gain 25 minutes+2 dis. from 5,
While the hour-hand moves 1 dis. the minute-hand
moves 12 dis.
.*. 25 min.+2 dis.=12 dis. or 25 min.=10 dis.
25-7-10=2J min. hour-hand moves.
2Jxl2=:30 min. minute-hand moves, Ans.
(152) 3+2=5; f of 10=6; f of 10=4.
(6-1-2) X (4-r-2)=6 ; '43560 ft.-7-6=7260, Ans.
(153) 3 X 15°=45° east, Ans.
(154) \/(80)2+(100) 2=128+ ; \/(100)2+(100) 2=141+.
128+Hl+«269+ ft., ANS.
MISCELLANEOUS. 159
(155) The money will run 10 and 5 yrs. respectively.
Am't of 11 at 10% for 10 yrs.=$2.00
" " " « 5 " =$1.50
$3.50
$1400-v^3.50=$400 ; $400Xl.50=$600.
$400X2.00=$800, Ans.
(156) 168-4- 2=sum of 2 sides=«S=84.
If X=one side, S — X=other.
X(S -X)=area=10|X 160=1728 sq. rds.
\/X2— 84 X4-(42) 2=v/l764— 1728.
X— 42=i 6. Sides=42+6=48 and 42— 6=36, Ans.
Note.— Many of the solutions of problems in this list
can be explained by such general formulae.
<157) \/(2) 2— (1)2=1.732; 1.732X3=5.196 area of triangle,
(4) 2 X. 7854=12.566 area of wheel.
(12.566—5.196)^-3=2.456 part in the water.
2.456
=.195+, Ans.
12.566
(158) (100)2 : (200)2 : : 4 : 16 da., Ans.
(159) 6—4=2 ; 1=12 ft. ; |=36 radius.
36X2=72 ft. diameter, Ans.
(160) 128-r-3.141 6=40.74+ diameter.
40.74^2.15474-=18+, Ans.
(161) \ of (754-90)=82| rds. ; \ mi.=160 rds.
(160X82^)4-160=82^ A; 82J^X$80=$6600, Ans.
(f62) (10) 2 x.7854x^ of 15=392.7 solidity of cone ;
(5) 2 X .7854 X 30^ X 9=5345.622+ area of land ; )
392.7 H-5345.622+=.0734+ ft., Ans.
(163) (6) 2 X 2.828+ =101.80+ cu. in., AJSrs.
i6o
MISCELLANEOUS.
(164) 1st term .03 ; No. terms 11 ; ratio 8.
(8)iox$.03=$32212254.72 last term.
$32212254.72X8
: =$36814005.39, Ans.
\-\)
14 /{10)2 (14)2 (14)2
=-+J +- =7+1=8.
- ^ - 2 4
(165) Sid
2 ' 2
14—8=6, Ans.
(166) P. W- of $6400 for 8 mos. at 6%=$6186.67-f .
$6400— $6186.67+=$213.33— dis.
$213.33— (5% of $6186.67 for 8 mos.)=$7.11-j-, AnS.
(167) f=f; l=A; T%+i^=H; i§=.625D; ^^=.375 a.
.375-f^Am't of $1 for 6 yrs.=.23xV
.625-
(( « « «
($290-^.7511) X.23x^^=$90
($290 ^ .75|f ) X .52f^=$200, Ans.
(i68) 20=G. C. D. or side of each field.
(320^20) X (180h-20)=144, Ans.
(169) (20) 2 X 16=6400 ft., Ans.
(170)
CD=1
OC=\/P +12=1.414.
OP=1.414+l=2.414.
OP:(CP=CD) ::10ft.:(X).
2.414 : 1 : : 10 ft. : 4.14, Ans.
MISCELLANEOUS. i6i
225
(171) (7i)2=— .
4
225
904^i ft.-T- =16tV ft., Ans.
4
(172) \/(12)2— (35X4)=2, Ans.
(173) (16^2)+(2h-2)=9.
(16-^2)— (2-^2)=7, Ans.
(174) (3)2=9; J^ of 9=2.25; n/1 80+2.25=13.5.
13.5— (i of 8)=12.
12+3=15, Ans. .
(175) [(7)3-133]-4-(3x7)=10.
\/{7)2-10x4=3 ; (J of 3)+(J of 7)=5.
7—5=2, Ans.
(176) 4x(v/2+l)=9.656+; 9.656+X2=19.31+, Ans.
(177) v^i of (41— 9)=4.
\/41— 16=5, Ans.
(178) (19)2—193=168.
\/l93— 168=5 ; J of (19—5)= 7.
19—7=12, Ans.
(179) 65-(7)2=16.
\/65+16=9.
(i of 9)+(i of 7)=8.
9—8=1, Ans.
(180) 20-^12=1 J.
1X3.1416=3.1416.
%/(!§) 2+(3.1416) 2 X 12=42.79+ ft, Ans.
(181) $12X7=$84; $5xl2=$60; 84— 60=$24.
12-t7=5; $24h-5=$4.80, Ans.
i6*. MISCELLANEOUS,
(182) (6)3 : (3)3 : : 25 : 3.12+ lbs., Ans.
(183) (3)2+ (5)2=34; %/30600-^34=30.
30X3= 90.
30X5=150, Ans.
(184) |=$1200; |=$2000; |1200+$500=$1700.
$2000— $1700=1300, Ans.
(185) 4x3=12, difference between the youngest and oldest.
1=12; 1=24.
24 — 4 = 20.
20 — 4 = 16.
16 — 4 = 12, Ans.
(186) A has 3 times as many as B.
J+f=f; 60h-|=45A.
\ of 45=15 B, Ans.
(187) 8=G. C. D.; (8)2=64, Ans.
(188) $5^(Hf— ifif)=$89.90,ANS.
(189) 4500 : 3000 : : 27 : 11
1800 : (1100). Ans, 1100 mi.
(190) (8 -J- .866) X 3.1416=28.99+, Ans.
(191) %/[ (100)2 +2800]-^2=80.
\/(100) 2— 2800=60.
(80 X 60) -H 160=30 A, Ans.
(192) 135-^9=15; 15+9=24.
24-^2=12.
12—9=3, Ans.
(193) (10) 2 X .7854=78.54 area of circle.
>/(10) 2— (5)2=8.66+.
8.66 X 5=43.3 area of triangle.
43.3—1 of 78.54=4.03 sq. ft., Ans.
(194) 60xl.l54x3x.80=$166.17+, Ans.
MISCELLANEOUS. 163
(195) 24X2.41+ =57.84+ side of field.
(57.84)2-^160=20.9+ A, Ans.
(196) J24-4-2)2=144; \/l44— 140=2 diflference of sides.
\/l44=12; 12+2=14.
24—14=10, Ans.
(197) 4-^2=2; \/l40 + (2)2=12.
12+2=14.
14— 4=10, Ans.
(198) [(30)2— (6)2]-^2=432.
>/432 + (3)2=21; 21+3=24; 24—6=18.
18X24=432, Ans.
(199) >/2&=5; 5X4=20.
(20-4-\/25) 2=16, Ans.
(200) \/420— 224=14 C.
224-^14=16 J, Ans.
(201) 1 : ^ : : 10 : 2J ft., Ans.
(202) 6 of the smaller circles will be tangent to the 7th lo-
cated at center, and will touch the outer large circle.
15-^3=5 ft., Ans.
(203) 8:10::l:(l^ft.}, ANS.
(204) n\\h\\ : (18) 2 : v^37:6=15.4.
18—15.4=2.6 ft. 1st piece.
1\ : 3J : : (18) 2 : ^l5i:2=12.3+.
18—12.3=5.7 ft. 2d piece, Ans.
(205) lOX (2— >/3J=2.68+ in., Ans.
(206) 12X|of (6+4)=60.
12x5Xi= 20
80 ft, Ans.
i64 MISCELLANEOUS,
{207) (74-17) X 30=720; 720-7-2=360.
17—7=10; 17x6=102; ^ of 102x17=867.
867—360=507 ; \/507x 2x6=78 rds.
102 rds.— 78 rds.=24 rds., Ans.
(208) 3 : 1 : : 10 : 3J, Ans.
(209) 12-7-1.154=6.9-1- ft.
or (x/242— 122)-^3=6.9-}-ft., Ans.
(210) 1.0-^=$1.01; lOX $1.01=110.10, Ans.
(211) 300-i-6=50 lbs., Ans.
(212) >/\ of (74)2=52.34- ft., Ans.
(213) L. C. M.=2520 ; 25204-5=2525, Ans.
(214) (3)24.(4)2=25; n/ (60) ^--25=12.
12X3=36.
12X4=48, Ans.
(215) 104-r-2=52; 3X160=480.
(52^2)2=676; v/676— 480=14.
26 4-14=40.
480^40=12, Ans.
(216) (2) 2 : (4) 2 : : 300 : 1200 ft., Ans.
(217) (10) 2 X. 7854X^=39.27 cu. ft.. Ans.
(218) (3) 2 X. 7854=7.0686.
(56x3)-^7.0686=23.764- ft., Ans.
(219) \ of (204-15)=17.5; (17.5) ^X. 5236=28064- cu. ft., Ans.
(220) 12-T-3=4 ; 4=side of equilateral triaugle.
6.164" =area of equilateral triangle.
6.16 : 43560 :: 1 : 70714- A, Ans.
(221) 100X80X120=960000.
Area of triangle whose sides are 100, 80 and 120=39684-.
Q60000~-(3968x4)=60.484-, Ans.
y^ri^CELLANEOUS. 165
(222) v/(12) 2— (6)2=10.3; (10.3xl2)-^(10.34-12)=5.oin., Ans.
(223) (6x8)-=-{6+8)=33„Ans.
(224) In the triangle ABC, let AB=12 ; BC=16 ; AC=20.
Bisect the angles. The point of intersection O will be
the center of the circle. From O draw OM perpen-
dicular to AB ; ON to BC ; OP to AC. In the 3 pairs of
equal triangles AP=AM ; PC=CN; BN=BM. Perim-
eter=2 APH-2 PC-f2 BN=48.
(H-2), AP+PC+(BN=OM=R)=24.
AP-|-PC=20.
24— 20=4 R; 4x2=8 diameter, Ans.
(225) v/(20.5) 2— (4.5)2=20; 20x4^X2=180.
20+204-9=49; 180-^9=3.6+.
3.6+ X 2=7.2+ ft., Ans.
(226) 5-5-5|f%=92%, Ans.
(227) V\ of (20)2=14.1+.
(14.1)2x1=80 sq. in., Ans.
(228) (5)2+(7)2=74; 518^74=7.
(5)2x7=175.
(7)2x7=343, Ans.
(229) 3.1416 : 5 : : 10 : Ans.=15.9+ miles, Ans.
mistakes in CcacDing
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A sample copy will be sent, postpaid, to any teacher for
$1.00 (regular price $1.25).
HINDS & NOBLE, Publishefi
3J 33-35 West I5th Stre^*. - New York Qty
For Teachers And Students
Ce$$on$ Outlined
tn
U. S. History^ Geography^ English Grammar
Physiology and Arithmetic
By G* Dallas Lind
Author of "Best Methods of Teaching in Country
Schools "
Cloth, 224 pages, 200 Lessons. Regular price, $1.2^
( To Teachers, $1.00^
A Specimen Outline Lesson in U. S. History-
Outline Lesson LVH 5
McKinley's Administration
''^ The peace we have won is not a selfish truce of artnt^
but one -whose conditions presage good to hutnanity.
Explosion of the " Maine "
Spanish- American War : —
Dewey at Manila
Sampson Bombards San Juan
Sinking of the " Merrimac"
Schley Destroys Cervera's Fleet
Stamp Tax
Battles of El Caney and San Juan HHl
Ponce Surrenders to General Miles
Manila Captured
Annexation of Hawaii
Treaty of Peace Signed at Paris
Peace Conference at the Hague
War with the Philippine Insurgents
See Montgomery's^ McMaster''s^ Lee's or any other recent
History 0/ the United States.
Have your pupils write a brief account of the
Spanish-American War.
HINDS & NOBLE, ^ ^ jfL New York Qty
Teacbers, Piipns, Candidates*
ATTENTION !
The most experienced teachers hare, after caitfol
preparatior , published three wonderful books.
In the first one they have put all of the Common
branches, over a dozen in all, and then have written each
branch in questions and then answered each question in
full, making over Seven Thousand Questions with the
Seven Thousand Answers, completely exhausting Gram-
mar, Geography, Arithmetic, History, Physiology, Spelling,
Reading, etc., so that any one, right at home, can become
greatly proficient in all these branches without the aid
of a teacher. This first book is worth fifty dollars o{
anyone's money in preparing a teacher or student or
civil-service candidate, for examination, and the book
sells for only $1.50.
The second book takes up twelve Normal branches
in the same way, thus being very desirable for students
who are fitting themselves to teach, also for teachers
who are studying for examinations for higher grade certifi-
cate.
And the third book takes up the High School
branches and exhausts them in a like manner, so any one
wishing to prepare for college can use this one.
For special description of each of these three books
separately see the following pages of this leaflet.
If you return this leaflet
with your remittance you may deduct jo cents if you
order one of the books; deduct yj cents if you order any
two of them; deduct $1.25 if you order all three of tl>e
^ooks.
Wby Did He Do It?
The froblishei* of a well-known "lescchers* monthly h«vio|
too,ooo circulation, knowing by experience thai
no premium for subscribers is so attractive to teachers
as a good question book, selected for that purpose
craig's common school question book. He has dis-
posed of over twenty thousand copies of it up to now.
The manager of said iubnthly is a level-headed publisher and
a clever business man; and he knows just how to supply
the high quality of merit demanded by teachers in whs^
they read and study, else he could not have built up tho
wonderful success which his monthly admittedly is, with
its unprecedented list of over 100,000 subscribers! He
tells why he selected Craig's Question Book, in a full page
announcement in his paper, addressed to the teachers of
the United States. The following zvords are wholly
kiSt and his alone; not an inkling of them had
reached us previous to his printed announcement:
stands the Test
TberO'are Question Books and Question Books, good*
bad and indififerent, all of more or less value, but there is
only one that can really be classed as standard and this
one is so pre-eminently superior to all others that it Is
Instinctively classed asttie leader. Craig's Question
Book has this distinction and justly, so. There is no more
critical class of buyers in the world than the American
school teachers and when any single book devoted to their
Interest is purchased by 192,000 of them (this is the record
of Craig's up to Dec. 31, 1902) it must have an abundance
of real merit back of it. Such has been the record of
the past and its future promises to be even more success*
ful than its past has been.
Thoroughly Revised,
Enlarged and in every way improved — made Over in fact
The publishers of this great book, ever on the alert to
keep in the front rank, realized that ' y the expenditure
of a few thousand dollars it could be m .de even more use-
ful in the great field it occupies. They set about the task,
and have so thoroughly performed the work and improved-
the book to such a degree that even its old friends woul^
**k recognize it but for the name.
How it was done.
The entire book was re- written, reset in new type, an elegant
mew cover design substituted for the old ; and printed on fine
paper substantially bound in doth, it presents an appearance as
attractive as the contents are reliable. In the old edition the
Questions are tn one chapter by themselves, followed in the next
by the Answers, numbered to correspond. Now the Questions
and Answers are printed alternately, the former in Italic and
the latter in Roman type, thus adding to the value of the book
in exactly the same proportion as it is rendered more handy.
No expense has been spared, nothing left undone, to bring this
work fully up to date in every sense, and the new Craig will
meet with even greater favor than the old.
Our Motive
In selecting this book from the dozen or more similar ones was,
perhaps, a selfish one, because it is so immensely popular (and
justly so) among the teachers of this country that it sells more
readily than any other. There are others which would yield us
a greater profit, but we have declined to handle them simply
because they lack the real merit which distinguishes this
work. We could not afford to sacrifice our reputation of always
giving at tlie smallest cost, the best procurable.
As a Real Help
In preparing for examinations, reviews, etc. , a good Question
Book can not be over-valued, and the teacher who possesses
this book can feel sure that she has the best, and always at
hand ready made material for conducting those reviews so neces-
sary to success. To the average teacher any one of half a
dozen departments in this book is well worth the price.
Contents of Book.
An aggregate of nearly 8,000 Questions and Answers, cover-
ing the following subjects, all carefully rewritten and brought
up to date : U. S. History, Geography, Reading, Gram-
mar, Letter Writing, Orthoepy. Orthography, Pho-
nology, Written Arithmetic, Theory and Practice
Teaching, Book-Keeping, Drawing, Alcohol and To-
bacco, Physiology, Participles, Infinitives, Writing,
Test Problems, Civil Gov't, Parliamentary Rules.
HINDS & NOBLE, Publishers of
Craig's Common School Question Book, With Answers, $1.50
Henry's New High School Question Book, With Answers, $i.s»
SherriU's New Normal Questions, with answers, $1.50
Quizzism, and its Key, |i.oo
Some ne<p SpeaRm
The Best American Orations of To-day (Blackstone) $1.25
Selected Readings from the Most Popular Novels • I.OO
Pieces That lijve Taken Prizes in Speaking Contests 1.25
New Pieces That Will Take Prizes in Speaking Contests 1.25
Pieces for E'Ufry Occasion (Le Row) - - - 1.25
How to Attract and Hold an Audience (Esenwein) I.OO
How to Use the Voice in Reading and Speaking (Ott) 1.25
Uow to Gesture, New Illustrated Ediiion (Ott) - I.OO
A Ten Weeks' Course in Elocution (Coombs) • 1.25
Fenno's New Science and Art of Elocution - - 1.25
Three-Minute Declamations for College Men - 1.00
Three-Minute Readings for College Girls • - 1.00*
Handy Pieces to Speak (o«c<7r<fi) - • • • .50
Acme Declamation Book - - . » . .50
Ross' Southern Speaker - - - • • I.OO
New Dialogues and Plays {Primary, Inter., Adv.) 1.50
Commencement Parts (Orations^ Essays, etc.) - L50
Pros and Cons {Questions of To-day Fully DiscusseJ\ 1.50
253 New Questions for Debate - - - . .15
How to Organize and Conduct a Meeting » - ,75
Palmer's New Parliamentary Manual - « - .75
Howe's Hand Book of Parliamentary Usage - - J(l
HINDS, NOBLE & ELDREDGE
3t-33-35 West J 5th Street. New York Cf|C^
• ^ ..',
UNIVERSITY OF CALIFORNIA LIBRARY
BERKELEY
Return to desk from which borrowed.
This book is DUE on the laM^aMKHflMled below.
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21-100m-ll,'49(B7146sl6)476
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