UC-NRLF
Examination Manuals
No. I.
Irving Stringham
||
WENTWOKTH & HILL'S
EXAMINATION MANUALS,
No. I.
ARITHMETIC.
BOSTON:
GINN, HEATH, & COMPANY.
1884.
Entered, according to Act of Congress, in the year 1883,
BY GEORGE A. WENTWORTH AND GEORGE A. HILL,
In the Office of the Librarian of Congress at Washington.
J. 8. CUSHING & Co., PRINTERS, BOSTON.
PREFACE.
THIS Manual consists of two parts : The first part contains
one hundred and fifty examination papers, the questions
for which have been selected mainly from the English, French,
and German collections of problems. These papers may be divided
into three groups. The first fifty papers are confined to the
Simple Rules, Fractions, and Weights and Measures ; the next
fifty papers cover all the subjects treated in ordinary text-books
except the Metric System ; the last fifty also include the Metric
System.
In each group the earlier papers will be found somewhat
easier than the later ones. The papers are intended to be hour
papers, but if any of them are thought to be too long for one
hour, the time may be increased, or the length of the paper
reduced by omitting one or more questions.
The second part - of the Manual is a collection of recent
examination papers actually set in various American and English
institutions of learning.
The Manual may be used in two ways.
First: To test the learner's knowledge in the usual way by
means of an examination. For this purpose the class will come
to the recitation-room provided with the Manual and blank books,
and the teacher will simply designate by number the paper to
be worked.
Secondly : To review^ the subject-matter of Arithmetic. This
may be done by assigning problems to be worked in the class-room,
800568
IV PREFACE.
or by assigning to each pupil a paper with directions to hand in
the solutions, neatly worked out, at a subsequent recitation.
The Manual will be found especially useful in preparing for
written examinations.
Answers to the problems in the first one hundred and fifty
papers, bound separately in paper covers, can be had by teachers
only, on application to the publishers.
G. A. WENTWOETH.
G. A. HILL.
SPECIMEN PAPER WORKED OUT,
1. In 674,381 inches how many miles, furlongs, rods, etc. ?
12)674381 in.
3) 56 198 ft. 5 in.
18732yds. 2ft.
2
11)37464 half-yds.
40) 3405 rds. 4^ yds.
8)85 fur. 5 rds.
10 mi. 5 fur.
10 mi. 5 fur. 5 rds. 4| yds. 2 ft. 5 in.
-4ns. 10 mi. 5 fur. 5 rds. 5yds. Oft. 11 in.
2, Find the G.C.M. of 269,178 and 352,002.
6)269178 352002
44863 ) 58667(1
44863
4)13804
3451)44863(13
3451
10353
10353
Ans. 6x3451 = 20,706.
The common factor 6 is first taken out from both numbers. Fit>m
the remainder 13,804, the factor 4, which is prime to 44,863, is ejected.
The resulting number 3451 is contained 13 times in 44,863, and there-
fore the greatest common measure is 6 x 3451 = 20,706.
EXAMINATION MANUAL.
3 Simplify
mPilty
--
3 11 W 396
12
1 _2_ 7 _ _7_ = 264 + 144 + 231 - 14
3 11 24 396 792
iofA = _2_; 1-ofl^JL. Irfl.i.
3 11 33 11 ££ 132 24 3 72
12
l_J±__l__jL = 792 - 48 - 42 - 77 = 625 .
33 132 72 792 792'
625 . 625 - A l
792 •"792""1'
4, Divide 0.025 by 500, and 0.03625 by 0.29.
0.125
500)0.02500 29)3.625
0.00005 29_
72
58_
145 0.00005 \ A
145 0.125 j '
5, Make out the following bill :
3J pounds of tea at 64 cents per pound ;
1£ pounds of coffee at 40 cents per pound ;
62- pounds of loaf sugar at 10 cents per pound ;
H pounds of butter at 34 cents per pound.
How much change out of $5 should Mr. Smith receive?
Mr. JOHN SMITH,
Dr. to JAMES HORN.
1883.
Aug. 17. Silbs. of tea @ 64 cts. . . . $2.08
li- Ibs. of coffee @ 40 cts. ... .60
6| Ibs. of sugar @ 10 cts ..... 65 •
1| Ibs. of butter @ 34 cts. . . . _ .51
$3.84
Received payment,
Ans. $5.00 -$3.84 = $1.16. JAMES HOEN.
ARITHMETIC. vii
6. If 18 men can dig a trench 200 yards long, 3 yards wide,
and 2 yards deep, in 6 days of 10 hours each, in how
many days of 8 hours each will 10 men dig a trench
100 yards long, 4 yards wide, and 3 yards deep ?
Men,
10: 18:
: 6 days.
Length,
200 : 100
Width,
3: 4
Depth,
2: 3
Hours,
8: 10
9
2
3
JLfi X W
iX^X^Xj
0 X ft _ 27 _
13J.
ra v- 5
ina y 2 y '> \
s C 0
2 2 .Ans. 13J days.
7, What alteration will be made in an income by selling
$10,000 of 4 per cent stock at 89J, and buying 5 per
cent stock at 105 ?
Income from 4 per cent stock = 0.04 of $ 10,000 = $400.
Proceeds of 4 per cent stock = 0.89J of $ 10,000 = $ 8925.
$1 of 5 per cent stock costs $1.05 ; therefore,
Amount of 5 per cent stock = $ 8925 H- 1 .05 = $ 8500.
Income from 5 per cent stock = 0.05 of $8500 = $425.
• Increase in income =$425 — $400 =$25.
8, A room measures 16 feet by 21 feet, and is 11 feet high.
There is one door 7 feet by 3 feet, and two windows
8 feet by 4 feet. Find the cost of papering it with
paper 2 feet wide at 5 cents a yard.
Distance round the room =16 + 16 + 21 + 21 =74 ft.
Area of walls of room = 11 x 74 = 814 sq. ft.
Area of door and windows = 21 sq.ft. +64 sq.ft. = 85 sq.ft.
Area to be papered = 814 sq. ft. - 85 sq. ft. = 729 sq. ft.
Area of one yard of paper =3x2 = 6 sq. ft.
Number of yards required = 729 -=-6 = 121 \.
Cost of the paper = 121-J x $0.05 = $6.07£.
Am. $6.07LV.
Vlll
EXAMINATION MANUAL.
9, A jar full of water weighs 1.325kg ; filled with mercury
it weighs 12.540kg. What is the capacity of the jar,
and its weight ? The specific gravity of the mercury
is 13.59.
12.540
1.325
11.215k8
13.59
1
12.59*8
0.890781.
12.59)11.215
10072
11430
11331
9900
8815
10870
Mercury in jar weighs 11.215k« more than water in jar.
A liter of mercury weighs 12.59ks more than a liter of water.
Capacity of jar
11.215
of a liter - 0.890781.
12.59
Weight of water in jar = 0.89078k«.
Weight of jar = 1.325ks - 0.89078ks = 0.43422ks = 434.22s.
Ans. 0.890781 ; 434.22*.
10, Extract the cube root of 5 to five places of decimals.
5.000(1.70997
3 x 102 =
3(10x7) =
/ ==
300
210
559
259
3 x 17002 = 8670000
3(1700x9)= 45900
92 = 81
8715981
45981
3 X 17092 - 8762043
4000
3913
87 000 000
78 443 829
8 556 171 0
7 885 838 7
670 332 30
613 343 01
1. 709.97 ~Ans.
For explanation of the method, see Wentworth and Hill's Prac-
tical Arithmetic, page 282.
EXAMINATION MANUAL.
ARITHMETIC.
1.
1, Write in words 15,006,021, and state how many times a
number is increased by annexing three ciphers to it.
2, Multiply 2,035,674 by 3096.
3, Divide 275,487 by 736, and prove that the result is cor-
rect.
4, How many times is 195 yards 1 foot 8 inches contained
in a mile?
5, Find the number of cubic inches in 1 cubic yard 24
cubic feet 760 cubic inches.
6, How many grains of gold in a cup weighing 8 ounces
4 pennyweights ?
2.
1, How much must be added to sixty million four hun-
dred six • thousand two hundred ninety to make
three hundred twenty million?
2, Multiply 456,978 by 789.
3, Divide three hundred thirty-seven million one hundred
three thousand twenty-five by eight hundred sixty-
one.
4, In 674,381 inches how many miles, rods, feet, and inches?
5, Find the difference between 30 years 8 months 3 weeks
6 days and 44 years 3 months 1 week 5 days.
EXAMINATION MANUAL.
3.
1, Write in words the sum of 4,300,702 ; 6,070,506 ; and
341,318.
2, Find the number which, subtracted from 80,000, leaves
57,735.
3, From the sum of eight million seventy-nine thousand
six hundred ninety, and three hundred eighty-five
thousand seven hundred nine, subtract their differ-
ence.
4, Divide 19,094,867 by 4009.
5, The circuit of a race-course is 137^ yards. How many
times must a bicyclist go round to complete 5
miles ?
6, Take 156 miles 160 rods 216 yards from 191 miles 80
rods 2 yards.
4.
1, Write in figures two million twenty thousand eighty-
seven.
2, Express in words and in figures the excess of the value
of one 5 over the other in the number 658,457.
3, Multiply seventeen thousand nine hundred forty-three
by five thousand seventy-nine.
4, Divide five hundred one million five hundred by three
thousand eight hundred fifty.
5, Reduce 125 square rods 23 square yards 6 square feet
108 square inches to square yards.
6, How many grains in a pound Avoirdupois ? in a pound
Troy?
ARITHMETIC.
5.
1, Write .in figures ten million eighty-three thousand six
hundred eighty.
2, Divide the product of 37,800 and 7950 by 630.
3, What number multiplied by 6702 will give 218,773,386?
4, How often is £1 17s. 6cZ. contained in £28 2s. 6cZ.?
5, An engine draws a train of 23 cars, each containing 5
long tons, 2123 pounds of coal. What is the weight
of coal in the train ?
6, A square drill-yard required 869 square slabs, each
measuring 3 square feet 86 square inches. What is
the area of the yard in square feet, etc. ?
7, Eequired the weight of a guinea, if 45 can be coined
from a pound of gold.
6.
1, A person walked 136 miles in 40 hours 48 minutes.
How many minutes was he in walking a mile ?
2, How many times must we take the number 7 to make
819?
3, By how much does the thirty-seventh part of three
thousand six hundred sixty- three fall short of a
hundred ?
4, Reduce 7,896,432 grains Troy to pounds.
5, If 56 acres of land cost $700, what will be the value of
13 acres 80 square rods?
6, A man agreed to buy a haystack, paying $ 30 for each
load. He found his wagon held 1 ton 392 pounds,
and that the whole stack weighed 10 tons 1288
pounds. How much has he to pay ?
EXAMINATION MANUAL.
7.
1, Find the circumference of a carriage wheel which re-
volves 1848 times in a journey of 3£ miles.
2, In 120,505 square feet how many acres, etc. ?
3, If the moon moves forward in her orbit 57° 13' 18" in
13 days, find the distance she averages a day.
4, A man can buy a white hat, which lasts 4 months, for
§0.75 ; he can buy a black hat, which lasts 9 months,
for $1.75. Which is the cheaper? What is saved
in 3 years by wearing the cheaper hat ?
5, Find the number of pounds Troy equal to 78 pounds 4
ounces Avoirdupois.
6, Reduce 1 acre 91 square rods 2 square yards to square
inches.
8.
1, Reduce 100,196,196 square inches to acres, etc.
2, Reduce 40 pounds 8 ounces 5 drams 1 scruple 7 grains to
grains, Apothecaries' weight.
3, Find the cost of half an acre of ground at 63 cents per
square yard.
4, The distance between two towns is 18 miles 40 rods 44
yards. How many telegraph poles will be required
between them, the poles being 8 rods apart ?
5, If $328 equal £74 2s. I0d., by how many pence does a
dollar exceed 4 shillings ?
6, How many cubic yards, feet, and inches in 175,983 cubic
inches ?
ARITHMETIC.
9.
1, In 36,845,371 ounces Avoirdupois, how many long tons,
cwts., etc. ?
2, In 1,749,134 seconds how many weeks, days, etc. ?
3, The latitude of St. Paul's in London is 51° 30' 49", and
that of St. Peter's in Home, 41° 53' 54". What is
one-fifth of the difference of their latitudes?
4, Reduce 875,679 chains 25 links to miles, rods, etc.
5, Reduce 7658 square chains 625 square links to acres,
square rods, etc.
6, Change 35 pounds 8 ounces 7 pennyweights 17 grains
Troy to Avoirdupois weight.
10.
1, Express in figures nine thousand seventeen million
fifty-nine thousand ninety-six.
2, How many days will 9867 pounds of hay last 13 horses,
if each horse eats 33 pounds a day ?
3, A boy has a bag containing 2360 chestnuts ; he takes out
7 dozen for himself, and then divides the rest among
19 school-fellows, keeping those remaining over.
How many chestnuts did he then have, and how
many did each of the other boys have ?
4, A city containing 758,043 inhabitants has 5 districts.
The population of the first is 78,967 ; of the second,
139,753; of the third, 145,069; the other two dis-
tricts have each an equal number of inhabitants.
Find the population of each of these two districts.
5, Reduce 367 acres 155 square rods 25 square yards 8
square feet 74 square inches to square inches.
6, Reduce 1,186,126 inches to miles, etc.
EXAMINATION MANUAL.
11.
1, Reduce 2 miles 3 furlongs 20 rods 1 yard to inches.
2, What do 12 dozen chains weigh, if each contains 2 ounces
9 pennyweights 3 grains of metal ?
3, Find the greatest common measure of 203 and 2291.
4, Find the least common multiple of 12, 21, 28, 30, 35.
5, Multiply T3T of If by 5J of J.
6, Add together 0.0023, 2.38, 250, 0.527.
7, Reduce 3 quarts 1 pint to the decimal of a gallon.
12.
1, Reduce 1 furlong 15 rods 1 foot 6 inches to yards.
2, If a person spends $2226.50 a year, how much does he
spend each day in an ordinary year ?
3, Find the greatest common measure of 2163 and 504.
4, Find the least common multiple of 18, 16, 63, 24, 56.
5, Find the value of 21 X If of l&X 3J of 1^.
6, Subtract 2.03 from 20.2.
7, Find the value of 0.625 of a gallon.
ARITHMETIC.
13.
1, Eeduce 357,000 inches to miles, furlongs, rods, etc.
2, At a festival 23,760 persons entered the enclosure be-
tween 10 AM. and 4 P.M. What was the average
per minute ?
3, Find the greatest common measure of 5292 and 1520.
4, Find the least common multiple of 4, 9, 16, 28, 42.
5, Divide 5J by -|.
6, If I sell -f of |- of an estate, what part of the estate
have I left ?
7, Multiply 3.26 by 1.02.
14.
1, A dozen persons hire an omnibus for $9.25. How
much more must each pay than if the party were
fifteen in number?
2, Find the greatest common measure of 3575 and 4719.
3, Find the least common multiple of 6, 15, 18, 35, 72.
4, Divide 20T\ by 17TV
5, Find the value of -| of an acre.
6, Divide 998.824392 by 0.018.
7, Reduce 5 ounces 12 pennyweights 16 grains to the deci-
mal of a pound.
EXAMINATION MANUAL.
15.
1, Find the greatest common measure of 5292 and 8316.
2, Find the least common multiple of 8, 12, 18, 24, 27.
3, Add together £ , -J-, -J.
4, Find the value of -ff^ of a bushel.
5, Divide 2 weeks 3 days by 3|.
6, Divide 160.68 by 3.9.
7, Reduce 3 quarters 3 pounds 2 ounces 2.816 drams to
the decimal of a long ton.
16.
1, Find the greatest common measure of 731, 2329, and
3502.
2, Find the least common multiple of 3, 8, 17, 40, 153.
3, Add if A, A-
4, Which is the greater £ of 4 or J of 5, and by how
much?
5, Find the value of 21 of 5 bushels -j- 1J of 2J pecks.
6, Divide 0.3964 by 0.75.
ARITHMETIC.
17.
1, Keduce f of a pound Troy to the fraction of a pound
Avoirdupois.
2, Divide 52 by 3.2.
3, Express 0.305 as a common fraction in its lowest terms.
4, Add together 2f , 41, 3T\.
5, Find the greatest common measure and least common
multiple of 125, 175, 225.
6, Divide f of £ by f of f .
18.
1, Which is the greater f of 1| or -f of 5J, and by how
much?
2, Simplify 21 -f f of 5|- + 4T7T + 5.
3, Add together -| and 2f , and subtract their sum from 4.
4, Multiply 0.026 by 3,3 ; by 0.33; by 33 ; and by 0.033.
5, Divide 1.8 by 500.
6, Express 0.0075 as a common fraction in its lowest terms.
10 EXAMINATION MANUAL.
19.
1, Add together 3J of 1| and 2f of If
2, Subtract I of H from J of 2f.
g3
3, Reduce to a simple fraction ~.
**§
4, Divide 611 by 0.13.
5, Reduce 7.2 feet to the decimal of a rod.
6, Find the value of 0.065 of an acre.
7, Reduce -J-|ff to its lowest terms.
20.
1, Subtract £ from f ; -f- from £ ; and $ from 1^ ; and add
together the results.
2, Multiply 2 yards 1 foot 7^ inches by ^-.
3, Reduce -f^ of a pint to the fraction of a gallon.
4, Divide 2175.68 by 100.
5, Reduce ^ff to its equivalent decimal fraction.
6, Reduce 15 square rods to the decimal of one-half an
acre.
7, Find the value of 0.009943 of a mile.
ARITHMETIC. 11
21.
1, Find the value in English money of 1572.4185 francs,
when the exchange is at 26.675 francs per pound.
2, Divide 101 by 1.01, and 0.101 by 10.1.
3, Reduce 14 hours 15 minutes to the fraction of 3 J days.
4, Reduce to a simple fraction ^— J
o + T
5, Find the greatest common measure and least common
multiple of 144, 176, 272.
6, How many plots of 2 1 acres each can be made out of an
estate one mile square ?
22.
L A man steps 2 feet 8 inches at each step. How many
steps will he take in 2 miles?
2, Reduce to its lowest terms |j J§.
3, Subtract 121| from 202£.
4, How can you determine that a number is divisible by
3 without actually dividing by 3 ?
5, Two pipes together fill a cistern in 1 hour, and one of
them alone fills it in H hours. How long will it
take the other alone to fill it ?
6, Divide 3.52 by 2.2 ; by 0.22 ; and by 22.
12 EXAMINATION MANUAL.
23.
1, In 640,825 seconds how many weeks, days, etc. ?
2, Reduce -J-f-fyJ- to its lowest terms.
3, Add 16ft, 1«, i A-
4, Subtract 3 1 from 30^.
5, Find the product of 1-fo X 3^-f X -^ X
6, If T7^- of an estate be worth §3003, what is the value of
the estate?
7, Reduce 213 rods 1 yard 2 feet 6 inches to the common
fraction of a mile.
24.
1, Divide 0.05625 by 0.0275.
2, Reduce £3 15s. 6.5 d. to the decimal of £4.
3, Westminster Hall is 237 feet long by G8 feet wide ;
Brussels Town Hall, 264 feet by 50 feet. How
many more persons could Westminster Hall accom-
modate than Brussels Town Hall, allowing f of a
square yard to each person?
4, Simplify 2^ + | X |- 21
5, Multiply 9-3^ by 16} of 1TV
6, Divide 5& -|| by If of 8j.
ARITHMETIC. 13
25.
1, Find the value of jJt-^J*L multiplied by •& of 6.
^ 6~ + 2" + -g"
2, Reduce to its lowest terms J|-f|f.
3, A can do a piece of work in 10 days, B can do the work
in 15 days. In what time can they both do it work-
ing together ?
4, Arrange in order of magnitude 2.5 X 0.075; 2.625-^-7;
5 X 0.05.
5, Reduce 0.972 to its equivalent common fraction.
6, Reduce to a decimal Tf f -3-.
7, Reduce 0.9 of a pound Avoirdupois to the decimal of 5
pounds Troy.
26.
1, How many cubic inches in a brick that is 9 inches long,
4 inches wide, 3 inches thick?
2, Reduce to a simple fraction 3| X 3T% X 2f\- X 2-^- X -£5.
3, What fraction of J- of a mile is 1 J feet ?
4, Reduce 6|- of 365^ days to the fraction of 3 years.
5, Express in figures seventy-three ten-thousandths.
6, Reduce 0.536 to a common fraction.
7, Divide 0.005868 by 0.036, and arrange the divisor, divi-
dend, and quotient in order of magnitude.
8, Divide 0.5 by 25 ; 87.5 by 2.5 ; and 0.055757592 by
0.009207.
14 EXAMINATION MANUAL.
27.
1, Divide 10.8528 by 1.02 and express the quotient as a
common fraction.
2, Reduce 2.5 gills to the decimal fraction of 3£ gallons.
3, Find the value of 14.1275 acres.
4, What is the value of 40 acres 132 square rods at $37.50
per acre ?
5, A railway train goes 200 miles in 8 hours. In what time
will it make a journey of 40 miles ?
6, How long will a journey of 15 miles 24 jods 3 yards
take at the rate of 3 miles 204 rods 3 yards in 56
minutes ?
28.
1, A race-horse goes 5 miles in 32 minutes. How long
will he be in going 1650 yards?
2, Reduce -J of ^ of a mile to the fraction of f of -jf of 8
miles.
3, Reduce 5.018 to its equivalent common fraction.
4, Simplify
5, Express 2 feet 3 inches as the fraction of 4£ yards.
6, Resolve 18, 16, 36, 44, 45, 48, 63, 121 into their sim-
plest factors, and find their least common multiple.
ARITHMETIC. 15
29.
1, Sound travels at the rate of 1120 feet in a second. How
far off is a thunder cloud, when the clap follows
the flash of lightning in 10 J seconds?
2, The four sides of a field are 23 chains 19 links, 17 chains
34 links, 6 chains 85 links, 24 chains 62 links. How
many yards around the field ?
3, Reduce 10,000 square yards to acres, etc.
4, Find the sum of 8 cubic yards 13 cubic feet 1234 cubic
inches, 5 cubic yards 14 cubic feet 976 cubic inches,
2 cubic yards 5 cubic feet 854 cubic inches, and 7
cubic yards 10 cubic feet 1012 cubic inches.
5, Express 1 peck 6 quarts 1 pint as the fraction of 6 bush-
els 1 peck 3 quarts.
6, Express 13 hours 15 minutes 17 seconds as the fraction
of 6 days 1 hour 48 minutes 7 seconds.
7, Find the value of -fa of 3 long tons 5 cwt. 101 pounds.
30.
1, There are 7 miles of road in a certain district. If the
average width of the road is half a chain, how
many acres of land consist of roads ?
2, Reduce 1012 quarts to bushels.
3, Reduce 673,856 seconds to days.
.4. A dishonest milkman mixes a pint of water with every
two quarts of milk. How many gallons will he
make in this way out of 20 gallons of pure milk ?
5, A well is 18 yards 2 inches deep, and the wheel is 4 feet
2 inches round. How many turns of the wheel will
raise the bucket ?
6, Express 1 day 1 hour 50 minutes 42 seconds as a decimal
of a day.
7, Express in days, hours, etc., the true length of a year,
365.242218 days.
16 EXAMINATION MANUAL.
31.
1, Find the least common multiple of 8, 10, 12, 25, 30, 36.
2, Add f of a score to -f- of a dozen, and subtract from the
result | of a hundred. What is the remainder ?
3, A cistern can be filled in 20 minutes by one pipe and
in 30 minutes by another. In how many minutes
will it be filled by both together ?
4, Express If of 7 yards 2 feet 9 inches as a fraction of
13 yards 7 inches.
5, A man walked 111 miles in 3 \ hours. How long would
he be in going 20 miles at the same rate ?
6, Divide 723.6 by 22.5 ; and 7.236 by 0.0225.
7, Find the value of 3.5 X 0.8.
32.
1, Find the value of 0.3 X 0.27.
2, If -| of a ton of coal costs $4, what will \\ cwt. cost?
3, Find the value of 0.2625 of a mile.
4, The highest mountain in the world is Dhawalaghiri, in
the Himalayas, and is 28,000 feet above the level of
the sea. Express this as a decimal of the earth's
radius, 4000 miles.
5, From 1 pound Troy of standard gold are coined 46.725
sovereigns. Find the weight in grains of each sov-
ereign.
6, The depth of a canal is 6 feet 4 inches, the width 19 feet
8 inches, and the length 20 miles. How many cu-
bic feet of water will it hold ?
ARITHMETIC. 17
33.
1, Add together -^, -^-, •£$, and -|.
2, Divide -^ by 6|.
3, Reduce 789,654,328 inches to miles.
4, Reduce £25 16s. Sd. to the fraction of £15 10s.
5, The upper floor of a house is 18 feet 4 inches above
the ground and is reached by two equal staircases,
separated by the landing of the first floor. How
many stairs are there in each staircase, if each stair
is 11 inches high ?
6, How many hurdles will it take each 5£ feet long to
make a square sheep-fold, each side of which is 40
rods?
7, If a quantity of wheat fills 1155 sacks, each holding
8 bushels 4 quarts, how many sacks will it take to
contain the wheat when each sack holds 6 bushels 3
quarts ?
34.
1, If 64 gallons of wine and 16 gallons of water are mixed,
how much wine is there in 2 quarts 1 pint of the
mixture ?
2, Find the total weight of 5792 iron bars, each weighing
23 pounds 10 ounces.
3, Reduce 0.056 of a square rod to the decimal of an acre.
4, Find the value of 0.58 of a common year.
5, The price of gold being £3 17s. 10 £ d. an ounce, find
the weight of a nugget worth £341.0925.
6, Find the greatest common measure and least common
multiple of 161, 253, 299.
7, Simplify 1^- + f of ^ - H of 6±.
18 EXAMINATION MANUAL.
35.
1. Add 0.60457; 46.70056; 5.80007; and 4.7896.
2, Divide 5.0666 by 21.56.
i 3, Reduce 2.025 miles to yards.
4. Find the difference between 0.44 of 1 week and 0.125 of
8 days.
5, If the weight of 1 cubic foot of water is 62^-f pounds,
find the error in calculating the weight of 1000 cu-
bic feet, on the assumption that 1 cubic foot weighs
1000 ounces.
6. Supposing the quick-step in marching to be 2 paces per
second, and the length of each pace to be 28 inches,
find the time in which a regiment will march 35
miles.
7, Simplify H-(H of J).
36.
1, Reduce 186 yards 2 feet 8.04 inches to the decimal of a
chain (22 yards).
2, Add together -fa of a square mile, y7^ of an acre, and
-f of a rood, giving the result in acres, roods, and
square rods.
3, Simplify 1 + 61 xM-^xJ,
4, Reduce 3 cwt. 14 pounds to the decimal of a long ton.
5, Find the rent of 215 acres 45 square rods at $5.62 an
acre.
6, If 4-J ounces Avoirdupois cost $8|^-, what will Sj-f
pounds cost?
ARITHMETIC. 19
37;
1. If a bankrupt has assets to the amount of $1020, and
debts to the amount of $3225, how many cents on a
dollar will his creditors receive ?
2. Two farmers bought a crop of hay. One took -| of it,
and paid $ 12. What had the other to pay ?
3. In a town of 450 people, 0.44 were men and boys,
0.38 were women and girls, and the rest were chil-
dren. How many were there of each ?
4. If the carriage of 12i cwt. for 50 miles cost $3^, what
will it cost to carry 17? cwt. the same distance?
5. Simplify (2 J + i)-f-(2f-i).
6. If | of a yard cost f of $1, what will || yards cost?
7. Divide 7.584057 by 11.7.
38.
1. In 4,076,412 dwts. Troy, how many pounds, ounces, etc. ?
2. Divide lOOf by 35.
3. Divide 18,454.9239 by 0.1225.
4. In 17,630,754 square inches, how many acres, etc.?
5. Subtract 8^ from 12^.
6. Subtract 6.04083 from 12.7.
7. A person sold •§ of his estate, bequeaths f of the re-
mainder to his son, and leaves the rest to be dis-
tributed equally among 3 charities. If each of
these charities receives $136.25, what is the value
of the estate?
20 EXAMINATION MANUAL.
39.
1. Find the value of -ff of a mile.
2. Keduce 2 weeks 2 days 19£ hours to the fraction of a
month (4 weeks).
3.. Reduce y5¥9Q- to a decimal.
4. A bankrupt's liabilities are £3768 17s. 6 d. "What are
his assets, if he can pay 13 s. 7? d. in the pound ?
5. Subtract -f-% dwt. from 2.6 ounces, and give the an-
swer as the decimal of a pound Troy.
6. Divide 218.4 by 0.168.
7. Divide 12 by
40.
1. Express 13 minutes 7£ seconds as the decimal of 1 hour.
2. Add 6, l\, ^, and ft.
3. Find the cost of 11 miles 120 rods 165 feet of railway
at §32,500 per mile.
4. Add 2.6 days and 0.85 of an hour, and give the an-
swer in minutes.
5. In 156,704 square inches, how many square yards, etc.?
6. Divide 8.4605 by 0.248 to three places of decimals.
7. Subtract 6f from Sf
ARITHMETIC. 21
41.
1. In 57,625,318 square inches, how many acres, square
rods, etc. ?
2. A bankrupt's estate amounts to £910 3s. Hd, and
his debts to £875. How much can he pay in the
pound ?
3. -What is the circumference of a wheel which makes 514
revolutions in passing over 1 mile 467 yards 1 foot?
4. Find the value of 5f — 4f + -f-^— If
5. From 21-J-31 take -i-Xf X-f-Xf.
6. Divide 18.13 by 0.00037.
42.
1. A piece of cloth, when measured with a yard measure
that is -f of an inch short, appears to be 10 £ yards
long. What is its true length ?
2. Divide 120,987.2 by 400.
3. Add |f 3-J-, 1/T, and -fr.
4. Simplify
y A -4y A U^
5. The weight of a cubic inch of water is 253.17 grains ;
that of a cubic inch of air 0.31 grains. Find to three
places of decimals how many cubic inches of water
are equal in weight to 1 cubic foot of air.
6. Find the price of 5 acres 72 square rods of land at
$47.50 per acre.
22 EXAMINATION MANUAL.
43.
1. Reduce 42 rods 1 yard 8 inches to the fraction of a mile.
2. Find the value of 1.46875 acres.
3. Divide the product of 6.225 and 8.25 by 0.0025.
4. What fraction multiplied by f will give f ? what frac-
tion divided by f will give -| ? what fraction sub-
tracted from -^- will give
5. Arrange in order of magnitude
6. A and B start at a distance of 64 miles from each other.
A walks 3J miles an hour ; B, 2£. If they start at
the same time, how many miles will they each walk
before they meet ?
7. A ship left England at noon, January 1, 1851. She
reached a port in Australia at midnight (Greenwich
time), April 23. If the length of the voyage was
18,225 miles, what was her average rate per hour ?
44.
1. Subtract 17.2398 from 27.06.
2. Multiply 46.2375 by 0.0074.
3. Divide 92.3784 by 0.623 to three places of decimals.
4. Find the product of T\, ^, 9f , and 2f
5. Subtract 4.42 of an hour from 3.64 of a day.
6. Reduce 136,240 square feet to acres, etc.
7. Reduce 234,567 grains to pounds, ounces, etc., Apothe-
caries' weight.
ARITHMETIC. 23
45..
1. The imperial gallon contains 277.274 cubic inches. What
is the size of a pint pot in cubic inches ? What Aveight
of water will it hold, if a cubic foot of water weighs
1000 ounces?
2. What number added to the sum of -f , f , f, and f will
make 4?
3. A field of 3 J acres is divided into 28 equal parts. What
fraction of an acre is there in each part ?
4. Find the sum of 17.01, 0.1303, 500.42101, 0.001, and
6.6.
5. Divide 6.2301533682 by 8.8964.
6. If 7 tons 336 pounds of coal cost $32.50, what will 1232
pounds cost?
46.
1. Find the wages of a man for 3 weeks 4 days 8 hours at
$8 per week, reckoning 6 days to a week and 10
hours to a day.
2. Eeduce 30 rods 2 yards 1 foot to the fraction of 150
rods 4 yards 2 feet 1 inch.
3. If f of an estate is worth $870, what is the value o
of it?
4. Express in the simplest form 3-| + -J of
T8
5. What number multiplied by ^ will produce 90J ?
6. What number added to lI7-5- + 3^- + 2^- + -js¥ will make
the sum total 10 ?
7. Give in feet the value of 7.0125 miles.
24 EXAMINATION MANUAL.
47.
1. Given the fractions -g%, T3/T, and -^¥7¥; express the differ-
ence of the first two as a fraction of the difference
of the last two.
2. Reduce ]||| to its lowest terms.
3. Divide 16.9 by 0.0013, and also by 1.3.
4. Reduce 0.53 and 0.00987 to equivalent common frac-
tions.
5. Find the value of 0.3925 of 2 years, each year contain-
ing 365i days.
6. Reduce 6 yards 2 feet 7.5 inches to the decimal of a mile.
48.
1. What decimal of 1 day is 23 hours 15 minutes 6 seconds?
2. Find the average of 21f , 73£ , 0, 3^, 82, 17^, H»
3. Add ^ of £5, $ of £9 13 s. 2| d., and -^ of 2s. 6d.
4. A and B can do a piece of work in 7 days, B and C can
do the work in 8 days, and all three together can do
it in 5 days. What part of the whole work can each
do in 1 day ?
5. What will be the cost, at 18 cents a square yard, of paint-
ing the walls of a room 17 feet 3 inches long, 15
feet 5 inches wide, and 13 feet 6 inches high, allow-
ing 54 square feet for windows, etc. ?
6. Find what fraction the sum of -^ £$, -jV> anc^ IT *s °f
2^ of 1| of f
ARITHMETIC. 25
49.
1. A person possessing -^ of an estate sold y of y^- of his
share for $120.62*. What would -J- of T8T of the
whole estate sell for at the same rate ?
2. Express as a fraction of $5 the difference between $7|-
andf of $7.
3. Subtract 2.63 dwts. from 12.13 ounces Troy, and express
the answer in pennyweights. "
4. In 76,128,976 inches how many miles, etc.?
5. Divide 78 by 361.059 to three places of decimals.
6. Find the value of 2.5 + — - 6.002.
50.
1. Find the average of 12Jf , 21, 7f , 0.034, 3.125, 0, 24.5,
and 12^. Express the fractional part decimally.
435.1x0.0046
2. Reduce to the simplest form
0.125
3. Divide the sum of 14.4 and 1.44 by their difference,
and express the result as a common fraction.
4. A can build a wall in 3i days, and B in 5 J days. In what
time will A and B together do it?
5. A brick 9 inches long, 4J inches broad, and 3 inches
thick weighs 9 pounds nearly. What would a brick
weigh if it were 12 inches long, 6 inches broad, and
4 J inches thick ?
6. Subtract 73.4698 from 108.30125.
26 EXAMINATION MANUAL.
51.
1. Add £, 2-f , and 13T% ; divide this sum by 13^ ; and
subtract the result from 5T3Q-.
2. A cistern can be filled in 50 minutes by one pipe, and in
1 hour 5 minutes by another. In how many minutes
will it be filled, if both are open together?
3. If a 4 per cent stock is at 82|, what will be the cost of
$1000 stock, and what sum will be gained by sell-
ing out at 86i ?
4. An army is besieging a town in which are 1000 men,
with provisions for three months. HowT many must
. leave at once, in order that the rest may be able to
subsist a year ?
5. Divide 7.619 by 0.0019.
6. Arrange in order of magnitude ^ -fj, -J-J, ^.
52.
1. A room is 20 feet 6 inches long, 15 feet 6 inches wide,
and 16 feet high. It has two doors, each 8 feet by 3
feet 9 inches ; it has one window 5 feet by 7 feet, and
two windows, each 5 feet by 4 feet. What will it
cost to paper the room with paper 1 yard wide, at
20 cents per yard ?
2. Divide 0.101 by 0.5; by 0.05; by 50; and by 5000.
3. Eeduce to a common fraction 0.01034.
4. Divide A of # by T% of -ftf
5. Find the square root of 488,601.
6. Find the simple interest of $1025 for 13 years at 43 per
cent.
ARITHMETIC. 27
53.
1. If -f of a yard of cloth cost -| -of a dollar, what will
-j^- of a yard cost?
2. Find the greatest common measure of 2526 and 2947.
3. Subtract 0.002 from 11, and multiply 0.01 by 1.01.
4. Divide 2f of If by 3£ of f of £.
5. If 0.5 of £1 buys 0.4 of a gallon, how much may be
bought for 6s. 3d?
6. A steam engine and a horse start together. The engine
does the first mile in 5 minutes, the horse in 4 min-
utes. After this mile the rate of the engine is 30
miles per hour, that of the horse 20 miles per hour.
Which wins in a three-mile race, and by how much?
54.
1. Divide 1.44 by 1.2 ; by 12 ; by 0.012 ; and by 120.
2. Find the square root of 449.44.
3. What is the cost of carpeting a room 21 feet by 30 feet
with carpet half a yard wide, running across the
room, at 75 cents a yard ?
4. Divide §1300 into three parts, in the ratio of 6, 4, 3.
5. If 12 men do a piece of work in 15 days of 12 hours
each, how many days of 9 hours will 10 men take to
do it?
6. Find the income produced by investing $4500 in 3 per
cent bonds at 90 ; and that produced by investing
$2850 in 3J per cent bonds at 95.
28 EXAMINATION MANUAL.
55.
1. Reduce 12 s. 6 d. to the decimal of a pound sterling.
2. Divide -J of £ of 4f of 2J- by £ of 4-J- of 3| of If
3. Find the compound interest on $100 for two years at
10 per cent.
4. If 24 men do a piece of work in 14 days of 9 hours, how
many men will do it in 12 days of 7 hours.
5. Find the least common multiple of 10, 14, 15, 21, 30, 42.
6. What sum invested in 3 per cent bonds at 92 will pro-
duce an income of $ 100 per annum ?
7. The gross receipts of a railway company are $231,100.
After deducting 35 per cent for working expenses,
and paying 6 per cent interest on $2,500,000 bonds,
what sum is left for dividing among the share-
holders ?
56.
1. Express as a decimal fraction the sum of -|, J, -|, J, T9-^,
2. Simplify _ _; and
O I 6 -
3. Divide 36.33 by 210 ; 35 by 0.05 ; 0.002 by 200.
4. Find the square root of 22.1841.
5. If 3 pounds of tea at $1.56 per pound, 5 pounds at
$1.20, and 7 pounds at $.60 are mixed, at what
price per pound must the mixture be sold to gain 2 £
per cent?
6. Find the interest of $ 535 for 9 months at 41 per cent.
ARITHMETIC. 29
57.
1, Find the greatest common measure of 124,321 and
197,451.
2, Reduce 0.075 of a pound sterling to the common frac-
tion of 4 s. 6 d. ; and 2 square rods 9 square yards 4
square feet 72 square inches to the common fraction
of 1 acre 60 square yards.
3, A man buys eggs at 11 cents per dozen, and sells them
at 2 cents apiece. What does he gain per cent ?
4, What sum, if put out at 3& per cent for 6 years, will
produce $28.87i-, simple interest?
5, Divide 1.69 by 0.13 ; 12.1 by 0.011 ; 0.001 by 0.01.
6, Find the square root of 4.1209.
58.
1, Find the simple interest on $387.50 for 5 years 3
months at 3£ per cent.
2, Find the least common multiple of 3, 5, 7, 9, 15, 63.
3, Divide l-a + i + ^) by 1-Jof 1 of ^.
4, Multiply 0.000725 by 31.25 ; and divide the product
successively by 6.25, 625, and 0.0625.
5, At what price per hundredweight must goods be sold,
which were bought at $5 per ton, in order to gain
6 per cent ?
6, A manufacturer makes a profit of 20 per cent, whole-
sale dealer 25 per cent, shopkeeper 40 per cent.
What is the first cost of an article bought at a shop
for $4.20?
30 EXAMINATION MANUAL.
59.
1, Divide $ 154 among 4 persons in the proportion of £,
i i i
2, In how many days of 12 hours will 72 men do a piece
of work which 60 men can do in 30 days of 9
hours ?
3, Find the interest on $354.27 for 3 years 2 months 12
days at 2i per cent.
4, $4500 is divided among A, B, C, and D. A receives
i of the money, B and C each f of the remainder.
How much is left for D ?
5, Express as common fractions 0.001375 ; 0.03 ; 7.19318.
6, A can walk 10 miles in 2i hours, and B can walk 11
miles in 2 \ hours. They start to walk a match of
55 miles. Which will win, and by how much time ?
60.
1, The profit made by selling beer at 1 d. per pint above
cost is 50 per cent. What is the gain per cent by
selling it at 6 d. per gallon above cost ?
2, Find the compound interest on $66.67 for 2 years at 9
per cent.
3, How much money must be invested in 3 per cent bonds
at 92 to secure an annual income of $150?
4, Find the L.C.M. of 12, 84, 120, 132, 156.
5, Keduce -|-|-|-f to lowest terms.
6, A piece, of work can be done in 50 days by 35 men.
After 12 days 16 men strike. How soon will the
rest finish the work ?
ARITHMETIC. 31
61.
1, Find the greatest common measure of 5522 and 6006.
2, Divide TV-TV by 3TV-2ff
3, Express as common fractions 0.06125 and 0.1237.
4, If a room is 27 feet 5 inches long, 14 feet 7 inches wide,
12 feet 10 inches high, how much paper -J- of a yard
wide is required to cover the walls ?
5, "What is the amount at simple interest of $1275 in 5
years 8 months at 3|- per cent ?
6, If I buy sugar at $7 per cwt., at what rate per pound
must I retail it to gain 7-f per cent ?
62.
1. If 8 men can reap 40 acres of wheat in 7 days, how
many acres will 24 men reap in 28 days ?
2. Find the square root of 2,900,209.
3. How many cubic feet of air in a room 10 feet long, 8
feet 6 inches broad, and 6 feet 6 inches high ?
4. A 4f per cent stock can be purchased at 91. What
per cent interest will this investment yield?
5. When the Centigrade thermometer marks 25 degrees,
what will Fahrenheit's thermometer mark ?
6. Find the greatest common measure of 210 ; 258 ; 903.
32 EXAMINATION MANUAL.
63.
1. amplify -I, and g^.
*
2. Express as decimals -^ yf TT» anc^ ' — ^— ••
db 1
3. How many miles will a ploughman walk, in ploughing an
acre of ground, if each furrow is a foot in breadth ?
4. A room is 12£ feet by 10 feet, and 7 feet high. How
many yards of paper 2 feet 6 inches wide will it
take to paper the room, if the waste is ten per cent ?
5. A plank is 3 inches thick, 18 inches wide, and 30 feet
long. How many board feet does it contain ?
6. Eggs are sold at the rate of 5 for 4 cents. At what
price were they bought if the profit was 20 per
cent?
64.
1. Find the square root of 0.00027 to four places of
decimals.
2. If I sell $2500 3 per cent stock at 95, and invest the
proceeds in 4? per cent stock at par, what difference
does it make in my income ?
3. What is the cost of papering a room 16 feet long, 12
feet wide, 10J feet high, with paper 21 inches wide
at 7 cents per yard, if the waste is 12J per cent?
4. Express -%fa as a decimal; and 0.1236 as a common
fraction.
5. Divide 22.4615 by 0.167 ; and 0.004095 by 0.273.
6. Find the least common multiple of 3, 8, 15, 21, 18.
AEITHMETIC. 33
65.
1. A owns £ of a vessel, B J, and C ^, and the rest belongs
to the master. What is the master's share ?
2. If two acres will maintain 3 horses for 4 days, how
long will 6 acres maintain 6 hordes ?
3. Divide 9.3828 by 1117; by 11.17; by 0.01117.
4. What is the difference between the simple and com-
pound interest on $550 for 3 years at 5 per cent?
5. A merchant sold goods for $750 more than he paid for
them, and cleared 15 per cent. What did he pay
for them ?
6. Two boats row a race of 1 mile 720 yards. One rows
31 strokes a minute, and clears 30 feet each stroke ;
the other rows 33 strokes, and clears 28 feet. How
many yards ahead will the winning boat be when it
passes the winning post ?
66.
1. What is the price of a Turkey carpet 20 feet 6 inches
long by 12 feet 9 inches wide, at $5.04 a square
yard?
2. If I invest $3570 in 7 per cent stock at 2 premium,
what income do I derive from it ?
3. A grocer bought 40 pounds of tea at 60 cents, and 90
pounds of coffee at 42 cents a pound. He sold the
tea at 96 cents and the coffee at 36 cents a pound.
What did he gain or lose ?
4. Find the least common multiple of 34, 51, 85, 120, 170.
5. Simplify 12.4 + 0.064-0.066,
0.002
6. Add i of | of 5s. 4rf., | of f of 6s., f of f of 2s.
34 EXAMINATION MANUAL.
67.
1. Find the cost of papering a room 21 feet long, 16£ feet
wide, 10J feet high, at 15 cents per square yard.
2. A can run 10 yards to B's 9. How many yards start
must A give B in a mile to make an even race ?
3. Simplify i— H-H-I). .
i
4. If I sell out $10,000 of 3| per cent stock at 94£, and
buy with the proceeds 6 per cent stock at 105, what
will be the alteration in my income ?
5. Find the true discount on $1025.62^ for 6 months at 5i
per cent per annum.
6. Reduce to its lowest terms IH4M.
68.
1. Find the L.C.M. of 2, 3, 4, 5, 8, 12, 72, 84.
+ °f
a ofA
3. Find the cost of paving a passage 15 yards 2 feet 6
inches long, and 3 yards 6 inches wide, with tiles
costing $3.60 per square yard.
4. Add together 53£, 36.875, 4|, I of 7J, and divide the
result by 0.01.
5. If 6 men can dig 5 acres in 8 days of 10 hours, in how
many days of 12 hours can 4 men dig 6 acres ?
6. At what rate of interest will $2560 amount to $3328
in 5 years ?
ARITHMETIC. 35
69.
1. If I sell out $1000 from 3 per cent stock at 88, and
buy 5 per cent stock at 110, what alteration do I
make in my income ?
2. If a man buys 560 tons of coal at 14s. 8>d. per ton, and
sells it at lie?, per cwt., what is his gain per cent?
3. Divide 42.5 by 0.017 ; and find the value of 0.625 of
3 pounds Avoirdupois.
4. Simplify 3 -ft + !)-
5. Find the square root of 1.00060009.
6. The gross yearly rental of an estate is $2100 ; taxes and
repairs amount to 25 per cent of the rental. The
owner sells the estate for 21 times the gross yearly
rental, and invests the proceeds in 3£ per cent
stock at 98. What does he gain or lose in his net
income ?
70.
1. If $1350 at simple interest amount to $1570.50 in 1
year 8 months, find the rate per cent.
2. If by selling wine at $3 a gallon I lose 6 per cent, at
what price must I sell it to gain 17 £ per cent?
3. Find the compound interest on $750 for 5 years at 2J
per cent.
4. Eeduce 347,894,178 square inches to acres, etc.
5. If $850 amounts to $913.75 at 2£ per cent, find the
time.
6. A room is 10 feet high, 5£ yards long, and 3 yards
wide. It contains a door 8 feet by 4 feet, two
windows each 5 feet by 4 feet, and a fireplace 6 feet
by 4 feet 6 inches. How many square yards on its
walls require to be painted ?
36 EXAMINATION MANUAL.
71.
1. The distance between the posts of a railway telegraph
is 60 yards. Find the rate of a train which passes
11 posts in 50 seconds.
2. Find the income from an investment of $5308.33 in
3 per cent bonds at 91.
3. A invests $1200, B $2400, in business. The net profit
at the end of the year is $ 720. How much should
A and B each receive, and what is the rate of
interest upon the investment?
4. Find the least common multiple of 5, 7, 16, 28, 48, 21.
5. If i of a ship be worth $292.25, what part of her will
be worth $1002?
6. If 10 men can reap 20 acres in 4 days, how many men
can reap 70 acres in 10 days?
72.
1. What sum of money will amount to $276.25 in 1 year
and 3 months at 5 per cent simple interest ?
2. When 3 per cent bonds are at 75, what sum must be
invested to produce an annual income of $ 120 ? •
3. Find the present worth of $1836, due 4 years hence, at
5 per cent simple interest.
4. What is the rent of a field containing 112 acres 109.5
square rods at $2.64 an acre?
5. Divide 1368.2394 by 2400.21, and by 0.00240021.
ARITHMETIC. 37
73.
1. Find the value of £2-f-i- of £140 10s. 6rf. + f of £1
Is.
2. Find the greatest common measure of 1288, 1736, 104.
3. If 120 men build a house 60 feet high in 15 days, how
many will build a house 55 feet high in 10 days?
4. Find the difference between the simple and compound
interest on $955 at 6 per cent for 4 years.
5. A garrison of 1000 men have provisions for 30 days.
At the end of 10 days a reinforcement arrives, and
then the provisions last only 5 days. What is the
number of the reinforcement?
74.
1. Express 0.466 as a common fraction.
2. A sum of money was borrowed at 5 per cent simple in-
terest. In 7 years it amounted to $810. What was
the sum borrowed?
3. If 100 men in 6 days of 10 hours can dig a trench 200
yards long, .3 yards wide, and 2 yards deep, in how
many days of 8 hours can 180 men dig a trench 360
yards long, 4 yards wide, and 3 yards deep?
4. Find the cube root of 42,508,549.
5. How many rods of fencing are required to enclose a
square park containing 832 acres 105 square rods?
6. Which is the better investment, 4 per cent stock at 120,
or 2$ per cent stock at 75?
38 EXAMINATION MANUAL.
75.
1. What is the length of the edge of a cubical cistern
which contains as much as a rectangular one whose
edges are 154 feet 11 inches, 70 feet 7 inches, and
53 feet 1 inch ?
2. For what must I sell a horse that cost me $75.50 so as
to gain 5J per cent?
3. By selling 12 pounds of- tea for $7.56, 1 gain 5 per cent.
What do I gain or lose per cent by selling 50 pounds
of the same tea for $31?
4. Find the amount of $4250 for 2 years 6 months at 5
per cent compound interest.
5. Reduce f ff and -|~f|-f to their lowest terms.
6. How can you tell without dividing whether a number
is exactly divisible by 11 ?
76.
1. Find the amount of $7234.25 at 4J per cent simple
interest, in 22 years 2 months 20 days.
2. If 20 men build a wall 800 feet long, 10 feet high, and
18 inches thick in 14 days of 8 hours, how thick a
wall will 15 men build 900 feet long and 15 feet
high in 21 days of 9 hours ?
3. Subtract 0.992748 from 1.
4. Find the cost of 3 acres 145 square rods of land, at $ 120
an acre.
5. What is the price of a silver bowl weighing 5 pounds
9 ounces 8 dwts., at $1.40 per ounce?
6. Add together &, f , -&, &&.
ARITHMETIC. 39
77.
1. How many tiles, each 7 inches square, will be required
to cover a floor 19 feet 3 inches by 13 feet 5 inches ?
2. Extract the cube root of 0.145531576.
3. If a tradesman, by selling an article at $1.98, loses 17£
per cent, what should he have sold it for to gain 40
per cent ?
4. What is the income of a man whose income tax at 4 d.
in- the pound amounts to 23 guineas?
5. If 2 horses can plough 7 acres of ground in a day, how
many horses will plough 161 acres in \\\ days?
6. In 1,250,784 seconds, how many weeks, days, etc. ?
78.
1. Divide 2054.95 by 0.0563.
2. A merchant sells tea to a tradesman at a profit of 60
per cent; but the tradesman, failing, pays only 12£
cents on the dollar. How much per cent does the
merchant lose by the sale ?
3. When a 3J per cent stock is at 93, find what price a
4J stock must bear that an investment may be made
with equal advantage in either stock.
4. Find the cube root of 134,217,728.
5. Find the product of 10£, &, ff and l£.
6. If 14 men can mow 168 acres in 12 days of 81 hours,
how many acres can be mowed by 20 men in 11
days of 7| hours?
40 EXAMINATION MANUAL.
79.
1. Between the years 1841 and 1851, the population of
England increased 14-^- per cent. In 1851, the
population was 21,121,290. What was it in 1841 ?
2. A merchant has teas worth $1.08 and 84 cents per
pound respectively, which he mixes in the ratio of
3 pounds of the first kind to 2 of the second kind,
and sells the mixture at $1.04 per pound. What
does he gain or lose per cent ?
3. A person invests $5460 in 3 per cent stock at 91 ; he
sells out $2000 stock when it has risen to 93?, and
the remainder when it has fallen to 85 ; he invests
the proceeds in 4| per cent stock at 102. What is
the alteration in his income ?
4. Extract the cube root of 5.78 to three places of decimals.
SO.
1. If 48 pioneers in 5 days of 12 J hours can dig a trench
139| yards long, 4J yards wide, and 2J yards deep,
how many hours a day must 270 pioneers work for.
42 days, in order to dig a trench 4910T1g- yards long,
4-J yards wide, and 3i yards deep ?
2. If a man rows 10 miles in 2J hours against a stream,
the rate of which is 3 miles an hour, how long will
he be rowing 5 miles with the stream ?
3. Find the price of 5 acres 127 square rods and 88 square
yards at $161£ per acre.
4. If a person selling sugar at 9J cents per pound loses
1.0 per cent, what did he give per hundredweight ?
ARITHMETIC. 41
81.
1, A square contains 40,092.0529 square feet. Find the
length of one of its sides.
2 Simplify (°-°75 X °-°75) ~ (Q-°05 X
J~ 0.75 — 0.05
3, A person invested $4706 in 3 per cent stock at 90 \ .
A year afterwards, when the 3 per cent stock had
fallen to 89, he sold out one-half of his stock and re-
invested it in 5 per cent foreign bonds at .52. What
change did the reinvestment make in his income ?
4, If 50 men dig a trench 120 yards long, 5 feet broad, 10
feet deep in 3 days of 10 hours, in how many hours
will they dig a trench 175 Yards long, 4 feet broad,
and 8 feet deep ?
5 Simplify Si+iiiH Si
1117 X
82.
1, Find the least common multiple of 14, 36, 84, 108, 144.
2 Einmlifr 9*-8» + 6*-5*
y8^-7|f + 6i-5f
3, If with a capital of $ 500 a tradesman gains $ 50 in 7
months, in what time will he gain $ 60.50 with a
capital of $385?
4, A certain 4i per cent stock is at a discount of 23.
What income should I get from $ 385 invested in it ?
5, Find the cost of papering the walls of a room 10 feet 8
inches wide, 19 feet 4 inches long, and 9£ feet high,
with paper 2 feet wide at 5 cents a yard, allowing
10 yards of the paper for waste.
42 EXAMINATION MANUAL.
83.
1. If 1 inch of rain on 4840 square yards gives 18,200
gallons of water, how many gallons will 0.875 of an
inch on a square mile give ?
2. If the amount of property liable to income tax be 525
million pounds sterling, how many pence in the
pound must the tax be to produce 17£ million
pounds ?
3. The circumferences of two of the wheels of an engine are
25£ feet and 16£ feet respectively. How many
more times will one turn round than the other in
4J miles?
4. If the shadow of an upright pole 9 feet high be 7 J feet,
what will be the height of a church spire which casts
a shadow 247? feet long?
, Q. ,.,
5. amplify
84.
1. Find the value of 3.75 of half-a-crown (2|s.) + 4.4 of a
guinea (21s.) + 1.024 of £22.
2. Find the length in yards of the side of a square enclosure
which contains 4 acres 144 square yards.
3. A plot of ground 50 yards long and 40 yards wide is to
be covered with sods 1£ feet long and 6 inches
broad. If the sods cost 75 cents per hundred, what
will be the -expense for turf alone ?
4. Find the present worth of $122.80 due 7 months hence,
at 4 per cent.
5. In a town where the annual death rate is 2£ per cent,
the average number of deaths a week (52 weeks to
the year) is 228. What is the population of the
town?
ARITHMETIC. 43
85.
1. A person transfers $3000 from a 4 per cent stock at 90
to a 3 per cent stock at 72. How much 3 per cent
stock can he purchase, and what will be the differ-
ence in his income ?
2. A cistern 5 feet deep, 16 feet long, 4 feet 6 inches wide,
is filled by one pipe in 45 minutes. In what time
will a cistern 6 feet deep, 20 feet long, 5 feet wide,
be filled by 3 similar pipes ?
3. Multiply 0.416 by 0.025, divide the product by 3.25,
and reduce the result to a common fraction.
4. A -clothier gains 25 per cent by selling cloth at $ 5 per
yard ; but a bale of 80 yards being damaged, he has
to reduce the price 10 per cent. What is now his
profit on the bale, and his gain per cent ?
5. Add 12^, 13fV> 17i and T&-
86.
i.
2. Find the difference between ^- of 200 rods and -f$ of £
of a mile.
3. What fraction of 560 pounds is equal to 0.1590 of a
long ton ?
4. $13,000 of 31 per cent stock is sold at 98. How much
money must be added to the sum realized in order
to secure an equal income in 3 per cent stock at 87 ?
5. An army of 120,000 men lost 15 per cent by desertion
to the enemy. What increase per cent did the
enemy gain, their number previously being 64,000?
44 EXAMINATION MANUAL.
87.
1. In 1870 three towns had populations of 17,650, 19,600,
and 18,760 respectively. In 1880, the population
of the first had decreased 18 per cent, that of the
second had increased 21 per cent, while the popula-
tion of the three towns had increased by 4691.
Find the change per cent in the population of the
third town.
2. What fraction of V5| is V0.000225?
5^ - 0.042 - 2.4 + ?|
' 16ft-*- 601
4. Find the square root of 1,079,521 and 0.1079521.
5. "What is the gain by investing $1950 at 971 and selling
out at 104, the brokerage on each transaction being
i per cent ?
88.
o
1. Find the value of - - correct to four places of
- -, • -, Vl9 - 4
of decimals.
2. Find the simple interest on $281.60 at 3£ per cent for
4 years and 2 months.
3. By selling a carriage for $73.15, I should lose 5 per
cent. At what price must I sell it to gain 15 per
cent?
4. Which is the better investment, 3 per cent stock at
64i, or 5 per cent stock at 1021 ?
5. A person has a certain capital, half of which is invested
in 3 per cent stock at 90, and the other half in 5
per cent at 110. His total income is $6883.50.
What is his capital?
ARITHMETIC. 45
89.
1. At what rate per cent will a given sum of money
double itself at simple interest in 30 years ?
2. A grocer has tea, which he must sell at 84 cents per
pound to gain 40 per cent. If he mixes it with tea
which cost him 54 cents per pound, in the ratio of 7
of the best kind to 3 of the poorest, and sells the
mixture in 10-pound packages at $7.76, how much
does he gain per cent?
3. How many times is 224 pounds 2 ounces contained in
6 long tons 8 cwt. 8 pounds ?
4. Find -|- of 8 miles 145 rods 3 yards 1 foot 6 inches.
5. The sides of two squares contain 77 yards 1 foot 9
inches, and 7 yards 2 feet 4 inches, respectively.
Find the side of a square whose area is equal to
the sum of the areas of the two squares.
90.
1. If a railway journey of 177 miles 120 rods takes 3
hours 56? minutes, what is the rate per hour?
2. Multiply 209 acres 145 square rods 3 square yards
by 13.
3. Two wines worth $8 and $6 per gallon respectively are
mixed together. If the mixture is worth $6.87?
a gallon, in what ratio are they mixed?
4. A tradesman pretends to charge 10 per cent above the
wholesale price, but he has adulterated his goods
with 50 per cent of a poorer kind, which costs only
-§• of the price. What is his real rate of profit ?
5. Express as decimals -£%, -^g-, and -/%.
46 EXAMINATION MANUAL.
91.
1. If the 2-penny loaf weighs 15 ounces when wheat is at
8 shillings, how is wheat selling when the Ss-penny
loaf weighs 2 pounds?
2. Find exactly the cube root of 1,277,289^-.
3. Reduce -^-ffflr to its lowest terms.
4. What fraction is 1 week 7 hours 12 minutes of the time
from Jan. 1, 1800, to Feb. 20, 1864, both days in-
clusive ?
5. Find the circulating decimal equivalent to 1 ^ 1 .
6. At what rate per cent will a person receive interest
who invests his capital in 3 per cent stock at 91 ?
92.
1. At what price must a person buy 8 per cent stock to
receive interest at the rate of 3£ per cent?
2. If a vessel sails 500 miles in 2 days 18 £ hours, how far
will she sail between May 20 at noon, and 8 o'clock
on the morning of July 10 ?
3. A person buys coffee at $24 per cwt., and chicory at
$10 per cwt., and mixes them in the ratio of 2 of
chicory to 5 of coffee. He retails the mixture at 30
cents per pound. What is his gain per cent ?
4. A and B enter into partnership. A puts in $2100,
B $1500. Four months after, C enters the partner-
ship with $2700. At the end of the year the
profit is 10 per cent on the whole capital. What
share of the profit belongs to each ?
5. If oranges are bought at the rate of 20 for 25 cents,
how many should be sold for $12 to gain 40 per
cent on the cost ?
ARITHMETIC. 47
93.
1. Find the ratio of the rates for freight on two railroads,
one of which charges $5.62J for carrying 4200
pounds 44 miles, and the other, $7.86£ for carry-
ing 5376 pounds 52| miles.
2. If the discount on $127.925 for 20 days be $0.175, find
the rate per cent.
3. A gold wreath, weighing 3 pounds 7 ounces 12 dwt.,
cost $1275. If it is made of gold worth $19.37|
per ounce, what is charged for the manufacture ?
4. Divide 24.109932 by 301.28.
5. Find the value of 0.90625 of a cubic yard.
6. Simplify 3 \ + 3T% + 2^ + 2
94,
1. Reduce 18 days 5 hours 40 minutes 20 seconds to the
fraction of 31 days 21 hours 30 minutes 10 seconds.
2. Show that the greatest common measure of two num-
bers is the least common multiple of all their com-
mon measures.
3. A bought 63 sheep, and sold $ of them at a profit of
15 per cent, \ at a profit of 50 per cent, and the
rest at a loss of 25 per cent. What did he pay for
the sheep, if his gain was $19.25 on the whole?
4. Find the simple interest on $500 for 8 years 3 months
at 1J per cent.
.5. Find the cost of 369 miles 120 rods 22 yards of tele-
graph wire at $73.33^ per mile.
48 EXAMINATION MANUAL.
95.
1. What sum will amount to $5431.80 in 6 years at 4J
per cent simple interest?
2. Reduce 11 rods 4 yards 4.5 inches to the decimal of a
mile.
3. Find the greatest common measure of 14,938, 23,474,
32,010.
4. Find the number of seconds from the beginning of the
year 1883 to Dec. 17, 9 A.M., and express the result
in words.
5. Extract the cube root of 5 to four places of decimals.
96.
1. Supposing the area of a circle to be 3^- times the square
of the radius, find the weight of a circular disc of
cast iron 7 feet in diameter, and 1-J inches thick,
knowing that a plate 1 foot square and 1 inch thick
weighs 37-^ pounds.
2. If £ of a sheep is worth $-f, and f of a sheep is worth
y1^ of an ox, what is the value of 100 oxen ?
3. Find the entire surface of a cube, the volume of which
is 14 cubic feet 705.088 cubic inches.
4. Find the cost of a draft for $400, payable 60 days
after sight, exchange being J per cent discount, and
interest 7 per cent.
5. A man bought a horse for $125 and sold him for $100.
What per cent of the cost of the horse did he lose ?
6. Multiply 4 acres 67 square rods 19 square yards 4
square feet 72 square inches by. 27.
ARITHMETIC. 49
97.
1. In what time will the simple interest on $375, at 4 per
cent, amount to $91.25?
2. Divide the number 702 into 3 parts, proportional to £,
i, and \.
3. Divide 75 miles, 79 rods, 3 yards by 75.
4. How many bricks, each 9 inches by 4J inches by 3
• inches are there in a pile 36 feet long, 9 feet wide,
and 12 feet high ?
5. Find the face of a draft, payable 60 days after sight,
that can be bought for $1250, when exchange is at
i per cent premium, and interest 7 per cent.
6. Find the square root of 0.9 to four places of decimals.
98.
1. After paying ^ of my money to one person, -J to an-
other, and -fa to a third, I had 7 cents remaining.
How much had I at first ?
2. A person walks at the rate of 3^- miles an hour. Three
hours after he has set out on a journey, he is fol-
lowed by another person, walking at the rate of 5
miles an hour. In what time will he be overtaken ?
3. A grocer mixes 72 pounds of tea at 69 cents a pound
with 90 pounds of tea at 60 cents a pound. At
what price per pound must he sell the mixture so as
to gain 10 cents a pound ?
4. Extract the cube root of J- to four places of decimals.
5. At what rate per cent will $3000 produce $250 in-
terest in 1 year 2 months and 24 days ?
50 EXAMINATION MANUAL.
99.
1. Find the interest of $1721.84 from April 1 to Nov. 12
at 4|- per cent.
2. At what rate per cent will $1025.20 produce $25.72
interest in 4 months 9 days ?
3. Find the principal that will produce $1339.28 in 2 years
7 months 24 days at 6 per cent compound interest.
4. Find the time in which $793.875 will amount to
$805.84 at 5£ per cent.
5. Find the proceeds of the following note :
DETROIT, Feb. 2, 1881.
Four months after date I promise to pay to the
order of John Horn four thousand five hun-
dred fifty and f-fa dollars, value received.
JAMES THORN.
Discounted at a bank at 5| per cent, Feb. 16.
100.
1. A bankrupt has goods worth $975, and, had they real-
ized their full value, his creditors would have re-
ceived 81-J- per cent of their claims ; but •§ of the
goods were sold at 17-J- per cent, and the remainder
at 23J per cent below their value. How many
cents on the dollar did the bankrupt pay ?
2. Find the value of 157 miles 144 rods of telegraph wire
at $57.50 per mile.
3. Reduce fffi , -J^ff to tneir lowest terms, and express
their difference as a decimal.
4. Extract the cube root of 1250.6894.
5. Extract to six places of decimals the square root of 19.
ARITHMETIC. 51
101.
1. If a person steps 80cm at each step, how many steps will
he take in walking round a square field containing
18ha 625qm?
2. How many cords of wood can be piled in a woodshed
128 feet long, 42 feet wide, 12 feet high, allowing
for a driveway 10 feet wide, running from one end
of the building to the other ?
3. The true discount on a bill of $470.89, due 4 years
hence, is $85.62 ; find the rate per cent.
4. If the retail price of a book is $6, and 25 are sold for
$ 102, what rate per cent of discount is allowed ?
5. A merchant insures a cargo whose value is $4500 at 5
per cent. For what sum should he insure so as to
cover both the loss of the cargo and the premium ?
6. A man sent $500 to his agent in Chicago, with which
to buy flour. The agent bought flour at $5 a bar-
rel, charging 2J- per cent commission for buying.
How many barrels of flour can he buy, reserving
for himself his commission, and how much money
will be left over ?
102.
1. Find the sum of 1871ccra, 5411, 4.51hl, and give the
answer in liters.
2. What is the commission on goods worth $767.73 at 7|-
per cent ?
3. Kequired the equated time for the payment of $700
due in 6 months, $800 due in 9 months, and $600
due in 10 months.
4. When 3 per cent stock is at 91 f, find how much can be
bought for $540, allowing i per cent commission
upon the stock bought.
5. Find the cube root of 0.75 to four places of decimals.
6. If 2 men can reap 2-J acres in 2f days, how long will
it take 11 men to reap 15 acres?
52 EXAMINATION MANUAL.
103.
1. If it takes 25 minutes for a man who reads 2 pages in
3 minutes to read a certain document, how long will
it take a man who reads a page a minute to read a
document 3 times as long?
2. A man sells $7500 of 6 per cent railway stock at 120,
and invests half the proceeds in 3 per cent stock at
93, and the other half in 5-|- per cent stock at 90.
Find the alteration in his income.
3. A piece of land 2449m square is sold for $35 a hektar.
How much does the land bring ?
4. If cloth is sold for $3.75 a yard at a loss of 10 per cent,
what should be the selling price a yard to gain 18
per cent ?
5. Find the cube root of 0.3 to four places of decimals.
104.
1. A company whose capital is $2,500,000 pays an annual
dividend of 6|- per cent, besides paying a tax of 1-J
per cent on its whole capital. Find the total annual
receipts, the expenses being 60 per cent of the gross
receipts.
2. Bought 4 lots of wool at $652.50 each, and sold the
whole at 20 per cent profit. What was the selling
price per lot ?
3. If the increase in the number of male and female crim-
inals is 1|- per cent, while the decrease in the num-
ber of males alone is 4f per cent, and the increase
in the number "of females is 9£ per cent, find the
ratio of male criminals to female criminals.
4. Find the cost of a carpet 75cm wide, at $4.25 a meter,
for a room 5.25m long, and 4.75m wide, strips run-
ning across the room, if there is a total waste of 3m
in matching the pattern.
5. Extract the square root of 0.2 to five decimal places.
ARITHMETIC. 53
105.
1. An army lost 18 per cent of its strength by sickness
and desertion, and then lost 14 per cent of the re-
mainder in battle. The number left was 84,624.
Of how many did the army originally consist ?
2. If 6 iron bars 4 feet long, 3 inches broad, and 2 inches
thick weigh 288 pounds, how much will 15 weigh,
each 6£ feet long, 4 inches broad, and 3 inches
thick ?
3. Find the cost of plastering a room 13m long, 12m wide,
and 7m high, at 30 cents a square meter, if 115qm are
allowed for base-board, doors, etc.
4. Find the cube root of 25 to three places of decimals.
5. In 1841, the population of Great Britain was 21,476,000,
and that of Ireland 7,310,000. In 1851, the popu-
lation of Great Britain had increased 8.45 per cent,
and that of Ireland had decreased 12.5 per cent.
Find the increase per cent in the population of the
whole kingdom.
106.
1. A ship, valued at $14,500, is insured at 3? per cent,
and her cargo, valued at $32,000, is insured at 5
per cent. Find the whole cost of insurance.
2. Into how many pills of 325mg each can a mass of 23.4g
be made?
3. The solid contents of a cube is 37 cubic feet, £4 cubic
inches. Find the cost of painting its outside at
33i cents per square foot.
4. What must be the side of a cubical cistern, which will
contain exactly 1000 imperial gallons of water, if an
imperial gallon contains 277.274 cubic inches?
5. If a compound consist of 1185 parts copper, 715 parts
tin, and 100 parts zinc, find the percentage of each
metal in the compound.
54 EXAMINATION MANUAL.
107.
1, A rectangular cistern 9 feet long, 5 feet 4 inches wide,
2 feet 3 inches deep is filled with a liquid that
weighs 2520 pounds. How deep must a cistern be
that will hold 3850 pounds of the same liquid, if its
length is 8 feet, and its width 5 feet 6 inches ?
2, Reduce to prime factors, and then find the greatest com-
mon measure of 35,035, 41,580, 24,255.
3, How many; square slabs of marble 150qcm on the surface
will be required to pave a court whose area is
50.70qm?
4, A person sells out his 3 per cent stock at 86 1, and gets
$34,000 ; he invests one half of this sum in 4 per cent
stock at 97, and the remainder in 3£ per cent stock
at 94. Find the alteration in his income.
5, If 56 cubic feet 1044 cubic inches of timber are required
to floor a room 29^ feet by 25i feet, what is the thick-
ness of the boards ?
108.
1, A merchant has teas worth $1.12? and 87-J cents per
pound respectively, which he mixes in the ratio of
3 pounds of the better kind to 2 of the poorer kind,
and sells the mixture at $1.08i per pound. What
does he gain or lose per cent ?
2, How many revolutions will the wheels of a carriage
make in travelling 41km, if the wheels are 125cm in
diameter? (The circumference is 3.1416 times the
diameter.)
3, In what proportion must wines worth $3, $4, $5.20,
$6, per gallon be mixed, so as to give a profit of
14|- per cent when sold for $4.80 a gallon?
4, Extract to four figures the cube root of 20.
5, If a railway train goes 27f miles in 2f hours, how far
will it go in an hour?
ARITHMETIC. 55
1O9.
1, In what time will §2275 amount to $2673.12£ at 5 per
cent, simple interest?
2, If a horse trots 23f miles in 2? hours, what is his rate
per hour ?
3, If twelve men can build a wall 6 feet high, 3 feet thick,
in 9 days, how many men would build a wall of the
same length, 5 feet' high, 4 feet thick, in 24 days?
4, A man pays $12,000 for 5a of land, and sells it for
$25.20 a square meter. How much does he make?
5, A river 30 feet deep and 200 yards wide flows 4 miles
an hour. Find the number of cubic feet of water
that passes a given point in a minute.
6, Extract to four figures the cube root of 0.002.
110.
1, A cistern has two pipes, one of which can fill it in 2
hours, the other in 3 hours. A third pipe can
empty it in 5 hours. If all these are opened when
the cistern is empty, in what time will it be filled?
2, A pile of wood is 8.50m long, 2.66m wide, 2.60m high.
How many sters of wood are there?
3, A clock is set at 12 o'clock on Monday ; at noon on
Tuesday it is 3 minutes too fast, What will be the
true time when the clock strikes 4 on Thursday
afternoon ?
4, If 20 men can do a piece of work in 12 days, how many
men will do another piece of work six times as
great in -^ of the time ?
5, If 5 per cent be lost by selling an article at $2.50, find
the gain or loss per cent by selling it at $ 3.12|,
6, Find the square root of 53107.2025.
56 EXAMINATION MANUAL.
Ill
1. Reduce 167,948,604 square inches to acres, etc.
2. A man contracts to perform a piece of work in 30 days,
upon which he employs 15 men. In 24 days it is
only half finished. How many additional men must
he employ to finish the work in time ?
3. A cistern can be filled by a spout in 2 hours, but on
account of a leak in the cistern the spout takes 2-j-
hours to fill it. How long will it take the leak to
empty the cistern ?
4. A country, the population of which is |LO millions, has
births yearly of 1 in 20, and deaths 1 in 30. What
will its population be 5 years hence ?
5. A beam is 14.14m long. Its other dimensions are
51.6cm, 174mm. Find its volume.
6. If a trader sells 13|- pounds for 14 pounds, how much
per cent does he gain fraudulently ?
112.
1. A wine which contains 7J per cent of spirit is frozen,
and the ice, which contains no spirit, is removed.
The proportion of spirit in the wine thus is increased
to 8J per cent. How much water in the shape of
ice is removed from 504 gallons of the original wine ?
2. Find to four places of decimals the square root of
0.001 and of 0.5 ; and also find what numbers have
0.1 and 0.03 for their square roots.
3. The diameter of a carriage wheel is 4 ft. Two persons
calculate the number of its turns in a given distance,
one calling the circumference 3 times the diameter,
the other 3-f times ; their results differ by 100 turns.
Find the distance.
4. A package of candles which weighs 465g is sold for 28
cents. What is the price of 10kg of the candles ?
5. Reduce to its lowest terms the roduct of 1
ARITHMETIC. 57
113.
1. Resolve into prime factors 5940, 19,008, and 269,568,
and write the greatest number that will divide them
all without remainder, and the smallest number
that they will all divide without remainder.
2. Divide 181.3 by 0.00037, and by 37,000.
3. Find the cost of carpeting a room 18 feet 6 inches long,
12 feet 6 inches wide, with carpet f of a yard wide,
at 75 cents per yard, strips running lengthwise, and
3 yards being allowed for matching the patterns.
4. If 3 men mow 20 acres in 11 days of 11 hours, how
many men will it take to mow a rectangular field
384 yards long and 300 wide, in 4 days of 12 hours ?
5. The difference between the simple and compound inter-
est on a sum for 3 years at 5 per cent is $23.12J.
Find the sum.
6. How many hektars in a square kilometer?
114.
1. A box is 3.75m long, 3.50m wide, and 50cm high. Find
how many liters of olive oil it will hold, and the
weight of the oil in kilograms, the specific gravity
of the oil being 0.914.
2. If A can do f of a piece of work in 4 hours, and B can
do f of the remainder in 1 hour, and 0 finish it in
20 minutes, in what time will they do it, all work-
ing together ?
3. When a common fraction is reduced to a decimal, in
what cases will the result be a terminating decimal,
and in what cases a circulating decimal ?
4. If by selling goods for $272 I lose 15 per cent, how
much per cent would I have lost or gained if I had
sold them for $336?
5. If oranges are bought at the rate of 20 for a dollar, how
many should be sold for $28 to gain 40 per cent?
6. Find the cube root of 84.9 to three places of decimals.
58 EXAMINATION MANUAL.
115.
1. If a man walk 11 yards in 5 seconds, how long will lie
be in walking a mile ?
2. A cubic foot of water weighs 62-1 pounds, and a room
18 feet 9 inches by 13 feet 4 inches is flooded to a
depth of 2 inches. What is the weight of water in
the room ?
3. Assuming that 3 hektars contain 35,881 square yards,
and that one hektar contains 10,000 square meters,
find the length of a meter in yards.
4. Add together 536.421, 53,642.1, 5.36421, and subtract
the result from 100,000.
5. If the price of candles 8J inches long be 18 cents for
a half-dozen, and that of candles of the same thick-
ness and quality 10* inches long be 22 cents a half-
dozen, which kind would you advise a person to buy,
and what would be the saving per cent if your
advice is followed ?
116.
1. Find the weight in kilograms of the air in a hall
23m long, 16m wide, and 10m high, the specific gravity
of air being 0.00129206.
2. A cubical block contains 9 cubic feet, 1029 cubic inches.
Find the number of square yards, etc., in its
surface.
3. A bar of metal weighing 100 ounces 16 dwts. is made
into coins, each weighing 1 ounce 8 dwts. How
many coins are there ?
4. A person investing in a 3 per cent stock received 3i
per cent interest on his money. What is the price
of the stock?
5. A bar of gold, weighing 196 pounds 10 ounces 10 dwts.,
is cased in lead, weighing 24 pounds 14 ounces.
Find the weight of the whole in Avoirdupois weight.
ARITHMETIC. 59
117.
1. A merchant buys 4000 bushels of wheat, one-fifth of
which he sells at a gain of 5 per cent, one-fourth at
a gain of 10 per cent, one-half at a gain of 12 per
cent, and the remainder at a gain of 16 per cent.
If he had sold the whole at a gain of 11 per cent,
he would have made $35 more. "What was the
cost of the wheat per bushel ?
2. If 1000 square yards of land produce a load of hay,
how many loads will 25 acres produce ?
3. Assuming 8000 meters to be equal to 5 miles, find the
number of square meters there are in an acre.
4. A person having a certain sum of money to invest finds
that an investment in 5 per cent stock at 11 7? will
yield him $29 more interest annually than an in-
vestment in 3 per cent stock at 92J. How much
money has he to invest ?
5. Find the simple interest on $281.63 at 3s per cent for
4 years and 2 months.
118.
1. A freight train is 8 miles ahead of an express that travels
at the rate of a mile in H minutes. 20 minutes
later the express runs into the freight train. At
what rate is the freight train running ?
2. A man bought 240 cows at Rotterdam, paying $71.50
for each. He paid -^ of their cost for their trans-
portation, and exchanged them for 299 horses which
he sold for $ 75 apiece. What did he gain per cent
on his expenditure ?
3. If a square field contain 10.24ha, find the length of its
side in meters.
4. Find the amount for $512 for 3 years at 6| per cent,
compound interest.
5. If a field containing 5i acres produces 112 bushels of
wheat, what is the area of a field which will pro-
duce 400 bushels of wheat at the same rate ?
60 EXAMINATION MANUAL.
119.
1, Multiply 4 acres 67 square rods 19 square yards 4
square feet 72 square inches by 27.
2, What is the weight of a cubic centimeter of water ? of
a liter of water? of a cubic meter of water? If a
cubic meter of gravel weighs 2.11 metric tons, what
is its specific gravity ?
3, If 7 men, working 16 days, can mow a field 1320 yards
long, and 880 yards wide, what will be the length
of the side of a field 1320 yards wide, which 4 men
can mow in 42 days ?
4, Divide 1.765 by 2470 to five places of decimals.
5, If 8 acres produce 220 bushels of corn, how much will
22 square yards produce ?
120.
1, If 3 acres of land cost $465.90, how much can be bought
for $6716.725?
2, From 0.315 of a gallon take 2.25 pints.
3, $19.68f is 2^ per cent of what sum?
4, A, B, and C rent a farm for $270. A puts 200 sheep
on it ; B, 150 ; and C, 100. After 6 months A sells
f of his flock to C, and 3 months later B sells f of
his to A. How much of the rent should each pay
at the end of the year ?
5, How many times a minute does the 'wheel of a carriage
turn, when the carriage is driven at the rate of
14km an hour, and the diameter of the wheel is 120cm?
ARITHMETIC. 61
121.
1, If a man walks llm in 5 seconds, how many kilometers
can he walk in an hour at the same rate ?
2, Find the cost of repairing a road 87 yards 1 foot 10
inches long, at the rate of $4 a rod.
3, A cask that weighs 236 pounds 4 ounces just sinks in a
square cistern of water, whose edge is 2 feet 6
inches. If the cask is removed, how far will the
water sink in the cistern, reckoning the weight of a
cubic foot of water to be 1000 ounces ?
4, A man paid $45.10, including a duty of 10 per cent, for
a watch. How much was the duty ?
5, If 19 men can build 38 yards of wall in 12 days, how
many will build 96 yards 2 feet 3 inches in 214-
' i?
122.
1, Find the amount of $875 at the end of 1 year and
3 months, at 4 per cent per annum, compound inter-
est, the 'interest accruing quarterly.
2, If 12 men build a wall 60 feet long, 4 feet thick, and
20 feet high in 24 days, working 12 hours a day,
how many men will it take to build a wall 100 feet
long, 3 feet thick, and 12 feet high, in 18 days,
working 8 hours a day ?
3, If the specific gravity of sea-water is 1.026, and that of
olive oil is 0.915, what is the weight of a hektoliter
of each in kilograms ?
4, What must be the length of an inner edge of a cubical
box which will hold 10 cubic feet ?
5, An agent, charging 2i per cent commission, receives for
his services $313. Find the amount of his sales.
62 EXAMINATION MANUAL.
123.
1. An agent received $5922 with which to purchase goods,
and is allowed 5 per cent commission on his pur-
chase. If the $5922 covers the cost of the goods
and his commission, how much was his commission?
2. How much per cent above cost must a man mark his
goods in order that he may take off 30 per cent
from the market price, and still make 30 per cent
on the cost?
3. If a pint contains 2&J cubic inches, how many pints are
there in a cubic foot of water ?
4. If 14 liters of water be poured into a vessel containing
' 6 liters of sulphuric acid, specific gravity 1.84, and
the mixture shrink to 19.944 liters, what is the spe-
cific gravity of the mixture ?
5. Find 0.015 of 17 acres 130 square rods.
124.
1. If 5 needlewomen can finish a certain quantity of work
in 10J- days of 9f hours each, how long would it take
3 needlewomen to do twice the same work, reckon-
ing 10 hours to the day ?
2. Find the square root of 0.196 to four places of decimals.
3. Find the greatest common measure of 837, 1134, and
1347.
4. A ship carries 5 chronometers, and estimates Greenwich
time by the mean time of the five. Two of them
lose respectively 39 seconds in 35 days, and 4.3
seconds in 6 days ; the others gain respectively 5
seconds a week, 1.3 seconds a day, and 23 seconds in
14 days. By how much will the estimated time be
in error after a cruise of 176 days?
5. How many square meters of surface will 240 sheets
cover, if the sheets are 303mm long and 195mm wide ?
ARITHMETIC. G3
125.
1, A bankrupt owes $5050. His assets are $378.75. How
many cents does he pay on a dollar ?
2, If 36 men dig a trench 72 yards long, 4 yards wide, and
3 yards deep, how many men will be required to
dig one 80 yards long, 4 yards wide, and 6 yards
deep in the same time ?
3, Eeduce to its simplest form the expression
3 of it of ?£- 1-1-
0± 0t * i
4, A person invests $6534 in 3 per cent stock at 90, and
on the stock rising to 91 transfers his stock to 3-J- per
cent stock at 93-J-. How is his annual income
affected?
5, Olive oil costs 60 cents a kilogram. What is the price
of a hektoliter, if the specific gravity of the oil is
0.914?
126.
1, The distance between two places measured on a military
map is 156mm. What is the actual distance between
the places if the map is made on the scale of 1 to
80,000 ?
2, How many horses will be required to plough 117 acres in
35 days, if 10 horses can plough 13 acres in 7 days?
3, If I buy 3090 yards of cloth at 92| cents per yard, and
sell the whole for $3205.87|, what is the gain per
cent?
4, Find the amount of $7123.13 at 4 per cent, for 2 years
and 3 months, compound interest.
5, How many bricks 81 inches long, 4i inches wide, 2s
inches thick can be stored in a building 17 2 yards
long, 10 yards wide, and 8J- feet high?
G4 EXAMINATION MANUAL.
127.
1. How many panes of glass 40cm by 80cm will be required
for the windows of a house if the total surface of
measurement of the glass in the windows is 203.52qm?
2. A 20 horse-power engine pumps 40 gallons of water
from a pit 100 yards deep in 3 hours. What quan-
tity of water will an engine of 35 horse-power
pump from a depth of 235 feet in 141 days, work-
ing night and day ?
3. A speculator buys 280 yards of carpet, expecting to
sell the whole at $1.38 a yard, and thereby make
15 per cent profit ; but 40 yards being ruined, what
did he gain or lose per cent by selling the remainder
at the expected rate ?
4. If a piece of land is bought for §3500, and a man who
owns -| of it sells % of his share for $800, how much
does he gain per cent by the transaction ?
5. Extract the cube root of 1.105507304.
128.
1. A tank is 1.50m wide, 3.20m long, and 80cm deep. How
many kilograms of alcohol, specific gravity 0.80,
will be required to fill it one-third full ?
2. How many men working for 11 cents an hour for 23
days of 9 hours can earn the same wages as 22 men
working for 11-J- cents an hour for 18 days of 9^ hours.
3. If goods cost $75.87-J-, at what price must they be sold
to gain 17^- per cent?
4. A can mow f of a field in 7| days, B can mow f of
the same field in 9J days. In what time can A and
B together mow the field ?
5. A train travels a certain distance in 4-f% hours at the
rate of 16|- miles an hour. How long will a train
going 19 J miles an hour take to travel the same
distance ?
ARITHMETIC. 65
129.
1. A rectangular sheet of tin of uniform thickness is 85cm
wide, 2.7m long, and weighs 536g. What is its
thickness, reckoning the specific gravity of tin at
7.3?
2. I pay for 180 yards of cloth at 92-J cents per yard, but
it is measured with a yard-stick -f of an inch short.
How much money does the seller unfairly take ?
3. What must a person have invested in 3 per cent stock
at 93^-, if a transfer of -f of his capital to 5 per
cent stock at 125 would increase his income $14.80?
4. If 20 shillings weigh 3 ounces 12 dwts. 12 grains, and
contain 5 dwts. lOij- grains alloy, how much pure
silver is there in a half-crown (2J shillings)?
5. Express by a common fraction the difference between
2.535 and 2.535.
130.
1. A, B, and C rent a field for $25.62. A puts in 15
sheep for 6 months, B 45 sheep for 8 months, C 81
sheep for 4 months. What should each pay toward
the rent?
2. The top of a building 236 feet high is reached by a
flight of steps, each 12cm. high. Find the number
of steps, if a meter is taken as equal to 3 feet Si-
inches.
3. How many ars of land in a strip lkm long and 7m wide?
4. An executor of an estate finds it encumbered with debts
to the amount of $4322.50 over and above its real-
ized value of $10,729.50. How many cents on a
dollar can he pay the creditors?
5. Extract the cube root of 437.245479.
66 EXAMINATION MANUAL.
131.
1. What fraction of a pound avoirdupois is a pound Troy,
and what fraction of an ounce Troy is an ounce
Avoirdupois?
2 *
3, Find the weight in kilograms of a bar of gold 10cm long,
30mm wide, and 25mm thick, its specific gravity being
19.36.
4, If $15 be gained on $360 in 8 months 15 days, what
sum will gain $21 in 1 year 6 months?
5, For how much must a man give his note to a bank, on
4 months at 6 per cent, to obtain $500?
132.
1, What sum will amount to $1104.75 in 3 years at 3£ per
cent, compound interest ?
2, What annual income will be produced by $13,000 in a
3 J per cent stock at 91 ?
3, If the circumference of a coach-wheel measures 17 feet
7.2 inches, how often will it turn round in travelling
8 miles 264 feet?
4, Keduce to its lowest terms -g-f|-J.
5, If a square meter = 1550.031 square inches, find to the
fifth decimal place the number of square centimeters
in a square inch, and the number of acres in a hektar.
ARITHMETIC. 67
133.
1, A tradesman's prices are 20 per cent above cost price.
If he takes 10 per cent off from the bill of a custo-
mer, what per cent profit does he make ?
2, If a man can do a piece of work in 77 hours, and a boy
can do the same work in 121 hours, in. how many
hours, minutes, and seconds can they do it, working
together ?
3, If the cost of papering a room 8J- yards long, 6f yards
wide, with paper 2 feet wide at 8 cents a yard be
$14.32, find the height of the room.
4, If 3 per cent more be gained by selling a horse for
$83.25 than by selling him for $81, what is the
cost of the horse ?
5, If a cubic yard = 0.76453cbm, find to the fifth decimal
place the number of cubic centimeters in a cubic
inch, and the number of sters in a cord.
134.
1, By selling out $4500 of 5 per cent stock at 112J, and
investing the proceeds in a 7 per cent stock, a per-
son increases his income by $168. 75. What is the
price of the 7 per cent stock ?
2, simplify 2fj x mn-
3, If a gram = 15.43235 grains, find to the fifth decimal
place the number of pounds Avoirdupois in a kilo-
gram and in a metric ton.
4, An article which costs $ 95.76 per cwt. of 112 pounds is
retailed at $1.08 a pound. If there is a waste of
5 per cent, what is the rate per cent of profit?
5, Find the square root of 0.1 to four places of decimals.
68 EXAMINATION MANUAL.
135.
1, Find the L.C.M.'of 7, 11, 21, 63, 91, 99, 117.
2, A plate of iron 137cm long, 643mm wide, 43.1mm thick
weighs 277.54kg. What is its specific gravity? -
3, If 135 men can dig a trench 48 yards long, 1 foot 3
inches wide, 3 feet 9 inches deep, in 5 days of 6
hours, how many men will be required to dig a
trench 90 yards long, 2 feet 6 inches wide, 3 feet
deep, in 27 days of 10 hours ?
4, A man has £ 10 13 s. 4 d. a week in rents. His tenants
cheat him out of y1-^ of his rent ; he pays 4 d. in the
pound for collection, and 9& d. in the pound for
taxes. How much a week has he to spend ?
5, Divide 4900 by 0.07, multiply the quotient by 0.63, and
divide the result by 0.049.
136.
1, If -f% of a cargo be worth $ 750, how much is -£$ of -f$ of
it worth?
2, A parcel of 5 pounds 7 ounces is carried 120 miles for
40 cents. How much will it cost to carry 16 pounds
5 ounces a distance of 90 miles at the same rate-?
3, If a meter = 39.37043 inches, find to the fifth decimal
place the number of centimeters in an inch, and the
number of kilometers in a mile.
4, Find the cube root of 7.6 to four places of decimals.
5, A person, by selling an article which cost 60 cents a
pound at 67 -J cents a pound, makes 5 per cent more
profit than if he had sold the whole for $267.67£.
Find the amount sold.
ARITHMETIC. 69
137.
1, Find the sum of % 7T\, 8^, 19, 10|i 12f .
2, A garrison of 1000 men, provisioned for 60 days, was
reinforced at the end of 18 days, and the provisions
were exhausted at the end of 30 days from that
time. Of how many men did the reinforcement
consist?
3, Two engines 40 miles apart ars approaching each other
at the rates of 25 and 35 miles an hour. Determine
the time and place of their meeting.
4, Find the simple interest on'$ 2187.50 for 219 days at 4*
per cent, reckoning 365 days to the year.
5, Find the area of a field 225m long, 100m wide. Express
the answer in hektars and ars.
138.
1, From 2000 subtract 852.2534, and divide the remainder
by 16.38.
2, If I invest $1200 in 3 per cent stock at 72, what is my
income, and what rate per cent do I get on my
investment?
3, If $36 worth of bread will be sufficient for 12 men 8
months, when corn is $ 1 per bushel, how many men
will require $100 worth of bread for 12 months,
when corn is $ 1.311 per bushel?
4, Find the time required to travel 3Pm 150m, at 1 minute
28 seconds a kilometer.
5, A broker receives $6150 to invest in cotton at 10i cents
a pound. His commission is 21 per cent for buy-
ing. How many pounds of cotton can he buy ?
70 EXAMINATION MANUAL.
139.
1. A collector's commission for collecting taxes, at H per
cent, is $41.31. What is the sum collected?
2. How many yards of carpeting 2 feet 8 inches wide will
be required for a floor 19 feet 7 inches long, 16
. feet 9 inches wide, if the strips run across the
room, and 2| yards are allowed for waste in match-
ing the pattern.
3. Find the value of a carboy (171) of sulphuric acid,
specific gravity 1.841, at 5 cents a kilogram.
4. If the ratio of the circumference to the diameter be
3.1416, find the diameter of a cylinder whose cir-
cumference is 16J feet.
5. How much more income will a person have by trans-
ferring $3975 of 3 per cent stock into 3|- per cent
stock, if the price of the 3 per cent stock is 93f ,
and of the 3J per cent stock 99f?
140.
1. Find the bank discount upon a note of $587, given
Feb. 29, 1880, for 3 months, and discounted April
30 at 6 J per cent.
2. Determine the number of cubic meters in a box 2 yards
long, 1 yard wide, and 2} feet deep, reckoning a
cubic yard = 0.76453cbm.
3. A reservoir is 24 feet 8 inches long, and 12 feet 9 inches
wide. How many cubic feet of water must be
drawn off to make the surface sink one foot ?
4. Divide 200 acres into four parts proportional to the
numbers 50, 35, 80, and 9.
5. Extract the cube root of 946,966,168.
ARITHMETIC. 71
141.
1. If coffee worth 66 cents, 77 cents, and 57 cents per
pound be mixed in equal quantities, and the mix-
ture sold at 702 cents per pound, what is the gain
or loss per cent ?
2. If 3 men, working 11 hours a day, can reap 20 acres
in 11 days, how many men, working 12 hours a
day, will reap a field 360 yards long and 320 yards
broad, in 4 days?
3. Find in yards the side of a square field containing 15
acres 109 square rods 3 square yards.
4. A man walks 10J miles the first day, 16£, 18 J, 27|,
21J- miles on the four following days respectively.
He then returns home by the same road in four days.
What was his average daily walk on his way home
and on his whole journey ?
5. How many tons of air, specific gravity 0.00129206, in a
space 70m by 50m by 35m ?
142.
1. By selling a horse for $64.75, 1 lost 7J per cent. What
per cent should I have gained by selling him for
$73.50?
2. The proceeds of the income tax at 5c?. in the pound
was equal to £5,250,000, How much would the
proceeds be, if the tax was 5 per cent ?
3. Find the number of liters in a vat 2m by 75cm by 50cm.
Also find the weight in kilograms of sulphuric acid,
specific gravity 1.840, required to fill it.
4. One horse goes 1} miles in 2 minutes 26 seconds ;
another, If miles in 3 minutes 36 seconds. How
much per cent does the first one go faster than the
second ?
5. Find the greatest common measure of j-f , 2J, 4, and 5}.
72 EXAMINATION MANUAL.
143.
1, Find the least common multiple of y1^-, 2-J-, 5, 6J, and -fa.
2, By selling goods for $116.85 I lose 5 per cent. For
what should I sell them to gain 3| per cent?
3, A spends £ of his money, then i of the remainder, and
then J of what he has left. He finally has $25.
How much had he at first ?
4, Make out a bill and receipt it, and show how much
change there will be from a twenty-dollar bill :
3J cwt. of coal, at 21 cents a cwt. ; 13 pounds of
cheese, at 15J cents per pound; 2f pounds of
tea, at 80 cents per pound ; 17 pounds of sugar,
at 11 cents per pound; 3? yards of flannel at
47 cents per yard ; 29 yards of gingham at 21 J
cents a yard.
5, Find the number of sters in a pile of wood 4.50m long,
2m wide, and 2.50m high.
144.
1, If 7 men earn $31 in 9^ days, how much will 17 men
earn in 2Gf days ?
2, Two persons have each a capital of $12,000. The one
invests in 3 per cent stock at 90f ; the other in 5
per cent stock at 1031 . What is the difference in
their incomes ?
3, If I buy 14 sheep for $157.29, and sell 6 of them for
$7.20 each, for how much a head must the re-
mainder be sold, that I may gain 4 per cent on the
whole ?
4, Find the G.C.M. of 1908, 936, 630, 21,294, 306.
5, A hektoliter of rape-seed weighs 63kg, and 321 of oil can
be extracted from it. How many kilograms of the
seed will it take to make a hektoliter of the oil ?
ARITHMETIC. 73
145.
1, The volume of a cube is 2 cubic yards 14 cubic feet 145
cubic inches. Find its edge, and also its diagonal
to two places of decimals.
2, By using false weights a grocer receives 17 cents instead
of 16 cents. Find the number of ounces in his false
pound, and his gain per cent.
3, A railway pays 3i per cent dividend. At what price
will its shares give 4? per cent to a purchaser?
4, A person sells his 3 per cent stock for 73£, and buys
with the proceeds 3-i per cent stock at 81 T, thereby
increasing his income $4.50. How much 3 per cent
stock has he ?
5, Reduce 150 hektars to acres, supposing a square meter
equal to 1.196 square yards.
146.
1, A profit of $127.60 is made by selling 2552 pounds of
butter at 45 cents a pound. Find the cost per
pound and the gain per cent.
2, For what sum must I insure goods worth $2192 at 2£
per cent, so as to cover their value and the premium
paid?
3, If $11.20 worth of paper is required for a room 25 feet
3 inches long, 19 feet 9 inches wide, and 12 feet high,
when the paper is f of a yard wide, find the cost of
each yard 'of paper.
4, Find the price of paving .a courtyard 25.34m long,
18.36m wide, at $1.08 per square yard. (Square
meter = 1.196 square yards.)
5, Find within an inch the diagonal of a square field con-
taining 3£ acres.
74 EXAMINATION MANUAL.
147.
1, .Find the difference between 30 chains, 15 links, and
126 rods. Express the answer in yards and decimal
of a yard.
2, Find the number of feet, board measure, in a stick of
timber 15 inches square and 32 feet long.
3, A watch is 10 minutes too fast at noon on Monday, and
loses 3 minutes 10 seconds a day. Find the time
indicated by the watch when the true time is a
quarter past ten on the Sunday morning following.
4, Find the cost of 5 acres 127 square rods 88 square
yards at $161.33^ per acre.
5, Find the weight in metric tons of a block of stone
12.37m long, 7.14m wide, 83cm thick, if the specific
gravity of the stone is 2.5.
148.
1, From two places which are 154 miles apart two persons
set out to meet each other, one walking at the rate
of 3 miles in 2 hours, the other 5 miles in 4 hours.
In how many hours will they meet ?
2, A regiment was reduced to 520 men after engaging in
two battles, in the first of which it lost 1 man in
every 25, and in the second -fg of the remainder.
How many men were there at first ?
3, Find the cube root of 11 to four places of decimals.
4, Frenchmen, on the average, consume yearly 1160g of coffee
and 9g of tea; and Englishmen, 473g of coffee and
1679g of tea. If tea be 3s. and coffee Is. 8d. per
pound, and a franc be worth 10^ d., find in francs the
value of an Englishman's consumption above a
Frenchman's.
5, Find the value of 2 pounds 5 ounces 8 dwts. 4 grains
of silver at $ 125 an ounce.
ARITHMETIC. 75
149.
1. Find the cost of 30 3-inch planks, 24 feet long and 11
inches wide, at §15 per M.
2. An agent sells 2200 barrels of flour at $4.50 a barrel,
and charges 2=} per cent commission. He invests
the proceeds in steel at I? cents a pound, charging
!-•>- per cent commission. What is his entire com-
mission ?
3. Two circular gold plates, each 1 inch thick and 6 arid
8 inches in diameter respectively, are melted into
one plate of the same thickness. Find the diameter
of this plate, knowing that the area of a circle
varies as the square of its diameter.
4. Find the cube root of 0.25 to four decimal places.
5. How many miles will be travelled in 1 hour 28 min-
utes 21 seconds at the rate of 50km an hour ?
150.
1. An agent sells 1000 barrels of flour at $5.50 a barrel,
and charges 2 2 per cent commission ; expenses for
freight, etc., are $500. With the net proceeds he
buys sugar at GT cents a pound, charging 2£ per
cent commission. How much sugar does he buy?
2. Find the number of feet board measure in 25 joists,
each 6 inches by 4 inches, and 14 feet long.
3. Find the value of 3 pounds 8 ounces 16 dwts. 12 grains
of gold at £3 17s. lOic?. per ounce.
4. A pond whose area is 3 acres is frozen over with ice
to the uniform thickness of 6 inches. If a cubic
foot of ice weighs 896 ounces, find the weight of
ice on the pond in long tons.
5. A jar full of water \veighs 1.325kg ; filled with mercury,
it weighs 12.540kg. What is the capacity of the
jar and its weight? The specific gravity of the
mercury is 13.59.
EXAMINATION PAPERS IN ARITHMETIC.
BOWDOIN COLLEGE, BRUNSWICK, ME.
Examination for Admission, June, 1883.
1. Find the difference between 0.0000005 and 0.00005.
2. Change 0.03125 to a common fraction in its lowest terms.
3. If the year is considered 365.25 days instead of
365.242264, how great will the error be in 1880
years ?
4. The dividend is 7423.973, the quotient is 12.130, and
the remainder is 0.413. What is the divisor?
5. What is the cost of 60.5 tons of coal when 0.9 of a ton
cost 1 6.66?
6. Find the square root of 6.7081. Of 0.004 to the nearest
ten thousandth. Of ^V
7. Keduce 6453m to kilometers. 4.15m to centimeters.
6.451 to milliliters. How many decigrams does a
dekaliter of pure water weigh ?
II.
DARTMOUTH COLLEGE, HANOVER, N.H.
Entrance Examination, June, 1883.
1. Find the G.C.D. of 66, 308, and 506.
2. Divide || by Ltl
78 EXAMINATION PAPERS.
3. Give the value of the kilometer in feet ; of the kiloliter
in gallons ; of the kilogram in pounds.
4. If there is a gain of 12-*- per cent on tea at 90 cents per
pound, what would be the gain per cent at 84 cents
per pound?
I 1 23
5. Find -*! — —f — to four decimal places.
il U.Uu^jO
III.
BROWN UNIVERSITY, PROVIDENCE, R.I.
Examination for Admission, June, 1883.
1. Reduce -J- of 6 per cent of 1.05 ~- -fa of T7-g- to the simplest
form.
2. If 17 men can reap a field in 9 days, how long would it
take to reap half of it if 5 men refuse to work ?
3. A man bought 200m of cloth in France at 16J francs a
meter ; he paid 12J cents a yard for duty and
freight, and sold it in Boston at $4.62|- a yard.
What was the gain ? (1 franc = 19.3 cents.)
IV.
MASS. INSTITUTE OF TECHNOLOGY, BOSTON, MASS.
Entrance Examination, June, 1882.
1. Find the L.C.M. of 105, 476, and 306.
2. A grocer makes a mixture of which 21.5 pounds contains
\ pound of rye, 12 pounds of wheat, 5 pounds of oats,
and 4 pounds of barley. How much of each ingre-
dient will be contained in 100 pounds of the mix-
ture?
ARITHMETIC. 79
3. Reduce to a decimal fraction — 3— . and from it subtract
0.01 of I. a°*>
4. In how many days will $3245 gain $80 at 7 per cent,
simple interest ?
5. Find the G.C.D. of 119 and 231.
6. Find the cube root of 0.012326391.
7. How many liters are contained in a cubical box 13
inches long, 13 inches wide, and 13 inches deep on
the inside ? (Given that lm = 39.37".)
8. How many grams of distilled water will such a box
contain ?
V.
Entrance Examination, Sept., 1882.
1. Reduce -S—^5 to its simplest form.
9T + 5¥
2. Reduce —? to a decimal fraction.
3. A and B together have $136, and -f of A's money is
equal to -| of B's. How much has each?
4. At $6.25 per ton, how many tons of coal can I buy for
$1000, and allow 2-|- per cent commission?
5. Find the square root of 0.00028562 to ten-thousandths.
6. Floor 10m by 6.5m, carpet 90cm wide ; .find cost of carpet
at $1.25 per meter.
7. In a parallelogram, given base — 640dkm, altitude =
180dkm ; find area in hektars.
8. A cylindrical vessel lm high is made of sheet-iron 2cm
thick, and holds 1001. What is its outer diameter ?
80 EXAMINATION PAPERS.
VI.
HARVARD COLLEGE, CAMBRIDGE, MASS.
Examination for Admission, June, 1883.
1. Find the difference between 3J X 6ff and £i&
2. A field is SS-/^ rods long, and 37? rods wide. Find its
area in acres and square rods. (Acre = 160 square
rods.)
3. Find all the factors common to 1001 and 616.
4. The distance from Boston to Albany is 320km. Find the
distance in miles, assuming the meter to equal 3-^-
feet.
5. A man, travelling 9 hours a day, goes 234 miles in 15
days. How far can he go in 30 days, travelling 8
hours a day ?
VII.
YALE COLLEGE, NEW HAVEN, CT.
Examination for Admission, June, 1883.
1. Divide 82.1 by 41, 8.21 by 0.41, and 0.821 by 410.
Carry the result in each case to four decimal places.
2. Find the value to three decimal places of
o TV -A T2 1 i 133
3. Divide * X by — -
4. Some sugar is adulterated as follows : -fy is worth 8
cents per pound, % is worth 10 cents per pound, y2-^
is worth 12 cents per pound, and the remainder, 33
pounds, is sand. What is the mixture worth per
pound ?
ARITHMETIC. 81
5. Bank stock which sells at 170 pays an annual dividend
of 12 2 per cent. What rate of interest does a buyer
receive ?
6. Find the depth in meters of a cubical cistern which has
a capacity of 30,000*. Give the. result to three deci-
mal places.
VIII.
SHEFFIELD SCIENTIFIC SCHOOL, NEW HAVEN, CT.
Entrance Examination, June, 1883.
1. Find the G.C.D. of 36,864 and 20,736.
2. Multiply f of jjf by f of i.
3. (i.) Give the table of metric weights.
(ii.) A cubical cistern holds 1331kg of water ; what is the
length of an inner edge ?
4. Divide 67.56785 by 0.035, and multiply the result by £.
Explain the position of the decimal point after
'division.
5. How much money should be received on a note of
$ 1000, payable in 4 months, discounting at a bank
where the interest is 6 per cent ?
6. If a man travel 117 miles in 15 days, employing only
9 hours a day, how far would he go in 20 days,
travelling 12 hours a day ?
7. Extract the square root of 10 to five places.
IX.
Entrance Examination, Sept., 1883.
1. (i.) Select the prime numbers between 50 and 100.
(ii.) What is the least number that can be exactly
divided by ^ 2£, 5, % and ^?
82 EXAMINATION PAPERS.
2. Reduce 0.00096 to its simplest equivalent common frac-
tion.
3. 7465 is 33£ per cent of what number ?
4. A broker bought 84 shares of railroad stock at 19 per
cent discount. He sold 35 shares at 27J per cent
discount, and the balance at 8 per cent discount.
Did he gain or lose, and how much?
5. Calculate the cube root of 3.7- to five decimal places.
6. Give the approximate value of the meter in feet ; of the
kilogram in pounds Avoirdupois.
7. Find the weight in kilos of 15 gallons of water.
X.
AMHERST COLLEGE, AMHERST, MASS.
Examination for Admission, June, 1883.
1. From 10 take six millionths.
2. Divide 3.6412 by 400.
3. Reduce 0.0625 to a common fraction in its lowest terms.
4. Find the G.C.D. of 1235 and 1495.
5. How many rods of fence will be required to enclose 640
acres of land in a square form?
6. What is the difference in time between Boston and San
Francisco, the longitude of the first being W. 71° 3'
30", and the second, W. 122° 24' 40"?
7. Sold a pair oxen for $175, and gained 5 per cent ; what
per cent would I have gained if I had sold them for
$200?
8. If 6 men in 15 days earn $135, how many dollars will 9
men earn in 18 days ?
9. What is the weight of 27hl of water?
ARITHMETIC. 83
XI.
WILLIAMS COLLEGE, WILLIAMSTOWN, MASS.
Entrance Examination, June, 1883.
1. Reduce -f- to a decimal, and extract the square root to
three places.
2. How long must the side of a square lot be to contain
one acre of ground ?
3. Find the interest on $1385.50 for 23 days at 7 per cent.
'4. Reduce 532km to miles.
XII.
TUFTS COLLEGE, COLLEGE HILL, MASS.
Examination for Admission, June, 1881.
1. Find the L.C.M. of 108, 217, 54, 31.
2. Find the prime factors of 927, 342, 861. With these
prime factors get the Gr.C.D of the given numbers.
3 Reduce the fraction
JLofH 2'of.I
12 f 4 11
4. If the rate of discount is 5 per cent per annum, how
much can be obtained on a note for $600, payable
in 4 months, discounted at a bank ?
5. If from the retail price of a book 20 per cent is deducted,
and a discount of 10 per cent is made on the bal-
ance, and then the book sells for $1.33, what is the
retail price ?
6. What is the meter ? Name its subdivisions. In 9780m
how many kilometers ? Give the units of volume in
the metric system; also, of weight.
7. What weight of mercury will a vessel contain whose
capacity is 20ccm, the mercury being 13.5 times as
heavy as water?
84 EXAMINATION PAPERS.
XIII.
TEINITY COLLEGE, HARTFORD, «CT.
Examination for Admission, June, 1883.
1. From the sum of of and 4-J subtract 6^-, multiply the
difference by f of J-J of 88, and find what fraction
the product is of 999.
2. Find the amount of $ 342.42, from Feb. 5, 1ST. , to March
15, 1881, with interest at 7 per cent; and reduce it
to pounds sterling ?
3. What is the weight of water in a tank, if it would take
98 minutes to empty it, at the rate of 8.71 a minute ?
If it were filled with oil at $18.75 a hektoliter,
what would the contents be worth ?
XIV.
WESLEYAN UNIVERSITY, MIDDLETOWN, CT.
Examination for Admission, June, 1883.
\ 3 ,5
1. Express the value of - - - - - - exactly as a
decimal.
2. What was the amount due January 15, 1883, on a note
for §175, dated April 1, 1882, bearing 5£ per cent
interest ?
3. A merchant sold \ of a certain lot of goods at a gain of
18 per cent, * at a loss of 5 per cent, and the re-
mainder at half cost. Did he lose or gain? What
per cent ?
4. Extract the square root of 0.01952, carrying the result to
four places of decimals.
ARITHMETIC. 85
5. What is the cost of digging a cellar 3dkm wide, 5dkm 4m
long, and 2m 6dcm deep, at the rate of 50 cents a
stere ?
6. Two men undertake to do a piece of work for $6.00.
One could do it alone in 5 days, the other in 8 days.
With the assistance of a boy, they finish it in 21
days. How should the money be divided ?
XV.
CORNELL UNIVERSITY, ITHACA, N.Y.
Entrance Examination, June, 1882.
1. Define : an abstract number, the prime factors of a
number, a quotient, a mixed number, cube root,
percentage, bank discount, compound interest.
2. Get the sum of five, five-tenths, thirty-seven thousandths,
one-thousand millionths, XIX, MDCCCLXXXI,
o.is.
3. Find all the common divisors of 225, 2025, 8100.
4. Divide A of 91 by -^ of 637.
5. What is the amount, at compound interest, of $500 for
2 years 6 months, at 7 per cent ?
6. Get the square root of 530 to three decimal places, and
give the reasons for the several steps in the work.
7. Give the common and the metric tables for liquid meas-
ure ?
8. How many liters in 10 gallons, 3 quarts, 1 pint, 3 gills,
the gallon being 231 cubic inches, and the meter
39.37 inches?
86 EXAMINATION PAPERS.
XVI.
STEVENS INSTITUTE OF TECHNOLOGY, HOBOKEN, N.J.
/Specimen Entrance Examination Paper.
1. What is a prime number?
2. Find the L.G.M. of 36, 48, and 72. Why can it not be
found by first dividing by 36 ?
3. Find the G.C.D. of 120, 228, and 720.
4. If John sells a book for 110 cents, and thereby loses 12
per cent, what did the book cost him ?
5. Find the square root of 0.4 to three places.
6. Find the cube root of 0.8.
7. Multiply 3 hundredths by 300 -thousandths.
8. Divide 300 thousandths by 3 hundred-thousandths.
XVII.
MADISON UNIVERSITY, HAMILTON, N.Y.
Entrance Examination, June, 1882.
7 1515
21 5 85 — 4 002
1. From - — — subtract '—— - - - , obtaining the
result to three places of decimals.
2. Extract the square root of 102.002 to two places of
decimals.
3. What is the interest on 51584 for 1 year, 2 months, and
20 days at 7 per cent ?
ARITHMETIC. 87
XVIII.
VASSAR COLLEGE, POUGHKEEPSIE, N.Y.
Specimen Examination Paper for Admission.
1. Find the greatest common divisor of 256, 480, and 1296.
2. What is the value of (^^- + 16 ~ '8 - |) X 7TV ?
3. What is the sum of '» °f^ and f-^A?
4. Divide two thousand five hundred one and four-tenths
by four thousand one hundred twenty-five ten-
millionths. Divide 1.29136109 by 184.3, and write
the quotient in words.
5. A gentleman bought a yacht for $3500, and sold it at
a loss of 20 per cent ; the buyer sold it at a gain of
25 per cent ; what did the latter receive for it ?
6. What sum of money, at 10 per cent compound interest,
will amount to $8651.50 in three years?
7. A cistern is 4m long, 24dm wide, and 80cm deep. How
much water will it hold in cubic meters? In liters?
8. The longitude of St. Petersburg is 39° 19' east ; of New
York 74° 41' west; when it is one o'clock in the
afternoon at St. Petersburg, what time is it at New
York?
9. Extract the square root of 4.932841.
88 EXAMINATION PAPERS.
XIX.
COLLEGE OF NEW JERSEY, PRINCETON, N. J.
Examination for Admission, Sept., 1883.
2. State and demonstrate a rule for finding the greatest
common divisor of any set of integers ; and make
use of it to find the greatest common divisor of
847, 1331, and 1573.
3. Prove that any circulating decimal may be reduced to
a rational fraction. To what fraction is the circu-
lating decimal 0.57 equal ?
4. Two bodies let fall at different instants from the same
point are found, \|-^ - seconds after the latter of
\ 981
them started, to have fallen, the one 25m, the other
100m. These distances being to one another as the
squares of the times during which the bodies have
been falling, how many seconds must the one body
have started before the other ?
5. What per cent is 3 of 6 ? What is the number to which
if 2 per cent of itself be added the sum is 516 ?
6. The amount of a certain principal at a certain rate of
interest for 6 months is $949.76, and for 1 year at
the same rate is $1003.52. Required the rate per
cent and principal.
7. The dimensions of a room are, length 4m ldm, breadth
3m 2cm, and height 3m lmm. Find its cubical contents
(in kilosteres) and the area of its walls (in centares),
ARITHMETIC. &9
XX.
JOHN C. GREEN SCHOOL OF SCIENCE, PRINCETON, N. J.
Entrance Examination, Sept., 1883.
1. Simplify |±|f.
2. Find the G.O.M. of 252, 315, 420, and 504.
3. Find the square root of 0.434 to three decimals.
4. If I sell goods at 4 per cent commission, and receive
$60, what amount have I sold?
5. Find the edge of a cubical can which will hold 27.57kg
of sulphuric acid, whose specific gravity is 1.8.
XXI.
UNIVERSITY OF PENNSYLVANIA, PHILADELPHIA, PA.
Examination for Admission, June, 1882.
i.
n a- r* 5i-0.042-2.
2. Simplify -
3. Simplify 0.6 of 3.3 + -of 17+0.4 of 5.75-
2-625 2.095238
4. Extract the square root of 5683 to four places of decimals.
5. A rectangular piece of ground is 32m 7dm long, and 19™
5cm broad. Find the cost of enclosing it with a path
lm 5dm broad, at 3 francs 5 centimes a square meter.
(i.) Path outside of the ground ; (ii.) path part of
ground.
6. A house cost $5000, and rents for $25 a month, with
$25 to pay annually for repairs and $50 for taxes ;
what is the difference in the income from this and.
from the same money invested in 6 per cent stock
at 96?
90 EXAMINATION TAPERS.
XXII.
UNIVERSITY OF MICHIGAN, ANN ARBOR, MICH.
Examination for Admission, June, 1883.
1. Reduce - - to a simple fraction, and state the pro-
(>
cess and principles.
2. Reduce 2 years 5 months 12 days to years and decimals
of a year.
3. Extract the square root of 0.4.
4. Give the denominations used in linear measure in the
metric system.
5. How are the measures of capacity and of weight in the
metric system related to the linear measures ?
XXIII.
LAKE FOREST UNIVERSITY, LAKE FOREST, ILL.
Entrance Examination, June, 1882.
1. Add ten thousand and one millionth ; four hundred
thousandths ; ninety-six hundredths ; forty -seven
millions sixty thousand and eight billionths.
2. Define integer, compound number, the power of a num-
ber, a fraction. How many classes of fractions ?
3. Find the interest of $375.75 for 4 years 5 months and
25 days, at 4? per cent.
4. If the wages of 72 men for 5 days is $450, how many
men may be hired for 12 days for $540?
5. A can build a wall in 18f. days, B in 3H days; how
long will it take both together to build it ?
ARITHMETIC. 91
6. What is the present worth of $3471.50, due 3 months
and 9 days hence, at 7 per cent ?
7. What is the interest at 4J per cent of $360.45, from
July 4, 1873, to November 3, 1875, allowing a credit
of $75, paid October 5, 1874?
8. Reduce to equivalent fractions, having a common
denominator, f of f , 2f , 5f , f of £ of 3 J.
9. On what principal at 7 per cent, in 1 year and 3 months,
will the interest be $15.40?
10. Extract the cube root of 225,866,529.
XXIV.
EDUCATION DEPARTMENT, ONTARIO.
Examination for Admission to High Szhools, June, 1883.
1. What is the object of division ? Write down the rela-
tion connecting the divisor, dividend, quotient, and
remainder.
Divide one hundred and eight billion four hundred and
nineteen million seven hundred and sixteen thou-
sand and one, by eighteen million seven hundred
and forty-eight thousand and five.
2. Find, by " casting out nines," whether the following is
correct: 349,751 X 28,637 = 10,015,819,397.
Find the weight of 500,000 bricks at 4 pounds, 2 ounces
each, and the cost, in dollars and cents, at 27s. Qd.
a thousand, allowing 4s. 2d. to make a dollar.
3. A merchant received from England the following in-
voice in sterling :
92 EXAMINATION PAPERS.
375 tons iron plates, at £8 15s. Grf. ; 107& tons bar
iron, at £11 14s. ; 10 tons bulb iron, at £10 10s. ;
17 tons T iron, at £15 10s. ; 48 tons steel, at £18
7s. 6 d. ; 15 tons rivets, at £ 11 1 s. Find the amount
of this invoice in Canadian currency, allowing the
shilling sterling to be equal to 24-^ cents.
4. At $1.75 per rod, what will it cost to fence a piece of
land 63.5 rods long, and 27.75 rods wide ?
5. Simplify 1 - 1 + J¥ - drtv + THfcr = J and
5.81 — 2.5^ 441
of 32 of 0.45 3760*
6. Gunpowder is composed of nitre, charcoal, and sulphur,
in the proportion of 15, 3, and 2. A certain quan-
tity of gunpowder is known to contain 20 cwt. of
charcoal ; find its wreight, and also the weight of
nitre and of sulphur it contains.
7. Bought 360 gallons of wine at §2.60 a gallon ; paid for
carriage, §17.20, and for duties, $86.50. If -^ of it
be lost by leakage, at what price must the remainder
be sold to gain $50 on the whole transaction?
8. Find the interest on a note for $257.81, dated January
3, 1883, and paid April 6, 1883, at 8 per cent per
annum.
9. The length of a second's pendulum is 39.37079 inches ;
if 64 French meters are equal to 70 yards, by what
decimal of an inch will the length of a second's pen-
dulum differ from one meter ?
10. At what times between 4 and 5 o'clock are the hands
of a clock (i.) coincident? (ii.) at right angles?
ARITHMETIC. 93
XXV.
EDUCATION DEPARTMENT, ONTARIO.
Examination of Third Class Teachers, July, 1883.
1. Add together -f- of £13, £ of -^ of f of £2 12s., and £
'0f9rf.
Reduce 13s. 4J c?. to the decimal of 19s. Gel.
2. Find by practice the value of 8596 pounds, at £10 18s.
*l\d. each.
3. A person borrows §500 on April 10, and on June 22
pays his debt with $510.20. At what rate per cent'
per annum was he charged interest?
4. A man having a certain sum of money to invest has an
opportunity of purchasing 7 per cent stock at 95,
but delays until it has risen to 110. What per cent
is his income less than if he had purchased at the
fipst price ?
5. At an international exhibition, one country was awarded
5 gold, 9 silver, and 11 bronze medals; and an-
other, 4 gold, 15 silver, and 10 bronze. Find a
ratio of values for such medals that these countries
may be regarded as equally fortunate.
6. In a box there is a certain number of- sovereigns, three
times as many guineas, and twice as many marks
(13s. 4<f.) as guineas. The entire 'amount in the
box is £815. How many coins of each kind are
there ?
7. Find when first after 2 o'clock the hour and minute
hands of a clock make an angle of 60 degrees with
. each other.
94 EXAMINATION PAPERS.
8. For each of three succeeding months the population of
a north-west town rose 50 per cent ; and at the end
of the third month was 2700. What was the popu-
lation at the beginning of the time ?
9. Leap year is omitted once in every century, except
those centuries whose number is divisible by 4.
What is the average length of a year ?
10. A cube is formed of a certain number of pounds Avoir-
dupois of a substance, and the same number of
pounds Troy of the same substance. What propor-
tion will a side of the cube bear to a side of a cube
formed of the same number of pounds as before, but
all Avoirdupois? (175 pounds Troy = 144 pounds
Avoirdupois.)
XXVI.
EDUCATION DEPARTMENT, ONTARIO.
Examination of Second Class Teachers, July, 1883.
1. Prove that l of f = ^V
Simplify (2-f- of 3TV)-f *-(H of 1A)-(1| of 4T of A)-
2. The pendulum of one clock makes 24 beats in 26 seconds ;
that of another, 36 beats in 40 seconds. If they
start at the same time, when first will the beats
occur together?
3. A can do as much work in 4 hours as B in 6 ; and B in
3|- as C in 5. A does half a certain piece of work
in 12 hours; in what time can it be finished by B
and C, working separately equal times, and C suc-
ceeding B ?
4. A note for $500, made March 9, at 3 months, is dis-
counted April 11, at 8 per cent. What is received
for the note ? (True discount.)
ARITHMETIC. 95
5. The unclaimed dividends on a certain amount of stock
which pays 6 per cent per annum amounted in 3
years to $1152. The stock was sold at a discount
of 12-1- per cent On its par value. What sum was
realized ?
6. Teas at 3s. 6c?., 4s., and 6s. a pound, are mixed to pro-
duce a tea worth 5s. a pound. What is the least
integral number of pounds that the mixture can
contain ?
7. A man buys 150 pounds of sugar, and, after selling 100
pounds, finds he has been parting with it at a loss
of 5 per cent. At what rate per cent advance on
the cost must he sell the remaining 50 pounds that
he may gain 10 per cent on the entire transaction ?
8. Ea'ch member of a pedestrian club walks as many miles
as there are members in the club, and the expense
of the trip is for each member as many pence per
mile as there are members in the club. The total
expense is £50 13s. lid. How many members are
there ?
9. The hour, minute, and second hands of a watch are on
concentric axes. When first after 12 o'clock will
the direction of the second hand, produced back-
wards, bisect the angle between the hour and the
minute hands ?
XXVII.
EDUCATION DEPARTMENT, ONTARIO.
Examination of Third and Second Class Teachers, July, 1883. —
Mental Arithmetic.
1. A hall- way is 90 inches wide, and takes 25 square
yards of oil-cloth to cover it. How long is it ?
96 EXAMINATION PAPERS.
2. A gentleman travels from Toronto to Montreal and
back. He goes at an average rate of 33 miles per
hour, and returns at an average of 30 miles per
hour, and he finds that he occupied one hour longer
in returning than in going. Find the distance from
Toronto to Montreal.
3. A can do a piece of work in 7 days, and B can do it in
8 days. A works at it for 2£ clays, and B works at
it for 3 days. C then finishes it in 3f days. In
how many days could C have done the whole wrork
alone?
4. By selling an article for §21 I would lose 12i per cent.
At what should I sell it in order to gain 12«} per
cent?
5. A merchant marked his goods at an advance of GO per
cent on cost. He gave one of his customers a dis-
count of 15 per cent off the marked price. What
was his gain on §6.80 received from that customer?
6. How much stock must I sell out of the 3 2 per cents, at
84, to enable me to buy $7700 4 per cent stock, the
value of the stock being proportional to the divi-
dends they pay ?
XXVIII.
EDUCATION DEPARTMENT, ONTARIO.
Examination of First Class Teachers, July, 1883.
1. Define a recurring decimal, and classify the several
kinds.
Prove, in any way, a rule for converting a mixed circu-
lating decimal into its equivalent vulgar fraction,
and apply your rule to convert 0.1013257.
ARITHMETIC. 97
2. Perform the operations here indicated, employing con-
tracted multiplication and division, and retaining 6
, 0.3372+0.03172 n nnr
decimals throughout : ^ '- 0.0004675.
0-140.00
3. In the expression, " 6 per cents are at 103," explain
fully what is meant.
A person sells a certain amount of 5 per cents Tor 86,
and invests in the 6 per cents at 103, and by so do-
ing changes his income by one dollar. Is the change
an increase or decrease ? How much stock does he
sell?
4. A man buys a note, drawn for 2 years at 6 per cent
interest, and which is now 6 months old, at 15 per
cent true discount. After keeping it 9 months, and
receiving one payment of interest, he sells it to a bank
at 8 per cent bank discount. What per cent does
he make upon his money while invested ?
5. A, B, and C, whose rates of walking are 3|, 4, and 5
miles an hour, respectively, walk on circular tracks
whose circumferences are 8, 10, and 15 miles, respec-
tively, and whose centres are in the same straight
line. At the same instant they start from points
on this line,. and on the same side of the centres.
Find (i.) when first they will be all on this line at
the same time ; (ii.) all at same time at the points
from which they started ; (iii.) whether they will
ever be all at the same instant at points on opposite
sides of the circles to the starting points.
6. I ead is 11.4 times, and zinc 7.2 times, as heavy as water.
If 3 pounds of lead and 2 pounds of zinc be melted
together, compare the weight of the alloy with that
of water.
98 EXAMINATION PAPERS.
7. A, B, and C start at the same time and from the same
point, to travel around an island 26 miles in circuit.
A goes 10 miles and B 4 miles per hour in the
same direction, and C goes 5 miles per hour in the
opposite direction. When and where will they first
be all together again ?
Algebraical symbols will be allowed in the three fol-
lowing questions :
8. It is required to make a hollow leaden cylinder, open
at both ends, 10 inches long, with its wall 1 inch
thick, and which is to weigh 25 pounds. Find its
outside diameter.
9. A conical vessel, 6 inches deep and 3 inches across the
mouth, is filled to 5 inches with water. Find the
diameter of the sphere which, when dropped into
the cylinder, will raise the water so as just to fill
the vessel.
10. The diagonals of a quadrilateral plane figure are 10
and 12, and they intersect at an angle of 60°. Find
the area of the figure.
XXIX.
COLLEGE OF OTTAWA, OTTAWA, CAN.
Matriculation Examination. Session 1881-82.
1. What is the exact value of ^2f + f of ^ + f) -5-
\ -7 i/
2. The sum of two numbers is 240; their L.C.M. is 1728.
What are the numbers ?
3. Define discount, and find the discount on a bill of £10,
due at the end of a year, at 10 per cent.
ARITHMETIC.
4. Find the simple interest of $442, at 4 per cent, for 5
years ; and the compound interest of $500, at 3 per
cent, for 2 years.
5. The sea covers -J--J- of the surface of the globe. The area
of Asia is -^y1- of that of Europe, whilst the area of
Africa is -2T2- ; the area of America is -y^ ; and the
area of Oceania is -|T. Africa having an area of
11,630,400 square miles, find the area of all the
other parts, and that of the entire globe.
6. Prove that the product of 71(71 + l)(2n + l) is always
divisible by 6, whatever be the whole number n.
XXX.
COLLEGE OF OTTAWA, OTTAWA, CAN.
Matriculation Examination. Session 1882-83.
1. A man has 3 farms of 56, 72, and 88 acres, respectively,
and wishes to fence them into the largest possible
fields, having each the same number of acres. How
many acres did he put in each ?
2. A grocer has a 4-pound, 5-pound, 6-pound, and a 12-
pound weight. What is the smallest tub of butter
that he can weigh by each without a remainder ?
3. A man owning ^-J- of a ship worth $48,064 sold ^ of his
share. What part of the ship did he sell ? "What
part does he still own ? and what is this part worth?
4. What is the worth of a silver cup weighing 10 ounces
16 dwt., at 12-J- cents a pennyweight?
5. The longitude of Ottawa is 75° 43' 22" W. of Greenwich ;
the longitude of Washington is 77° 3' 1". What is
the difference in time between Ottawa and Wash-
ington ?
100 EXAMINATION PAPERS.
6. A lad at the age of 14 received a legacy of $5000 ; he
then lent it at 8 per cent simple interest. What is
his legacy worth when he is 21 ?
7. Two men hire a pasture for $ 50 ; one put in 20 horses
for 12 weeks, the other 25 horses for 10 weeks.
How much should each pay ?
8. A milkman bought 40 gallons of new milk, at 16 cents
a gallon, and 60 gallons of skimmed milk, at 8 cents
a gallon, which he mixed with 12 gallons of water,
and sold the whole at 24 cents a gallon. What was
his profit ?
9. Simplify , x(3fx5*)-l7|,
and find their sum.
XXXI.
McGiLL UNIVERSITY, MONTREAL, CAN.
School Examination, June, 1883.
1. What is the meaning of numeration? notation? addi-
tion ? subtraction ? multiplication. ? division ? Divide
three hundred sixty millions nine hundred nineteen
thousand eight hundred fifty-six by eighty-three.
2. What letters are used in Roman notation, and how are
they combined to express numbers? Change 9909
into Roman notation.
3. What is the difference between a vulgar and a decimal
fraction ? Convert -- into a decimal.
4. Multiply 2.604 by 1.234, and divide the result by 0.004.
5. Find the value of 21 acres 3 roods 12 poles, at $45 per
acre.
ARITHMETIC. 101
6. Find the L.C.M. of 3, 5, 9, 12, 17, and 20; and the
G.C.M. of 441 and 693.
7. Calculate the simple interest on $580 from May 16,
1882, to October 8, 1883 (both days inclusive), at 5
per cent per annum.
8. If the wages of 12 men for 8 days of 8 hours each be
$135, what will be the wages of 25 men for 12 days
of 10 hours each ?
9. Find the cost of planting a rectangular field measuring
34 poles 2 yards by 26 poles 3 yards, at $6.50 per
square pole, leaving a path 4 feet wide all round the
field.
10. If 25 pounds of tea, at 60 cents per pound, be mixed
with 30 pounds, at 47 cents, find the price of the
mixture per pound in order that there may be a
profit of 18 per cent.
11. If a house had been sold for $7992, there would have
been a gain of 8 per cent on outlay. How much per
cent is lost or gained by selling it for $7511 ?
12. Find the distance between the opposite corners of a
rectangular floor which measures 8 feet 3 inches by
12 feet 6i inches.
XXXII.
UNIVERSITY OF CAMBRIDGE, ENG.
Second Previous Examination, Dec., 1880. — Time allowed, 2% hours.
1. Find the G.C.M. of 2301 and 3717, and the L.C.M. of
192, 204, and 272.
2. Divide 3& - 4J + IJf by If + 5# - 7^.
102 EXAMINATION PAPERS.
3. A kiloliter contains 35.32 cubic feet, and a gallon con-
tains 277.274 cubic inches ; how many gallons are
there in a kiloliter?
4. Add together -| of a guinea and a half, 0.855 of a
pound, and 1T77 of 2f of If of 18s.
5. Extract to three places of decimals the square roots of
G and 0.287.
6. Find as recurring decimals the square of 0.4, and the
square root of O.G94.
7. Calculate the cost of paper for a room 18 feet long, 16
feet broad, and ,12 feet high, allowing 40 square
feet for doors and windows, the price of the paper
being 2s. 4d. per piece of 12 yards long and 21
inches broad.
8. A Cambridge Poor Rate, at lie?, in the pound, is made
up of the Union Contribution, 5Jc/. ; the Borough
Rate, 4d.- the Asylum, etc., l±d. The rate on a
certain property aritounts to £100 8s. 5f/. ; how
much of this is for the Borough Rate, and at what
amount is the property assessed ?
9. Find the difference between the amount of £1205, put
out for 2 years at 5 per cent compound interest, and
the present value of the same sum due 2 years
hence at 5 per cent compound interest.
10. The 11.45 Exeter express from Paddington stops first
at Swinden, 77J miles distant, at 1.12. In the whole
journey, 194 miles, 15 per cent of the time is ex-
pended in 'stoppage, etc. ' At what time is the train
due at Exeter?
11. What income would be derived from investing £9350
in 5^- per cent preference stock- at 137^-?
ARITHMETIC. 103
XXXIII.
UNIVERSITY OF CAMBRIDGE, ENG.
Previous Examination, June, 1881. — Time allowed, 2} hours.
1. Arrange in order of magnitude the fractions J-, •£$, T7j,
and T9y- ; and find the difference between the greatest
and least.
2. Simplify t=-f of f^-j of f-= | of 585.
3. Find a decimal which shall differ from -J-J by less than
TTuTFTF'
Q. rf 1.875 , 3.5
amplify --- x _.
Find the sum of
2.4, 0.313, 0.567, 7.056, 4.17, and 0.4304122.
4. Calculate the value of \3 + 2 V2 correctly to two places
of decimals.
5. Find by practice the value of a nugget of gold weigh-
ing 3 pounds 11 ounces 18 pennyweights 4 grains
at £3 17s. Qd. per ounce.
6. A lawn-tennis ground is half as long again as it is
wide. The cost of levelling at 9cZ. per square yard
is £176 8s. Oc?. Find the cost of enclosing it with
an iron railing at 7s. 6cl. per yard.
7. A sum of £650 is due from A to B on a certain day,
and £495 12s. 6d. is also due 7 months later. Show
that, reckoning interest at 5 per cent, if A pay both
debts at the end of 3 months, neither of them will
lose.
104 EXAMINATION PAPERS.
8. Brussels carpet is 2 feet wide, costs 6s. Qd. a yard, and
will last 5 years. Kidderminster carpet is 2-^ feet
wide, costs 5s. a yard, and will last 3 years. Which
is the cheapest, not reckoning interest on your outlay?
9. Two men and three boys can level and turf 352 yards
of a cricket-ground in 4 days ; and three men and
two boys can complete 276 yards in 3 days. Com-
pare the rates of working of a man and a boy.
10. A man has £7220 stock in the 3 per cent consols.
When they are at 102|- he sells, and invests in the
2-J- per cents at 90-J-. Find the change in his income.
(Brokerage is J per cent.)
11. A steel rod, 1 foot long and 1 inch square, weighs 3-J-
pounds, and will just support 50 tons. What is the
greatest length of steel wire which, when hung up
by one end, will just not break by its own weight?
XXXIV.
UNIVERSITY OF CAMBRIDGE, ENG.
Second Previous Examination, Dec., 1881. — Time allowed, 2} hours.
1- Simplify
(^ ~ i) < ~
2. Find the difference between -§ of 31 acres 2 roods 27
' poles, and -J of 18 acres 1 rood 0 poles.
3. Reduce 5 days 16 hours to the decimal of a week.
,0.321x0.321-0.179x0.179
Find the value of -- o.331_0.179 "
ARITHMETIC. 105
4. Find the square roots of 27^ and 90,018.0009.
A Christmas dole is given to the inhabitants of certain
almshouses, consisting of as many shillings to each
as there are inhabitants. The sum so expended is
£9 16s. Qd. How many inhabitants are there?
5. At what rate per cent will the simple interest on £236
6s. 8 d. amount to £17 14s. 6d. in 2J years?
6. Find the present worth of £ 1250 Os. 2^d. due 7 months
hence at 3^- per cent.
7. What sum of money must be invested in 4-J- per cent
stock at 83J to bring in an income of £ 219 ? (Brok-
erage is ^ per cent.)
8. A man walking 18 miles finds that in 1 hour 40 min-
utes the distance, he has walked is -f- of the remaining
distance. Find his rate of walking.
9. A cubical cistern, open at the top, costs 15 guineas to
line with lead at Is. 9d. per square foot. How
many cubic feet will it contain ?
10. A man's income is increased by £200 ; but the income
tax being reduced from 6 d. to 5 d. in the pound, he
pays the same amount of tax as before. What is
his income ?
XXXV.
UNIVERSITY OF CAMBRIDGE, ENG.
Previous Examination, June, 1882. — Time allowed, 2| hours.
1. Keduce |^|| to a decimal, and 2.48027 to a vulgar
fraction in its lowest terms.
106 EXAMINATION PAPERS.
3. Find the cost of 7 cwt. 2 quarters 23 pounds at £11
Is. Sd. per cwt.
4. A man who has sold tea at half-a-crown per pound,
making a profit of 25 per cent, lowers his price so
as to gain only 2c?. per pound. In what ratio must
his weekly sale increase that he may make twice as
much as before ?
5. Find the amount of £325 IGs. Sd. in 3J years at 4£
per cent simple interest.
6. If a bill of £932 2s., due Dec. 19, be paid June 6, find
the true discount to be allowed, reckoning interest
at 4 per cent per annum.
7. The amount of sunshine recorded in Jersey last year,
in the month of April, was 33 per cent of the possi-
ble amount ; and the average length of the night in
that month is 10 hours 30 minutes. Find how
many hours of sunshine there were in the month.
8. The length of a side of the base of the Great Pyramid,
which is square, is 500 Egyptian cubits :
(i.) Find the area covered by it in acres, roods, etc.,
knowing that an Egyptian cubit is equal to 18.24
English inches,
(ii.) Find the height of the Pyramid in cubits, having
given that the height of a model of the Pyramid,
the area of whose base is 8 square feet 73 square
inches, is 22.225 inches.
9. Which is the more profitable stock to invest in, 3 per
cent at 83£, or 3^ per cent at 97?
10. Two men undertake to do a piece of work for 1 guinea.
One could do it alone in 6 days, the other in 7 days.
With the assistance of a boy they finish it in 3 days.
How should the money be divided?
ARITHMETIC. 107
XXXVI.
UNIVERSITY OF OXFORD, ENG.
Local Examination, Junior Candidates, May, 1881.
• Time allowed, 2 hours.
Every candidate is required to satisfy the examiners in the first
part of this paper. The second part is intended for those candidates
only who offer mathematics as a subject, and is not to be attempted
by any until they have done all they can do of the first part. Atten-
tion should be paid to spelling and hand-writing. No credit will be
given for any answer, the full working of which is not shown.
I.
1. Express in words 90,999,090,009 ; and in figures, two
thousand millions four hundred thousand and sixty.
2. Multiply 810,901 by 809,101 ; and 1 ton 0 cwt. 0 quar-
'ters 5 pounds by 449.
3. Divide 25,600,160,001 by 159,601; and £183 12s.
Hd. by 58.
4. A field containing 18 acres 36 poles is divided into
allotments, each containing 1 rood 14 poles. How
many of them are there ?
5. Reduce 28 quarters 5 bushels 1 peck 1 gallon to pints.
6. Simplify f^ ~^- ; and divide 0.00036 by 0.006.
T5" * '12
7. Express 2 yards 3 inches as the fraction of 1 mile 30
perches.
8. If it cost £9 5s. 4 d. to carpet a room whose floor con-
tains 278 square feet, how many square feet are
there in one which can be carpeted for £12 4s. 8d. ?
108 EXAMINATION PAPERS.
II.
9. Find the simple interest on £11,000 for 4.4 years at
3.15 per cent.
10. The external length, breadth, and depth of a box are
6 feet 2 inches, 3 feet 8 inches, and 2 feet, respec-
tively, and it is made of wood 1 inch thick. Find
the quantity used.
11. Two pipes running together can fill a cistern in 8
minutes, and one of them alone can fill it in 24
minutes. How long would the other alone take ?
12. If 12 men, working 8 hours a day, do -f of a piece of
work in 20 days, how many days will 15 men,
working 10 hours a day, take to do -J of it ?
XXXVII.
UNIVERSITY OF OXFORD, ENG.
Local Examination, Senior Candidates, May, 1881. — Time allowed,
2 hours.
No credit will be given for any answer, the full working of which
is not shown.
1. How many times is £27 15s. 7f d. contained in £1356
6s. 9d ? and how much remains over?
2. Multiply 1 acre 3 roods 7 poles 4 yards by 17.
3. Add together 3^, &£-, JJ, and 1J of •&•
4. In a row of 25 houses, each house has 17 windows,
each window 4 panes, and each pane measures 18
inches by 9 inches. What will be the cost of glaz-
ing all these windows at 6 d. per square foot ?
ARITHMETIC. 109
5. Multiply 47.025 by 0.128; divide 1.05 by 0.875; and
f (1.005 + 0.201) X (1.005 - 0.201)
find the value of L 1.005 x 0.201
6. Reduce £5 17s. *l\d. to the decimal of £100; and
find the value of 0.709 of 5 tons 3 cwts. 14 pounds.
7. Find the cost of 227 tons 15 cwts. 21 pounds at £ 12
13s. 4e?. per ton.
8. Extract the square root of 36,180,225 and of 0.000144.
9. Find the simple interest and amount of £225 13s. 4c7.
for 2J- years at 4f per cent per annum.
10. If the value of 47 pounds 1 ounce of silver be £184
16s. -J-cf., what is the value of 84 pounds 9 ounces?
11. If 27 men mow a field of 90 acres in 7 days, working
8 hours a day, how many men will be required to
mow 200 acres in 16 days, if they will work 10
hours a day ?
XXXVIII.
UNIVERSITY OF OXFORD, ENG.
Local Examination, Junior Candidates, June, 1882. — Time allowed,
2 hours.
Every candidate is required to satisfy the examiners in the first
part of this paper. The second part is to be attempted by those can-
didates only who offer mathematics as a subject. Attention should
bo paid to spelling and handwriting. No credit will be given for
any answer, the full working of which is not shown.
I.
1. Add together seventeen hundred and seventy, a hun-
dred and seventy thousand and seventy, and
seventeen million eight hundred and twenty-nine
thousand ; and express the result in words.
110 EXAMINATION PAPERS.
2. Multiply 302,050 by 702,090 ; and 4 days 22 hours 33
minutes 49 seconds by 401.
3. Out of a salary of 25 guineas per quarter, how much
will be saved in a year, when the expenditure is at
the rate of 5s. 3d per day?
4. Divide 40,301 acres 0 roods 38 rods 9 yards by 251.
5. Find the number of quarters, bushels, etc., in 2559
pints.
6. Find the value of
Gfr of it) + (II ^ f i) ; and of A cwt. + 3 poun(L
7. Divide 4.00004 by 0.0011; and reduce 0.00126 to a
vulgar fraction.
8. If 6-J- tons of coal cost £6 15s. 5d, what will be the
price of 5 tons 3 cwts. ?
II.
9. If 5 men and 9 boys could do a piece of work in 17
days, in how many days would 9 men and 12 boys
do it, the work of 2 men being equal to that of 3
boys?
10. Find the simple interest on £2970 16s. 8d for 3 years
73 days at £3 2s. 6 d. per cent.
11. A man buys goods which he sells again for £11 18s.
-J-d, making a profit of 16 per cent; what is the
buying price ?
12. Pipes A and B can fill a cistern in 3 minutes and 5
minutes, respectively, and C can empty it in 7-J
minutes. In what time will the cistern be filled
when A, B, and C are all open ?
ARITHMETIC. Ill
XXXIX.
UNIVERSITY OF OXFORD, ENG.
Local Examination, Senior Candidates, June, 1882. — Time allowed,
2 hours.
No credit will be given for any answer, the full working of
which is not shown.
1. Reduce 121 quarters 1 bushel 1 peck to quarts.
2. Into how many allotments, each containing 2 roods 10
perches, can a rectangular field 450 yards long and
121 yards be divided ?
3. Reduce to their simplest forms the fractional expressions,
_
6-*
4. Square 109.901 and 0.23.
5. Extract the square root of 35,445.5929.
6. Reduce f| of £2 2s. 9<£ to the vulgar fraction of £2
2s. l^d. ; and express in money 0.304375 of £5.
7. Find the weight of a quantity of metal worth £2 2s.
9c?., having given that 2 tons 8 cwts. 3 quarters 12
pounds is worth £1.
8. How much is gained or lost per cent by buying a
number of oranges at 5 for twopence, and selling
half of them at two a penny and half at three a
penny ?
9. Find the simple interest on £7446 12s. 2-fd. for If
years at 4f- per cent.
10. During 365 days 6 hours the earth makes 366^ revo-
lutions about its axis. How long will it take in
making 879 revolutions ?
112 EXAMINATION PAPERS.
11. If 3 men can reap 8 acres in 5 days, working 8 hours
a day, in how many days can 8 men, working 12
hours a day, reap 192 acres?
XL.
UNIVERSITY OF OXFORD, ENG.
First Examination of Women, May, 1880. — Time Allowed, 2 hours.
1. Forty-five telegraph posts, placed at equal distances,
extend a mile ; how far apart are the posts?
2. How many articles at £3 7s. Qd. each are worth as
much as 324 articles at £1 12s. Qd. each?
• 2597 , If
3. Snnphfy — + ^.
4. Divide 25.6 hy 16, 2.56 by 0.16, and 0.09 by 0.04.
5. Find the value of
tV 7ard + *ttrP°le + TTBT rood + inrfinr acre ;
also of 0.00008544921875 of a ton, and 0.1805 of a
guinea.
6. If 12 men or 15 women do a piece of work in 252
days, in what time can 11 men and 2 women do
the same piece of work ?
7. Find the cost of papering a room 11 yards 2 feet
4 inches long, 6 yards 2 feet wide, 5 yards 2 feet
6 inches high, with paper 1 yard 4 inches wide, at
3 d. a yard.
8. Sugar is bought at \\d. a pound, and sold at £18 13s.
4d. a ton ; find the gain or loss per cent.
9. Divide a sovereign between A, B, C, so that A may
have fourpence more than B, and B tenpence more
than C.
ARITHMETIC. 113
10. A gives a fifth of a cake to B, and then a quarter of
the remainder to C, and then a third of what still
remains to D. What portions of the cake will A, B,
C, D respectively have ?
11. Which is the better investment, a four per cent stock
at 120, or a five per cent stock at 166|?
XLI.
UNIVERSITY OF OXFORD, ENG.
First Examination of Women, June, 1882. — Time allowed, 2 hours.
1. How many coins, each weighing 15 dwts. 18 grains,
can be made out of 16 pounds 10 ounces 7 dwts. 18
grains of metal ?
rt n. ,.,, 24 of 5-j
2. Simplify
3. Keduce 6 cwts. 2 quarters 24 pounds to the fraction
of a ton; and hence find the value at 17s. 6d. per
ton.
4. If turf is sold in pieces 30 inches long and 9 inches
wide at £1 Os. 10 d. per 100 pieces, what is the
price per square yard ?
5. Find the cost of 1095 chests of tea at £7 17s. 7-Jd. per
chest.
6. Keduce 0.00544 to a vulgar fraction in its lowest
terms; multiply 0.544 by 0.125; and divide 27.6
by 276 to six places of decimals.
7. Keduce 2| of 4%d. to the decimal (i.) of half-a-crown,
(ii.) of 7 half-crowns.
8. If 165 bales of goods cost £431 4s. 8%d.t what will
264 of the same cost ?
11-1 EXAMINATION PAPERS.
9. Find the simple interest on £844 4s. 4d for 3J- years
at 4J per cent.
10. The material for a dress cost 7 guineas : if the price of
the material chosen had been 25 per cent higher
than it is, and half as much again had been used,
by how much would the cost have been increased?
11. Divide £3 2s. 6d. between three persons so that the
first shall have 7s. Qd. more than the second, and
the second 5s. more than the third.
12. If -Jg- of the pupils of a school are in the sixth form, ^
in the fifth, ^ in the fourth, and 96 in the lower
forms, what is the whole number of pupils in the
school ?
XLII.
UNIVERSITY OF OXFORD, ENG.
First Examination of Women, June, 1883. — Time allowed, 2 hours.
1. Divide 436 acres 3 roods 3 yards 4 feet 72 inches by 19.
5 + ^
2, Simplify 1H of 6J-7| o
3. What fraction of £2 19s. %d. is £1 12s. 9
If the larger of these sums is the value of 12 penny-
weights of gold, of what weight of gold is the other
the value ?
4. A person, purchasing a carpet for a room 21 feet long
and 15 feet 9 inches wide, chooses a material which
is j- of a yard wide, and the pattern of which is
ARITHMETIC. 115
complete in each yard of length. How much carpet
must he buy in order that the pattern may be un-
broken, if the strips are to run lengthwise in the
room ?
5. Find the cost of 11 tons 3 cwts. 3 quarters 1G pounds
at £3 12s. lid. per cwt.
6. -Multiply 25.3125 by 2.56; divide G4S by 0.0256; and
from the sum of 2.6 and 3.583 subtract 5.05.
7. Eeduce £5 18s. IQi-d, to the decimal of £25; and
find the value of 0.025 of £1 + 0.35 of 17s. 6 J. + 0.2
8. If the food of 11 persons for 13 weeks costs £112 12s.
3d., what will it cost to feed 26 persons for 11 weeks
5 days?
9. At what rate per cent per annum will £40 10s. be the
simple interest on £432 for 2J years.
10. A grocer buys 6 cwts. of tea for £70, and sells 41 cwts.
at 2s. 6d. per pound. At what price per pound
must he sell the remainder to bring his profit on the
whole to exactly 20 per cent ?
11. A person, who had 2 sons and 4 daughters, left an
estate of 2800 acres to be divided between them so
that each son might have twice as much as each
daughter. If one of his sons has a family of 4 sons
and '2 daughters, and leaves his share to be divided
in the same manner, how many acres will each of
his daughters inherit ?
12. From a cask of wine, worth 2s. 3d. per gallon, a sixth
part is drawn and replaced by wine worth only Is.
3d. per gallon. What is now the value per gallon
of the wine in the cask ?
HG EXAMINATION TAPERS.
XLIII.
SCIENCE SCHOOLS AND CLASSES, ENGLAND.
Mathematics, First Stage, May, 1880.
Not more than three questions are to be answered. The num-
ber of marks assigned to each question is given in brackets.
1. Divide 285,651 by 77, using only short division. Obtain
the remainder correctly, and explain briefly how
you obtain it. [6.]
2. What interest per cent does a man get for his money by
investing in the three per cents at 90 ?
How much must he invest to give him an income of
£1153 a year. [6.]
3. Add together f of a guinea, ^J of a half crown, l-^
shillings, and ^ of a penny, and reduce the whole
to a decimal fraction of a pound. [8.]
4. A man owns three bills, of which one could be paid by
a certain number of florins, another by twice that
number of half crowns, and the third by six times
that number of shillings. The bills amount in all
to £ 7 3 s. 0 d. What are the several amounts ?
[12.]
5. Copper weighs 550 pounds, and tin 462 pounds to the
cubic foot. What will be the weight of a cubic foot
of a mixture of 6 parts copper to 5 parts tin ?
[12.]
6. A plate of metal is 106.58 inches long, 14.6 inches wide,
and 2 inches thick. Supposing it to be melted, and
cast into an exact cube, what would be the edge of
the cube? [12.]
ARITHMETIC. 117
XLIV.
SCIENCE SCHOOLS AND CLASSES, ENGLAND.
Mathematics, First Stage, May, 1881.
Not more than three questions are to be answered. The number
of marks assigned to each question is given in brackets.
1. Make out a bill for the following :
1 cwt. of indigo at 14s. Qd. per pound.
1 ton of cloves at Is. 2d. per pound.
5 cwt. 3 quarters 18 pounds spelter at 4J d. per pound.
7 cwt. 1 quarter 14 pounds block tin at £ 64 per ton.
Subtract 10 per cent discount for cash. [7.]
2. Divide 0.736 by 2.85, and 2.85 by 0.0736, in each case
to four places of decimals, and find the product
formed by multiplying the two quotients together.
[7.]
3. Find the G.C.M. and L.G.M. of 3024, 4752, and 7488.
[8.]
4. A man invests £3600 in 3 per cent stock at 90. He
sells out at 80, and lends -| of his money at 4 per
cent, and f at 5 per cent. How long must the loan
last, so that when he re-invests his money in 3 per
cents at 90, his gain on interest (simple) may exactly
equal his loss upon principal ? [12.]
5. The sides of a rectangle are 16 feet and 10 feet long
respectively. Find, to four places of decimals, the
length of the diagonal of a square whose area equals
that of the rectangle. [12.]
6. Seventy-five per cent of the area of a farm is arable ; of
the remainder 85 per cent is pasture, and the rest is
waste ; the area of the waste is 3 acres 0 roods 20
poles. What is the area of the farm? [12. ]
118 EXAMINATION TAPERS.
XLV.
SCIENCE SCHOOLS AND CLASSES, ENGLAND.
Mathematics, First Stage, May, 1882.
Not more than three questions are to be answered. The number
of marks assigned to each question is given in brackets.
1. The cost of labor in producing a certain article was
£18 19s. lie?. It was made by five persons, who
severally spent 2, 3, 4^-, 6, and 8 days upon it. How
should the money be divided among them ? [6.]
2. Eeduce to their lowest terms the fractions
| of 0.0603 . i + l + i
3. Arrange Q * » o» Vl.81, and 1.346 in order of magni-
tude, and find to five places of decimals by how
much the sum of the largest and smallest of these
numbers differs from twice the other number. [8.]
4. "What is discount? How is it commonly calculated?
If a sum of £ 1000 becomes due three months hence,
what is its present value as commonly calculated,
and what as correctly calculated, interest being
reckoned at 5 per cent? [10-]
5. Given that a meter equals 3.2809 feet; find how many
square meters there are in 1000 square yards. [10.]
6. A cubic foot of copper weighs 560 pounds. It is rolled
into a square bar 40 feet long. An exact cube is
cut from the bar. What is its weight to four deci-
mals of a pound? [12.]
ARITHMETIC. 119
XL VI.
SCIENCE SCHOOLS AND CLASSES, ENGLAND.
Mathematics, First Stage, May, 1883.
Not more than three questions are to be answered. The number
of marks assigned to each question is given in brackets.
1. What is a decimal fraction ? What is a recurring deci-
mal? Express -^ as a recurring decimal, and
0.0173535 as a vulgar fraction. [6.]
2. Show that the square root of 0.37 exceeds the cube r.oofc
of 0.217 by a difference which very nearly equals
rk- [10.]
3. A publisher sells books to a retail dealer at 55. a copy,
but allows 25 copies to count as 24 ; if the retailer
sells each of the 25 copies for 6s. 9 d., what profit
per cent does he make ? [8.] .
4. In building a wall, 22,500 bricks are used at £1 12s. a
thousand, 135 bushels of lime at Is. ^.\d. a bushel,
16-J loads of sand at 3s. 6d. a load; the labor is
reckoned at 9 s. 6 d. per thousand bricks laid ; and
300 coping stones are used at Is. *I\d. apiece, in-
cluding cost of laying. Make out the above in the
form of a bill, and find the amount after deducting
7^- per cent for prompt payment. [8.]
5. The capital of a trading company consists of 4000 A
shares of £80 each and 2000 B shares of £25 each;
in dividing the profits, 5 per cent of the amount of
each share is first paid, and then the remainder, if
any, is divided equally amongst the shareholders.
The profits of the undertaking in one year were
£34,853 12s. 6-J-cZ.; how much would be paid to
the holder of an A share and how much to the
holder of a B share ? [10.]
120 EXAMINATION PAPERS.
6. An imperial gallon is 277.274 cubic inches ; a Win-
chester bushel, 2150.42 cubic inches ; how many
Winchester bushels are equal to 100 imperial
bushels? [6.]
XL VII.
CIVIL SERVICE OF GREAT BRITAIN.
Open Competitive Examination for Out-Door Officers of Customs,
July, 1876. — Time Allowed, 2% Hours.
1. Add together 4f , 2-f, if, and ^
2. Subtract 3-J-} from 5^--
3. Multiply together 5-J, T<V, T%, and 2£ .
4. Divide 5f by if.
5. Add together 0.00867, 1.92, 0.806, and 143.9576.
6. Subtract 382.7043 from 400.1036.
7. Multiply 381.42 by 0.0065.
8. Divide 1522.038 by 0.372.
9. Express f- of 4s. 1 d. as the decimal of 5 guineas.
10. Add together f , if, 11T45, and if
11. Subtract 8f from 9TV
12. Multiply together -J-f, 3-f-, 3-J, and if
13. Divide 4|£ by 10T4T.
14. Add together 0.725 of a bushel and 2.079 of a gallon,
and give the answer in pints and the decimal frac-
tion of a pint.
15. Subtract 10.869 of an ounce from 1.203 of a pound
Troy.
ARITHMETIC. 121
16. Multiply 905.8 by 87.06.
17. Divide 0.0054837 by 0.0135.
18. Eecluce 0.70596 of 3s. 11$ d. to farthings and the deci-
mal of a farthing.
19. Reduce 4 tons 2 cwt. 1 quarter 11 pounds to ounces.
20. If 2J pounds of rice cost 7 d., how much may be bought
for £6 17s. Id.?
21. Find (by practice) the cost of 455,436 articles at £2
13s. 10$ d. per dozen.
22. In what time will £1225 amount to £1417 18s. 9c?.
at 3 per cent per annum simple interest ?
23. In 8,476,321 inches, how many miles, furlongs, poles,
etc.
24. If 2$ acres of pasturage can support 5 oxen for 3$
days, how many would be required to support 26
oxen for 17-J days?
25. Find (by practice) the value of 5 quarters 2 bushels
1 peck of wheat at £4 18s. a quarter.
26. Find the amount of £4750 in 3 three years at 5 per
cent per annum, compound interest, neglecting frac-
tions of a penny.
XL VIII.
CIVIL SERVICE OF GREAT BRITAIN.
Open Competitive Examination for Men Clerkships in the Lower
Division of the Civil Service, Nov., 1876. — Time allowed, 3 hours.
1. A and B together earn £3 16s. in 8 days, A and C
together can earn £7 13s. in 17 days, and B and
C together £12 15s. in 30 days. How much can
they severally earn alone ?
122 EXAMINATION TAPERS.
2. Express 32,567,325 in the duodenary scale.
3. A merchant selling goods at a certain price loses 5 per
cent ; but, if he had sold them for £4 more, he would
have gained 3 per cent. What did the goods cost
him?
4. Multiply by duodecimals 3 feet 2 inches by 5 feet 7
inches, and the product by 6 feet 8 inches. What
does the answer become when expressed in cubic
inches and the decimal fraction of a cubic inch ?
5. Extract the square root of 109ff|, and find the side of
a cube containing 2,048,383 cubic inches.
6. What is the present worth of £1801 11s., payable 6J
years hence, at 5 per cent per annum ?
7. A bill upon Amsterdam is bought at 12 florins per
pound sterling; the proceeds purchase at Amster-
dam bills upon Hamburg, at 34J florins for 40 marks ;
these are forwarded to Paris and sold at 185 francs
per 100 marks. What is the rate of exchange be-
tween London and Paris?
8. A train is just 27 minutes in passing through the Mont
Cenis Tunnel, the length of which is 11,220 meters ;
find the speed of the train in miles per hour. (One
meter equals 39.39 inches.)
9. In Reaumur's thermometer the freezing point is zero,
and the boiling point 80° ; in Fahrenheit's ther-
mometer the freezing point is 32°, and the boiling
point 212°. What will Reaumur's thermometer
mark when Fahrenheit's marks 47°, and what will
Fahrenheit's mark when Reaumur's marks 93° ?
10. A and B rent a pasture for £138 per annum ; A puts
in 200 sheep and B 160, but at the end of six
months they dispose of half their stock, and allow 0
to put in 120 ; what should A, B, and C pay sever-
ally towards the rent at the year's end ?
AEITHMETIC. 123
11. It is noticed that the water in a reservoir 38 feet long
and 26 feet wide, which is known to leak, sinks one
inch in 12 hours. A pipe discharging 60 gallons
per minute will fill the reservoir in 45 hours, allow-
ing for the leakage. Find within an inch the depth
of the reservoir. (A cubic foot of water contains
6.25 gallons.)
12. A man invests £26,180 in the 3 per cents at 931, but
after a time sells out half at 921, ancl invests the
proceeds in the 4 per cents at 97. Find to a penny
the difference in his income.
13. Find the value of 3.6 of 0.954 of 0.428571 of 2s. 3d.
14. A watch gains 1 minute and 15 seconds a day. It is
set right at noon on the 12th of November. What
will be the true time when it points at noon on the
following Christmas day ?
15. The first of a line of 10 sentries, standing at equal
distances from each other, wishes to send a message
of 20 words to the last. The men begin to walk
at the same instant, and walk even distances right
and left of their posts alternately, and each time
they meet pass on 5 words. The transmission of
the message occupies 48 minutes, and the men walk
at the rate of 3 miles per hour. How far is the
first man from the last ?
XLIX.
CIVIL SERVICE OF GREAT BRITAIN.
Competitive Examination for the Excise, Dec., 1876. — Elementary
Arithmetic. — Time Allowed, 2} hours.
1. In 372,483 ounces, how many tons, cwts., quarters, etc.
2. If cotton is shipped at 4 guineas a cwt., what is the
weight of a bale costing £ 21 9s.?
124 EXAMINATION PAPERS.
3. Find (by practice) the value of 27 pounds 6 ounces 6
dwts. of gold dust at £3 10s. 6d. an ounce.
4. Find the simple interest on £6250 for 18 years at 2J
per cent per annum.
5. Add together 5f , |f, if > and 3i-
6. Subtract 9^ from 10TJ^.
7. Multiply 6^j- by ff
8. Divide 31$ by Iff.
9. Add together
371.87001, 0.0031, 0.00631, and 5786.44321.
10. Subtract 185.939131 from 186.847.
11. Multiply 323.211 by 0.20343.
12. Divide 343.5777 by 0.525 to three places of decimals.
13. What fraction of a sovereign is 0.345 of £1 4s. ?
14. Reduce 3 quarters 7 bushels 1 gallon to pints.
15. The market price of wheat being £3 4s per quarter,
what will be the value of 11 bushels and 3 pecks?
16. Find (by practice) the dividend on £3760 15s. at
17s. Qd. in the pound.
17. Find the amount of £4096 in 3 years at 1J per cent
compound interest (neglecting fractions of a penny).
18. Add together 5|i, £, 3o4T, and 1^.
19. Subtract -j^ from T7^.
20. Multiply together 5-^, ^, ff , and 1^.
21. Divide |£ by 6|.
ARITHMETIC. 125
22. Add together 11.431, 0.00101, 243.734, 400, and
1.3743.
23. Subtract 876.315 from 1000.01.
24. Multiply 7.3406 by 0.00437.
25. Divide 0.003634 by 0.0632.
26. Find the value of 0.0625 of an acre.
27. Reduce 1 mile 7 furlongs 5 perches 2J- yards to inches.
28. If 49 men can empty a reservoir in 65 days, pumping
8 hours a day, how many hours a day must 196
men pump to empty it in 26 days?
29. Find (by practice) the value of 7719 articles at £1 7s.
6d. per dozen.
30. At what rate per cent will £461 10s. amount to £611
9s. in 13 years at simple interest?
31. Add together f , •&, Iff, and |f
32. Subtract 12^- from 15^. .
33. Multiply together T7¥, 3^-, l-fa, and ^.
34. Divide 5f by
35. Add together .1.001 of a cwt. and 0.039 of a quarter,
and give the answer in ounces and the decimal frac-
tion of an ounce.
36. Subtract 0.335 of a gallon from 12.51 of a quart, and
give the answer in pints and the decimal of a pint.
37. Multiply 0.003631 by 200.001.
38. Divide 28.028 by 4900.
39. Reduce 13s. Qd. to the decimal of £3.
120 EXAMINATION PAPERS.
L.
CIVIL SERVICE OF GREAT BRITAIN.
Competitive Examination for the Excise, Dec., 1876. — Higher Arith-
metic.— Time allowed, 3 hours.
1. An estate is divided among three persons, A, B, C, so
that A has -f of the whole, and B has twice as much
as C. It is found that B has 27 acres more than C.
How large is the estate ?
2. 2 cwts. 1 quarter 3 pounds of an article is bought for
15s., and 17 pounds is sold for Is. 3d. What profit
is made per cent ?
3. What fraction of 300 yards is 1 furlong 2 poles 6 yards
2 feet ? Express the answer as a decimal.
Express as a fraction of an acre the ground taken up
by a path 3 feet broad round a house, the front of
which is 57 feet, and side 37 feet long.
4. Extract the square root of 30,789^^-, and the cube
root of 2,326,203.125.
5. How many ounces of silver are there in a piece of
plate costing £59 10s., the price of silver being
0.255 of £1 per ounce, and the cost of manufacture
-J- the value of the silver used ?
6. Explain what is meant by the L.C.M. of two or more
numbers?
Find the L.C.M. of 3696, 286, 19,656.
7. Find the value of 1.72 of 0.276 of 15.
8. How much must a man invest in 3-J- per cents at 91
in order to receive £ 590 per annum, after paying
4 d. in the pound income tax ?
ARITHMETIC. 127
9. The difference between 'the discount and interest on a
debt due a year and a quarter hence, at 4 per cent,
is 5s. What is the debt?
10. A tradesman's prices are 12 per cent above cost price.
If he allows £1 6s. 3d. discount on a bill of £21,
what profit does he make per cent ?
11. A man rents a house from the first of January at £142
per annum, payable half-yearly. He sublets it for
£160 per annum, payable quarterly. Allowing
simple interest at 4 per cent, what will he make by
the transaction in- 3 years ?
12. A cistern containing 600 gallons measures externally 7
feet in length, 2 feet 1.1 inches in breadth, and 5 feet
6 inches in height. The sides being H inches thick,
what is the thickness of the bottom ? (A cube foot
of water contains 6-^- gallons.)
13. The map of a country is drawn on the scale of ^ of
an inch to a mile. What area on the map will
• represent a lake 4000 acres in extent ?
14. A fast train leaves a place A for another place B at
the same moment that a slow train leaves B for A.
The fast train takes 2 hours on the journey, and, if
the slow train kept its time, they would meet at a
distance from B equal to -| the whole distance from
A to B. Instead of this, the place where they meet
is at a distance from B equal to -J the distance from
A to B. How much behind time will the slow
train be when it arrives at A ?
15. A round column stands on a cubic pedestal of the same
material, whose edge is 6 feet. The column is hol-
low, the external and internal diameters measuring
5 feet and 4 feet, respectively. If the weight of the
column be the same as that of the pedestal, what is
its height ?
128 EXAMINATION PAPERS.
LI.
CIVIL SERVICE OF GREAT BRITAIN.
Open Competitive Examination for Clerkships of the Superior Class
in the India Office, 1879. — Elementary Arithmetic. — Time allowed,
2j hours.
1. Reduce 6 tons 3 cwts. 2 quarters 14 pounds to ounces.
2. What must be given for a piece of silver weighing 73
pounds 5 ounces 15 pennyweights, at the rate of 5s.
9 d. an ounce ?
3. Find (by practice) the value of 1 ton 3 cwts. 1 quarter
14 pounds at £3 10s. per ton.
4. Find the simple interest on £840 15s. for 6-| years at
3 per cent per annum (neglecting fractions of a
penny).
5. Add together fj, 4J-, |f, and 1^.
6. Subtract 7f<T from 12^.
7. Multiply SA by 2&.
8. Divide 3-^ by 2Jf
9. Add together 3106.8157, 0.0624, 0.00441, and 43.2875.
10. Subtract 84.937658 from 100.3062431.
11. Multiply 947.36 by 0.00423.
12. Divide 950.562 by 19.56 to three places of decimals.
13. Reduce 0.0016395 of a pound Troy to grains and the
decimal of a grain.
14. Reduce 8,868,097 square feet to acres, roods, perches,
and yards.
ARITHMETIC. 129
15. If 10 men' can build a wall 65 feet long and 5 feet high
in 3^ days, in how many days will 6 men build a
wall 80 feet long and 4 feet high ?
16. Find (by practice) the dividend on £g236 10s. at 4s.
7 d. in the pound.
17. Find the amount of £ 7205 in 3 years at 6 per cent
compound interest (neglecting fractions of a penny).
18. Add together -J-, TV, •&, and 4i-
19. Subtract 1£ from 3^.
20. Multiply together -f , -f-, If, and 1-J.
21. Divide 10J- by 1-^,
22. Add together 16.41215, 9.376, 0.00403, 177.42, and
27.03067.
23. Subtract 17.2398 from 27.06.
24. Multiply 46.2375 by 0.00743.
25. Divide 92.3784 by 0.623 to four places of decimals.
26. Find the value of 1.025 of £1 13s. 4d.
27. In 406,395 pints how many bushels, pecks, gallons,
etc.?
28. If the 6d. loaf weigh 4 pounds, when wheat is at 36s.
a quarter, what should the \d. loaf weigh when
wheat is at 48s. a quarter?
29. Find (by practice) the value of 17 ounces 10 penny-
weights 12 grains at £1 13s. 4d. an ounce.
30. At what rate per cent will £2100 amount to £5250 in
3 years?
31. Add together 5f , -3J-, f , and |f.
32. Subtract 8-J from
130 EXAMINATION PAPERS.
33. Multiply together 10-J-, 2£, f and 3^. '
34. Divide 10|- by 13.
35. Add together 3.062 of a day and 1.5347 of an hour,
and give the answer in minutes and the decimal
fraction of a minute ?
36. Subtract 5.017 of a furlong from 1.358 of a mile, and
give the answer in yards and the decimal fraction
of a yard ?
37. Multiply 34.0069 by 0.005006.
38. Divide 0.038452 by 0.1005 to three places of decimals.
39. Reduce £1.00065 to farthings and the decimal of a
farthing.
LII.
CIVIL SERVICE OF GREAT BRITAIN.
Open Competitive Examination for Clerkships of the Superior Class in
the India Office, 1879. — Higher Arithmetic. — Time allowed, 3
hours.
1. If 26 sheep be worth 5 oxen, 2 oxen be equal in value
to 3 horses, and 7 horses can be purchased for 91
guineas, find the value of 1 sheep.
2. Simplify the following, and express the results as deci-
mals :
(i.) (2-H)x(3-
r-\ 2J- of 3 U of _
(1L' 3frf2 ~ 4 of 2 " 2} + I
(iii.) 0.16 -f- 0.0027.
3. Divide 987,654,321 by 3509, and 0.00321 by 0.000011.
Find the value of 2.0136 of £2 1 s. 3d.
4. Explain what is meant by the G.C.M. and the L.C.M.
of several arithmetical quantities.
ARITHMETIC. 131
Find the G.G.M. of 5049, 4301, 3553.
The driving-wheel of a locomotive engine is 27|- feet in
circumference, and the fore-wheel 16 feet. Two
particular spokes, one in each wheel, are observed
pointing vertically upwards. How far will the
engine travel before the same two spokes are again
simultaneously in the same direction, and how often
will this happen in 9 miles ?
5. What is the present worth of £1866 16s., payable 2
years hence at 3 per cent per annum?
6. The area of a rectangular piece of ground is 87 acres
1 rood 26 perches. What is its length, its breadth
being 462.5 links?
7. A block of granite is 17.7 feet broad, 9.4 thick ; what
length must be cut off so as to contain 554.6 cubic
feet?
8. Find the square root of 1,874,161. Extract to 4 places
of decimals the cube root of 0.002.
What must be the side of a cubical cistern which is to
contain 1000 gallons of water, if a gallon contains
277.164 cubic inches?
9. A grocer mixes 2 kinds of sugar at 4d. and 61 d. per
pound, taking 3 pounds of the first to 2 of the sec-
ond. At what price per pound must he sell the
mixture to gain a profit of 20 per cent ?
10. Divide £144 10s. among 3 persons in the proportions
of 0.3, 0.33, and 0.3.
11. A merchant invests half of a sum of money in the 3 per
cents at 92, and the other half in the 3-^ per cents
at 98. Which is the better investment? If he
receives £44 as income, what is the amount of the
sum?
134 EXAMINATION PAPERS.
22. A ditch has to be made 360 feet long, 10 feet wide at
the top and 3 feet wide at the bottom, the angle of
the slope of each side being 45°. Find the number
of cubic yards to be excavated.
23. A circular pond has an area of 346|- square yards.
Find to the nearest penny the cost of fencing it
round at 4s. 6c?. per lineal yard.
24. A cubical block contains 1 cubic yard, 2 cubic feet,
541 cubic inches. Find the cost of covering the
entire surface with lead at Is. C>d. per square foot.
25. A hemispherical punch-bowl is 5 feet 6 inches round
the brim. Supposing it to be half full, how many
persons may be helped from ifc in hemispherical
glasses If inches in diameter ?
LIV.
CIVIL SERVICE OF GREAT BRITAIN.
Open Competitive Examination for Admission to the Royal Indian
Engineering College, July, 1880. — Time Allowed, 3 hours.
1. Add together 4fl, 7^, If |f , and l|f
2. Subtract 2-f$ from 3^.
3. Multiply together 1^, 17|, l^f, 1-^, and 2^.
4. Divide 7-& by
5. Add together 17.429, 0.0173, 1156.8, and 0.0001723.
6. Subtract 60.25738 from 356.17.
7. Multiply 7.18 by 0.0919.
8. Divide 331.8553 by 55.3.
9. Express 1 peck 1 gallon 3 quarts as the decimal of a
quarter.
ARITHMETIC. 135
10. Add together |f , ^, and
11. Subtract 19JL- from 20^-
12. Multiply together 2-J, 1-g^, 1^, and -^
13. Divide 7{| by l|f .
14. Add together 2.25 of a cwt. and 5.76 of an ounce, and
give the answer in quarters and the decimal of
a quarter.
15. Subtract 18.75 dwts. from 2.12875 pounds, and give
the answer in grains arid the decimal of a grain.
16. Multiply 42.317 by 10.075.
17. Divide 48 by 0.144.
18. Reduce 19.062 furlongs to inches and the decimal of
an inch.
19. A steel plate is 11 feet 6 inches 5' long, 3 feet 2 inches
8' wide, and 1 inch 3' thick. Find, by duodecimals,
the number of cubic feet, cubic inches, etc., it con-
tains.
20. Two circular courts measure 40 and 50 feet in diam-
eter. The paving of the former costs £ 74 16 s. 8 d.
Find the cost of paving the latter at the same rate.
21. A rectangular room has its length, breadth, and height
as 7, 6, 5, respectively. Its walls were decorated at
a cost of 2s. 6d. per square yard, and its ceiling
finished at the same rate. The bill for the whole
was £86. What will be the expense of covering
the floor with carpet at 7 s. per square yard ?
22. Find the cost of constructing a hemispherical dome of
stone, the internal diameter of which is 45 feet, and
, uniform thickness 18 inches, at 4s. \d. per cubic
foot of masonry.
136 EXAMINATION PAPERS,
23. The diameters of a conical frustum of marble are 17^-
and 10-|- inches, and the height 24 feet. Find its
volume.
24. A and B receive 1GOO cabbages to plant, but of these
10 prove worthless. A plants 5 while B plants 4,
and the rows are equal. After some hours they
have, not sufficient between them to complete an-
other row, A having 45 to spare and B 6. A then
finds he has planted three rows more than B. How
many did each plant, and how many cabbages in a
row?
25. A fast train, travelling at the rate of 36 miles per
hour, leaves Dover for London, 79 miles distant, at
8 A.M., and is shortly after followed by a slow train
whose speed is 24 miles per hour. The former train
meets at 8.45 the express from London, which covers
48 miles in the hour ; and the slower train from
Dover meets the express 12-|- minutes later. Find
at what time the express leaves London and the
slow train Dover, supposing both trains to travel
uniformly between Dover and London.
LV.
CIVIL SERVICE OF GREAT BRITAIN.
Competitive Examination of Candidates nominated for Appointments
in the India Forest Department, Jan., 1880. — Elementary Arith-
metic. — Time allowed, 2% hours.
1. Eeduce 4 tons 1 cwt. 11 pounds to ounces.
2. If 1 pound 2 ounces 5 pennyweights of gold cost £69
9s. 4-|-<f., what is the price per ounce?
ARITHMETIC. 137
3. Find (by practice) the value of. 2 cwts. 2 quarters 21
pounds at £4 per ton.
4. Find the simple interest on £3650 for 8 years at 3J
per cent per annum.
5. Add together f , f , J, and -fa.
6. Subtract 2ff from 4^.
7. Multiply 5-J- by 1£.
8. Divide 5^- by 2J-.
9. Add together 0.20765, 0.00631, 6758.13247, and 5.973.
10. Subtract 39.984 from 400.29.
11. Multiply 62.093 by 2.568.
12. Divide 14.9455 by 35.5.
13. Keduce 0.325 of 10 cwts. to pounds.
14. Reduce 2 pounds 3 ounces 4 pennyweights to grains
Troy.
15. If 3 acres 2 roods of land cost £375, what will be the
value of 4 acres 2 roods 29. perches ?
16. Find (by practice) the value of 32,679 articles at £1
11s. Qd. per dozen?
17. Find the amount of £2930 in 3 years at 2 per cent per
annum compound interest.
18. Add together 2f , -ft, 3 J, and f
19. Subtract 15-ff from 20-^-.
20. Multiply together 2} , 4£, 5f , and f
21. Divide if by 2|.
138 EXAMINATION PAPERS.
22. Add together 0.61692, 243.734, 400, 67.45213, and
2.683.
23. Subtract 284.7654 from 321.07659.
24. Multiply 2.8456 by 0.00325.
25. Divide 85.5 by 0.00684.
26. Express 3s. 9d. as the decimal of a pound.
27. In 1,320,765 square inches, how many acres, roods,
perches, etc. ?
28. If the second class railway fare is -f- that of the first,
and the third class J that of the second, and a first
class passenger can travel 125 miles for £1 11s. 3d.,
how far can a third class passenger travel for 8s. 4 d. ?
29. Find (by practice) the dividend £269 17s. &d. at 13s.
10 d. in the pound.
30. In what time will £1050 amount to £1548 Is. IQ^d.
at 5J per cent per annum simple interest ?
31. Add together 5||, 2f , ^ and |f.
32. Subtract 9-^- from 19^,.
33. Multiply together if, 2f , yfc, and 1^.
34. Divide 4| by 6f .
35. Add together 0.32 of a pound and 0.45 of a shilling,
and give the answer in pence and the decimal frac-
tion of a penny.
36. Subtract 0.428 of a gallon from 3 quarts 1.25 pints,
and give the answer in pints and the decimal of a
pint.
37. Multiply 0.07864 by 0.000973.
38. Divide 16.8951 by 28,300.
39. Express 3 furlongs 2 poles as the decimal of 2J miles.
ARITHMETIC. 139
LVI.
CIVIL SERVICE OF GREAT BRITAIN.
Competitive Examination of Candidates Nominated for Appointments
in the India Forest Department, Jan., 1880. — Higher Arithmetic. —
Time Allowed, 2J hours.
1. Find the square root of 64.55961801, and of 70|i|.
2. Resolve 2520, 2772, and 30,888 into their prime fac-
tors, and thence deduce their L.C.M.
3. Find the value of ^4f .-*- ^Tju") X °'3^ X °'2^ of
11 shillings. * 7 • 42 /
4. Divide £3293 6s. 6d. among 5 persons in the propor-
tion of the fractions -|-, ^, ^, ^, and ^-.
5. Multiply (by duodecimals) 4 feet 3 inches 7 parts by
2 feet 6 inches 3 parts, and the product by 8 feet 9
inches. What does the answer become when ex-
pressed in cubic feet, cubic inches, and the fraction
of a cubic inch ?
6. Find the length of the edge of a cube containing 12
cubic feet 1216 cubic inches, and the cost of cover-
ing this cube with copper at 10|- d. per superficial
foot.
7. A plot of land, containing 4 acres 3 roods 20 perches,
is valued in 1879 at £1681 17s. 6d., being 15 per
cent more than it was estimated to be worth in
1878. What was the estimated value per acre in
1878.
8. A man has £5000 of stock in the 3 per cents. He
sells out when they are at 98, and invests £2000 in
India stock at 104, paying 4 per cent, and the re-
mainder in railway shares at 87|-, paying 5 per cent.
Find to a penny the alteration in his income.
140 EXAMINATION PAPEKS.
9. A cistern, measuring inside 4 feet 9 inches long, 3 feet
G inches wide, and 3 feet deep, is filled with water.
Find approximately the number of gallons it con-
tains, and the weight of water on a square inch of
the bottom. (A cubic foot of water is equal to 6.25
gallons, and weighs 62.321 pounds.)
10. A sovereign of standard gold weighs 5.136 dwts., and
a shilling of standard silver weighs -^Q- of a pound
Troy. What weight of standard silver is equivalent
in value to 5 ounces of standard gold ?
11. A water-tank can be filled by one tap in 3 hours, and
by another in 2 hours. It can be emptied by a
third tap in 1 hour 24 minutes. The tank being
empty, all three taps are opened at once. Kequired
the time of filling it under these circumstances.
12. A starts to walk from London to Croyclon, a 'distance
of 10 miles, at the same moment that B leaves Croy-
don for London. A walks at the rate of 3 miles an
hour, and B at the rate of 2J miles an hour; but,
soon after they started, A met with an accident
which caused him to lose 15 minutes on the road.
At what distance from London will they meet ?
YB I /44c5
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