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114.5
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3.2
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3.6
4.0
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1.8
1.6
A APPLIED IfVMGE
Inc
1653 East Main Street
Rochester, New York 14609 USA
(716) 482 - 0300 - Phone
(716) 288- 5989 - Fax
,t
PROBlwKMS
IN
d-}
■^X
ARITHMKTIC
M
Suitable for Candidates
preparing for the Entrance Examinations
to the Prince of Wales College
and Normal School.
SELECTED FOR USE IN THE
SCHOOLS OF PRINCE ED\^•ARI) ISLAND
¥i
BY .^
D. J. JvIACLBOD
>;H1EF superintendent ok gDUCATIUN
^
HASZARD & MOORE, VICTOIUA ROW
1892
\J./ / .c
mml EDWAR3 ISUNO
pUBLiC ABCK^VES
ACCESSION No-
2feH^
ITEM ^lo....
*.Ji.^«»-*— -M).'- -•**•
I^ROHL.l:!:i\lS
IN
ARITHMETIC
Suitable for Candidates
preparing for the Entrance Exaini nations
to the Prince of Wales Collep".
and Normal School,
SKI.KCTEU FOR USK IN THE
SCHOOLS OF I'RINCE EDWARD ISLAND
OY
IJ. J. rvlACLEOD
CHIKK SUl'EklNTENDKNT OF KUUCATIOX
CharlottetoUju^
HASZARD & MOORE, VICTOI ^ ROW
1892
PROBLEMS IN ARITHMETIC
SUITABLE FOR CANDIDATES I'REl'ARING FOR THE ENTRANCE
EXAMINATIONS TO THE PRINCE OF WALES
COLLEGE AND NORMAL SCHOOL.
1. Show which is the least and which the greatest of .he
folIow-.g fractions :~l of 9,1, U of 9, ^ of 8.2.
2. If telegraph posts are placed 80 yards apart, and a train
passes one every 4 seconds ; how many miles an hour is it
running ?
3. A regiment marching 3/^ miles an hour takes no steps in
a mmute. What is the length of the step ?
4. llow many yards of carpet 15 inches wide will cover the
floor 01 a room 22 j^ ft. by 19 ft.?
5. Simplify 83-1^ of 2j\ of i| + 2Kt^-7.
6. Find the sum of 6.27, 18.651, and 12.345, and the differ-
ence between .34027 and .27.
7. If a room be 12 ft. square, what must its height be in order
that the area of the walls may amount to 60 sq. yds.?
8. A stone house is 36 ft. by 24 ft. How many perches of
mason work are there in the basement walls if they are 24 in '^,
thick and 9 fi. hi|_:
rROHLKMS IX
acre
9- I'Mi'l the cost of a square mile of prairie land at $3.25 per
\
10. A field in tlie form cf a rectan^de is 15 chains long and 40
rods \vi<le. I low many acres does it contain ?
11. The estimated value of a school district is $450,000.
How many mills on the dollar will have to he levied to raise a
tax suflirient for $1,200 school expenses?
12. A wheal held of ^^ acres will averaj^'e a yield of 22
hushels to the acre. What is the slandin^^ ^.rain uorth if wheat
IS worth $1.25 a imshel and it costs $1.60 an acre to prepare it
for market ?
13. What will it cost to hy the brick of a house 36 ft. hy 30
ft. and 21 ft. hijjh, with a Oat roof and double waPs, at $2.75
per thousand }
14. How many feet of iX-in. flooring are required for a
verandah around three sides of a house 40 ft. long and 24 ft.
wide, if the verandah is 8 ft. wide.
15. Find the cost of the lumi)er Un the dressed d(jor facings
of 15 doors, each 7 ft. high and 2 ft. S in. wide, the facings being
6 in. wide, at $iS per M. feet
16. Find the cost of laying a double roof 50 ft. long, rafters
^24 ft. long, with shingles 4 in. to the weather, at $3.60 per M.
17- rind the cost of lathing and plastering a room 12 ft. by
14 ft. and 9 ft. high, with laths at 30 cents a bunch, and plaster
at 10 cents a scpiare yard.
18. What will it cost f(^ survey 36 miles of railway at $1. i2>^
per chain ?
19. Find the cost of carpeting a stairway of 24 steps, each
12 in. wide, and having a rise of 8 in., allowing 2 ft. extra for
the projection of the steps ; the carpet costing $i.2q oer vard.
'i
iNrniMF/nc
■
20. From a lot 40 r.xls s(|uarc I sol. I 40 s(|iiarc 1. .Is. What
is tlu' value (.f '.he remainder at $120 |)er ;u-re ?
21. How many Irct of lumber in n sidewalk 160 yds. loni;,
S ft. wide, and f,'. in. thick?
22. What time vnouM 36 men, workitij; jo>^ hours a dav,
reciuire to Imild a wall uhidi 24 men working; 9 hours 20 minutes
a (!.iy, ran huild in 9 days ?
23. I low many revc.Intions will he made hy a wheel which
revolves at the rate of 360 revolutions in 7 minutes, while
another wheel, which revolves at the rate of 470 in 8 minutes,
makes 658 revoj 11 lions .•'
24. If I borrow ^'500 for 13 months when money is worth 4>^
per cent., how much ouj.;hL I to lend in return for 15 months
when money is worth 3^4 per cent }
25. If 7 men, working 16 days, can mow a field 1320 yards
hmiT, and half a mile wide, what will l,e the length of a field
1320 yards wide, which 4 men can mow in 42 days ?
26. Fifteen horses, having four {t'Mi\<, a day, can be kept for
two months for 16 guineas, what will be the cost of keeping 20
mules for 5 months, giving them three feeds a day, a infse's feed
being % of a mule's ?
27. Sixty thousand bricks are required for a wall 50 yards
long, 15 ft. high, and i ft. \o)A in. thick. Knowing each brick to
be 9 inches long, and 43^ inches wide, find its thickness.
28. A man left ]ns eldest son one-third of his property ; his
two other sons, each, one-seventh ; his three daughters, each,
one-tenth; the remainder of hi> property, which amounted to
^680, he left in legacies. What was the whole amount he left ?
29. Divide ;^3,8oo among A, B, and C, so that A shall have
twice as much as B, and C shall have one-sixth of B's share.
Il .
6 PROBLEMS JN
30. A cistern has three pipes, A, B, C, which together can fill
It in 15 minutes. The pipe A l.y itself could fill it in an hour ;
B could fill it in 45 minutes ; in what time could C fill it ?
31. A can mow a field in six days of 9 hours ; B can mow it
in 8 days, and C in 12 days. Supposing that A after mowing
for a day is joined l,y B, and that after another day they are
joined by C, when would the work be finished ?
32. Divide 1.56 by 156.25; and subtract 4.156 from 13.^5.
2,Z' Find the value of 3.751875 of ^3 6j. ^d.
34. Find the simple interest upon £2> 375 for 2% years at 6
per cent, per annum.
35. A room is 20 ft. 9 inches long, 15 ft 3 in. wide, and 12 ft
high ; find the cost of papering it with per ^ feet wide at
^Yzd. a yard.
36. Simplify .031339 X 3. i■3-^/^2^.
Z1' If a tradesman with a capital of ^500 gain ^60 in seven
months, how much will he gain in a year with a capital of ^^420?
Z^. Two men or 5 women can do a piece of work in 12 hours,
how long will 5 men and 2 women take to do it ?
39- If 3^nien or 5 women can do a piece of work in 20 days
in what time will it be done by 8 men and 20 women working
together ?
40. Reduce 3. 1136 miles to yards.
41. Find the circumference of a wheel which makes 1048
revolutions in 3j^ miles.
42. Reduce 100,196,196 square inches to acres, etc.
43- In 1,749,134 seconds, how many weeks, days, etc.?
44- Keduce 1,186,126, inches to miles, etc.
ARITHMETIC
45- Keduce % of a pound Troy to the fraction of a pound
Avoirdupois.
46. Find the vahie of .009943 ^^f a mile.
47- Divide loi by i. 01, and .101 by 10. i.
48. Reduce 14 hours 15 minutes to the fraction of y/^ days.
49- Divide .05625 by .0275.
50. Divide .5 by 25; 87.5 by 2.5, and .055757592 by
.009207. ^
51. Resolve 18, 16, 36, 44, 45, 48, 63, 121 into their simplest
factors, and find their least common multiple.
52. 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.
53- A well is 18 yards 2 inches deep, and the wheel is 4 ft.
2 inches round. H. many turns of the wheel will raise the
bucket ?
54. Find the value of .2625 of a mile.
55. Add .60457 ; 46.70056 ; 5.80007 ; and 4.7896.
56. Reduce 2.025 miles to yards.
57- If a bankrupt has assets to the amount of $1,020 and
debts to the amount of $3,225, how many cents on the dollar
will his creditors receive ?
58. A person sold % of his estate, bequeaths % of the
remainder to his son, and leaves the rest to be distributed
equally among three charities. If each of these charities
receives $136.25 what is the value of the estate ?
59. A hat IS the circumference of a wheel which makes 514
revolutions in passing over i mile, 467 yards, i foot ?
8
PROBLEMS IN
60. A j)iece of cloth when measured with a yard measure that
IS 2./ of an inch short ai)pears to be lo/X yards long. What is
its true length ?
61. Reduce 42 rods, r yard, 8 inches to the fraction of a
mile.
62. Divide the product of 6.225 an<l 8.25 by .0025.
63. Find the sum of 17.01, .1303, 500.42101, .001 and 6.6.
64. Divide 6.2301533682 by 8.8964.
65. What numi)er added to iA + 3nT + 2iV + ^T will make the
sum total 10?
66. Give in feet the value of 7.0125 miles.
67. Find the average of 21*, 7:14. o ;J-W K'? 7*7=' ci ns
68. 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 one day ?
69. Divide 78 by 361.059 to the three places of decimals.
70. Find the value of 2. 5 +
1-5
.02
6.002.
71. Fin.l tlie average of 12^, 21, 7^, .034, 3.125, o, 24.5,
and 12^. Express the fractional part decimally.
72. Reduce to the simplest form 435- 1 ^ .0046
.125
73. A brick 9 inches long, 4>< inches broad, and 3 inches
thick weighs 9 ]:)ounds nearly. What would a brick weigh if it
were 12 inches long, 6 inches l)road, and 4>< inches thick ?
74. A man buys eggs at 11 cents per dozen, and sells them at
2 cents apiece. 'vVhat does he gain per cent ?
75. What sum, put out at s}4 per cent for 6 years, will
produce ^28.^7/2, simple interest ?
ARITHMETIC 9
76. Divide I - (^f ^,- }^ l,y I - t of 1. of ,v.
77. At what price per Inindredweight must goods be sold,
which were bought at $5 per ton, in order to get 6 per cent ?
78. A r walk 10 miles in 2,i.< h.ours, and \\ can walk 11
miles in ^ > hours. They start to walk a match of 55 miles.
Which will win and by how much time ?
79- If a room is 27 ft. 5 inches long, 14 ft. 7 inches wide, 12
feet 10 inches high,, how much paper y^ of a yard wide is
recjuired to cover the walls?
80. If I buy sugar at $7 per cwt., at what rate per lb. must I
retail it to gain 7f per cent ?
81. 8implify-i^-4^-°-^'^^'^-^-°66
will
0.002
82. Find the cost of papering a room 21 feel long, i6>i feet
wide, 10,14: feet high, at fifteen cents per square yard^
83. 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 ?
^ 84. If $850 amounts to $913.75 at 2]/. per cent, find the
time.
85. A^ room is 10 ft. high, ^y^ yards long, and 3 yards wide.
It contains a door 8 ft. by 4 ft., two windows each 5 ft. by 4 ft.,
and a fireplace 6 ft. by 4 ft. 6 inches. IIoW many square yards
on its walls require to be painted ?
86. If 120 men build a house 60 ft. high in 15 days, how
many men will build a house 55 feet in 10 days ?
87. A garrison of 1000 men have provisions for 30 days. At
the end of 10 days a reinforc
last only 5 days. What is tl
ement arrives, and th_^ nrovisionq
le number of the reinforcement 1
lO
PROBLEMS IN
88. A sum of money was Ixjrrowecl at 5 per cent, simple
interest. In seven years it amounted to $810. What was the
sum borrowed ?
89. If icxD 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 ?
90. By selling 12 pounds of tea for $7.56, I can gain 5 per
cent. What do 1 gain or lose per cent, by selling 50 pounds of
the same tea for $31 ?
91. 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 ft. long and 15 feet high in 21 days of 9 hours?
92. If 2 horses can plough 7 acres of ground in a day, how
many horses will plough 161 acres in ii)4 days?
93. -^If 14 men can now 168 acres in 12 days of 8}( hours,
how many acres can be mowed by 20 men in 11 days of 7-*-
hours ?
(0.075 ^ <^-075) - (0.005 X 0.005)
0.75-0.C5
95. Simplify 3i±4±5i X ^t±4^^±4f
q6. Smip ify -^ ^- '' -^^
OllT 7x5+0^-57^
97. Fmd the cost of papering the walls of a room 10 feet 8
inches wide, 19 feet 4 inches long, and g}4 feet high, with
paper 2 feet wide at 5 cents a yard, allowing 10 yards of the
paper for waste.
^Q c- i-r S^ -0.042- 2.4 + 7f
98. Snnplify — -— ' -—^ — —
99. Find the circulating decimal equivalent to toVt'
94. Simplify
now
irs,
7*
ARITHMETIC ,j
l(X). 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 ?
loi. Divide 24.109932 by 3CI.28.
102. x\ bought 63 sheep, and sold % of them at a profit of 15
per cent., f 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?
103. If -1- of a sheep is worth %%, and f of a sheep is worth
tV of an ox, what is the value of ICXD oxen ?
104. How many bricks, each 9 inches by 4^ inches by 3
incher., are there in a pile 36 feet long, 9 feet wide, and 12 feel
high ?
105. After paying ^ of my money to one person, ^ to
another, and -^^ to a third, I had 7 cents remaining. How much
had I at first ?
106. A person walks at the rate of 3^ miles an hour. Three
hours after he has set out on a journey, he is followed by another
person, walking at the rate of 5 miles an hour. In what time
will he be overtaken ?
107. 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 ?
108. Find the interest of $1,721.84 from April ist to
November 12th, at 4^ per cent.
109. If two men can reap 2^ acres in 2^ days, how long
will it take 11 men to reap 15 acres ?
no. An army lost 18 per cent, of its strength by sickness and
desertion, and then lost 14 per cent, of the remainder in battle.
The number left was 84,624. Of how many did the arniy
originally consist ?
42
PJWBt.EMS IN
III. If 6 iron bars 4 feet long, 3 inches broad, and
thick weigh 288 pounds, how much will 15 1
2 inches
. ^«irs weigh, each 6^
feet long, 4 inches broad, and 3 inches thick ?
112. A rectangular cistern 9 feet long, 5 feet 4 inches wide,
2 feet 3 inches deep is filled with a liquid that weighs 2.520
pounds. Mow deep n ust a cistern be that w.:ll hold 3,850
pounds of the same liquid, if its length is 8 feet, and its width
5 feet 6 inches ?
113. In wiiat time will $2,275 amount to $2,673. 12^ at 5
per cent ?
114^ If 12 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 ?
115.^ 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. I2>^.
116. Reduce 167,948,604 square inches to acres, etc.
117. A man contracts to perform a piece of work in 30 days,
upon which he employs 15 men. In 24 days it is half finished.'
How many additional men must he employ to finish the work in
time?
118. Reduce to its lowest terms the product of i +i + ii +^
+ ^V + ffV. -yd rs- - -f + iP(r.
119. If 3 men mow 20 acres in 11 days of 11 hours, how
many men will it take .0 mow a rectangular field 384 yards, long
and 300 yards wide, in 4 days of 12 hours ?
120. 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 ?
121. If oranges are bought at the rate of 20 for a d
many should be sold for $28 to gain 40 per cent ?
a cioiuir, now
ARil'HMETJC
13
'72
<^i
122. Add tcgethcT 536.421, 53, 6^1, 5.36421, and subtract
the result from 100,000.
123. If 1,000 square yards produce a load of hay, how many
loads will 25 acres produce ?
124. Find the simple interest on $281.63 ^^ S'A ]ier cent for
four years and 2 months.
125. A freight train is S miles ahead of an express that travels
at the rate of a mile in i^ minutes. Twenty minutes later the
express runs into the freight train. At what rate is the freight
train running ?
126. If Y men, working 16 days, can mow a field 1,320 yards
long, and 880 yards wide, what will be the length of the side of
a rield 1,320 yards wide, which 4 men can mow in 42 days ?
127. Divide 1.765 h) 2470 to five places of decimals.
128. If 8 acres produce 220 bushels of corn, how much will
22 yards produce ?
129. $19.68;^ is 2^ per cent of what sum ?
130. If 19 men can build 38 yards of wall in 12 days, how
many men will build 96 yards, 2 feet, 3 inches in 21^ days ?
131. If 12 men build a wall 60 feet long, 4 feet 'hick, and 20
feet high in 24 days, working 12 hours a day, how many men
will It take to build a uall 100 feet long, 3 feet thxk, and 12
feet high, in 18 days, working 8 hours a day?
132. 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 ?
133- If a pint contains 28^ cubic inches, how many pints
are there in a cubic fool of water?
134. Find .015 of 17 acres, 130 square rods.
14
PROHLEMS IN
135' ^^ 5 needlewomen can finish a certain ({uantity of work
in lo;^ (lays of 9;^ hours each, how V>\\<^ would it take 3 needle-
women to do twice the same wo'-k, reckoning 10 hours to the
day?
136. Find the srjuare root of , 196 to four places of decimals.
137. How many horses will he required to plough 117 acres
in 35 (lays, if 10 horses can plough 13 acres in 7 days ?
138. If I buy 3,090 yards of cloth at ()2y2 cents per yard, and
sell the whole for $3, 205.87 j^, what is the gain per cent ?
139. How many bricks %% inches long, ^% inches wide, 2^
inches thick, can be stored in a building 17^ yards long, 10
yards wide, and 8)^ feet high ?
140. How many men working for ll 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 ?
141. A can mow | of a held in 7^ days, B can mow f of the
same field in 9;^ days. In what time can A and B together
mow the field ?
142. 'A train travels a certain distance in 4/5^ hours at the rate
of i6| miles an hour. How long will a train going \^% miles
an hour take to travel the same distance ?
143. I pay for 180 yards of cloth at 92>^' cents per yard, but
it is measured with a yard stick yi of an inch short. How
much money does the seller unfairly take ?
144. What will be the price of ^^540 stock at 76?
145. What stock at 95 can be bought for ^855 ?
lifO. r» uaL aUiiUai in;-v;mc Xb Cicilvco irutll £i^\'00 %/2 PCF
cent stock ?
ARITHMETIC
15
147. When stock is at 5 per cent premium I sell out /66cx>
nf this stock ; what money do I receive ?
14S. What is the rate of interest when the 3 per cents are
at 72 ?
149. How much money shall I receive for ;^"5400 stock at 10
per cent discount ?
150. The 3^ per cents being at 91^, what amount of stock
can be had for £^94^ ?
151. The liroker's charge being % per cent what will he re-
ceive on ;^2400, 4 per cent stock at 85 ?
152. I want to secure an income of ^600 a year; what
amount of 3 per cent stock must I buy to produce it ?
153. What income will be produced by the investment of
^6700 in the 3X per cents at 102^, taking brokerage into
account ?
154. If ;^4000 I0.5-. l)e invested in the 3 per cents at 92, what
will be gained l)y selling out at 96 ?
155. By investing in the 4)4 per cents at 95 I get an income
of jCs^o ; what sum did I invest ?
156. When the 3>^ per cent stock is at 93 j^, how much must
be sold out to realize ;^6oo, brokerage being taken into account?
157. Plnd the change in a person's income who transfers
;^2400 from the 3 per cents at 90 to the 3j^ per cents at 96?
158. How much stock is obtained by investing ^{^4500 in bank
stock at 210, brokerage being taken into account ?
159. Which is the better investment, the 3^-^ per cents at 86,
or interest at 3|^ per cent ?
1 6
PROlUJiMS IN
l6o. What nnnunl income will a person receive who invests
^2000 n, 4 per <-ent stock at 95, and ^',000 in 3 per cent stock
:u /, 105 ?
J's\. *i ' "' '"u ^' '^" ' ^"^'^ "^ ''' *'^^>" ' ^ *^'-^ ^'4 times
N^Iiat H docs in the same tim(^ and IJ dcvs 3^" what C does in the
same tune. How l„ng would it take each to do the work ?
162. Bo.ght a ninnbcr of cattle for $2000; had I luuud.t 20
head more at a cost of ten dollars per head less, my entire outlay
would have been $2800. How many cattle were purchased ?
163. Kind interest on a note for $515.62, dated March isl,
^^11^ and paid July i6th, 1875, at 8%.
164. A man mowing grass v\alks pt the rate of .35 miles an
hour and in 70 minutes mows a grass plot of 1056 square yards-
how broad does he mow ? 1 / • .
165. A tradesman has a cash price for goo<l., ami a nine
months credit price : money being worth 8% per annum simple
interest, hnd the ratio of the prices.
166. Find what (juantity must be added to
f iiilii of ^^"^^^ iL?'" '^^ I
l3iof2| ifof^+^j^ of 4i|
t'. make it equal to / ^-L"^ ^ "^ 3f ^ ^&H \
167. Seven-tenths of the selling price of certain goods is two
per cent less than cost. Find the gain per cent at which the ,
goods are sold.
168. I sold a quantity of Uank of Commerce stock at iiq
and mvested in Consolidated Bank stock at 92, which I after-
wards sold at 98, and re-purchasing my Bank of Commerce stock
which has risen to 120, I found I had gained $125 by the
operations. How much Bank of Commerc^^ <u.A.. u^,^ j /
./■»
ARITHMETIC
'7
• •/wl
169. A l)()y hires witli a farmer f..r $100 a year and a suit of
clothes, i)ut leaving' at the end of 7 months, receives $50 and
the suit of chuhes. Find the value of the clothes.
170 Two sums of money are to he (hvideil amon^' three
persons, one sum equally and the other in the proportion of 3,
5» and 8; the shares of the first two amount to $64.56 and
$81.36 : determine the sums.
171. If the rates of wages of a man, a woman, and a child,
be as 6, 3, and i ; and 25 men, 30 women, and j6 children get
$640 for 10 days' work; hnd how much 32 men, 36 women,
and 72 children should get for 8 days' work.
172. A man has a triangular field of which the sides are 115;^
feet, 1281^ feet, and 13434; feet ; hnd the length of the longest
boards of equal length thai can be used in fencing it without
cutting a board.
173. A publican uses measures which are false to the extent
of 5% ; but his brewer gave him in every barrel only 35 gallons.
The publican buys at $5.04 a barrel and sells at 4 cents a pint.
What does he gain on a sale of 200 barrels ?
174. What sum must be insured on a house worth $665, so
that in case of loss the owner may receive f of this sum, and
■dso f of the premium, which was at 6 per cent ?
175- If a number be increased 20%, and the amount be
increased i6%%, the result will be 280 ; find the number.
176. Sold wheat at $1.00 per bushel and gained $30 on the
quantity sold; had I sold it at $I.I2X I would have gained $42
on the same quantity. How many bushels did I sell ?
177- Seven men engage to do a piece of work in a certain
time, but three of them failing to come, the work was prolonged
Ty-z days. In what time would the seven men have it done ?
1 8
r/WHLKMS IN
\
178. A nicrc'lKint sells 90 Ihs. of lea an<l coffee for $76, the
tea at 90 cents, and the coffee at 40 cents j)er Ih. 1 low many
)l)s. <'■' oar h ^i(l he sell?
i7< tiwer in s*Hin|T goods sells 15^ oz. for a pound, how
ll^Uch aoe.s '" cheat a customer who buys to the amount of $40?
180. Sold }^'oods for $2.10 and gained ', ^ of the price.
Whui part of the cost would be gained by selling at $2.60?
f.*?F Reduce to its simplest {'orm
1 .ooH
\ I .003' 500
.ot;
25
182. A man bought a store and contents for $4720; he sokl
the same for 12^% less than he gave, and then lost 15% of the
selling price in bad debts. Find his entire loss.
183. A ells goods to B at a loss of 4%, \\ sells them to C at
a loss 6 '4^%, C sells them to D for $390.60, gaining 8^-^% ; fuul
the prime cost of the goods.
184. A and B invest capital in the proportion of 3^ to 4.
After five months A withdraws one-half his capital, and B with-
draws two-thirds of his. At the end of the year they have
gained $7,090 ; find each man's share.
185. A bankrupt has book debts equal in amount to his
liabilities, but on $24,000 of them he realizes only 6673 cents in
the dollar, and the expenses of the bankruptcy are 5% on the
l)o?M< dei)ts ; he pays 65 cents in t-he dollar ; find the amount of
his liabilities.
186. Simplify
8|-^of^ iof->iofJ 2.8 '>.
6^xi
of \ ■ 2i.KixA
•2
T
.16
(1
ARirilMETlC
19
187. Ue<luce 2\ of 3.\ of !, of 3I I'lnglish ells to the fraction
of \ of \ of 5'( French ells.
158. A can ilo a piece I work in 5, H ; « o. xnd C in 8 days.
If A and H work at it tuo days each, how lonp will it take H
and (' to hnish it ?
159. A man huys land at $60 pei acre. If he sell Vs *>» it to
A at $So per acre, /, of the remainder to B at $22 for % of an
acre;, and the rest, which is 120 acres, to (^ at $75 for % <»f an
acre ; what is his gain or loss ?
190. Sold tea at 90 cents per lb., having gained .vV, ' i the cost,
finii the selling price per lb. if he had lost nV
191. A man can row a boat from A to H (a distance of 30
miles) in 7j^ hours if there be no current ; how long would it
take him to row it if there was a current of I j^ miles per hour
from B to A ?
192. When the 3 per cents were at 90, I found lint by selling
out and investing in India 4 per cents at 95 I could
improve my income by £2^ ds. Find the amount u my stock
in the 3 per cents.
193. A own I of a vessel and B the remainder ; the vessel is
sold, A receiving Co per cent of his share of the mone) , and B
20 per cent of bis ; B afterwarchi received $4000 fi >m the
purchaser, and the balance then due was divided ecpially >etween
A and B. What is the ship sold for ?
194. A man sells out \ of stock in a certain railway, )aying
2% half-yearly dividends, and invests in Bank of Con nerce
stock at 120 and paying 4% half-yearly dividends ; he fines that
\\\% ifjf.cjnie is tlius increased .*'?'J'2'X i find the amount < ; his
railway stock.
f
20
PROBI.EMS IN
195. A man's income is derived from tlie proceeds of $4550
at a certain rate \^L■: cent, and $5420 at one per cent more than
the former rate ; his whole income being $453, find the rates.
196. A farmer gives for a horse a bill of $272, due in two
months, and sold him at once for a bill of $316, due in 5
months ; find the farmer's gain or loss, true discount being
reckoned at 4^^ per cent.
4 of jJ- -^ c\^ '^
2 4. 4 _ 1
-=- f of i of % of a rod to the
197. Reduce ^
■2
fraction of 2 furlongs.
198. A grocer, by selling 10 lbs. of tea for a certain sum,
gained 20 per cent ; afterwards he increased his price, giving
only 9 lbs. for the same money. How much per cent did he
make at his increased price ?
199. Find^ihe expense of papering a room 21 ft. long, 15
wide, and 12 high, with paper 30 inches wide, at 18 cents a
yard, allowance being made for a door 7 ft. by 3 ft., and two
windows each 5 ft. by 3 ft.
200. An insurance company took a risk at 2^%, and reinsured
t of the risk at 2%; the premium received exceeded the premium
paid by $42 ; fiml the amount of the risk.
201. Simplify! If + f of ^_-|_|^2,W.
202. A sum of money was divided among A, B, and C ; A
received .939 of ^f of it"; B, ^^ of it, and C, $3015.30; find
the amount divided.
203. A trench 80 yards long, 10 feet deep, and 9 feet wide,
was completed by 20 men in I2>^ days, of ten hours each ; and
a trench 76 yarfls long, and twelve feet deep was completed by
thirty men in ^% days, of 9^-2 hours each ; how wide was the
liUor trench ?
ARirHMETfC
21
$4550
204. The cost of carpeting a room 10^-2 yards long, with
carpet 27 inches wide, and costing $1.35 a yard, was $93.15 :
find the width of the room.
205. A grocer mixes 60 lbs. of tea at 65 cents a lb., with 80
II1S. at 60 cents a lb.; at what rate per lb. must he sell the
mixture to gain 30% ?
206. A person loaned $480 for two months and 13 days, at
9% : what interest did he receive ?
207. I send $5250 to a commission merciiant in Montreal,
who charges 5% for investing, with instructions to purchase
certain goods, deducting his commission from the amount of
money sent him : find his commission.
208. A coal dealer bought 784,000 lbs. of coal, at $4.50 a ton
(2240 lbs.), and sold 524,500 lbs. of it at the rate of $5.50 per
short ton (2000 lbs.), and the balance at $4.20 per short ton :
find the whole gain.
209. From a pound Troy are coined 46!^ sovereigns ; find
(in £ s. d.) the price per oz. of gold.
210. Divide $29.50 between two persons, so that one shall
receive half as much again as the other. *
i^
6-5
IT
211. Simplify i of H-TTT of H + A of -^
211. The sum paid for 494 gallons oil, inchiding a duty on
each gallon which amount§ to \ of the cost price of a gallon, is
$1719.12 ; find the duty on a gallon.
213. A person insured a house for | its value at \\% annually;
after paying 6 premiums the house was destroyed, llie entire loss
being $1945. Find value of the house.
22
PROBLEMS IN
214. A parcel of 12 lbs. weitrht is carried 80 miles by rail for
56 cents, and the rate for the distance over 50 miles is two-thirtls
of the rate for the first 50 miles ; how far can a parcel of 8 lbs.
be carried for 16 cents ?
215. A and 15 agree to do a certain piece of work for $25 ; A
could do it in 8 days, and B in 10; but C joining them, the
work is done in 3 days : how should the money i>e divided ?
216. State the difierence between " True " and " Bank " dis-
count. I owe a man $575, and gave him a note at 60 days :
what must be the face of the note to pay him th<:: exact del)t,
when discounted at (iiank discount) i/^/o a month?
217. A drover bought oxen at $40, cows at $30, and sheep at
$10 a head ; there were 2^ times as many cows as oxen, and 5
times as many sheep as cows, and the whole cost was $1440 ;
how many of each did he buy ?
218. Find the cost of painting a room 20 ft. 3 in. I)y 18 ft. 6
in., and 10 ft. high, having two windows, each 7 ft. by 4 ft., at
the rate of 50 cents a square yard.
219. The true discount on $1235.68^^ for 210 days is
$31,173^; find the rate per cent.
220. What sum of money must be divided among A, H and
C, so that A may have $1.44, and C $2.25, and that B may have
as much per cent more than A as C has more than B ?
221. Divide the number 474 into three such parts that three
times the first may be equal to 5 times the second and to eight
times the third.
222. Simplify,
ARiriL\]ETlC
23
223. A wine merchant pays $175 for a hogshead of wine, and
bottles it off into an equal number of quart, pint, and half-pmt
l)ottles : how many dozen of each has he, and at what must he
sell it per dozen to gain 5% of his outlay ?
224. What must l)e the face of a note so that when discounted
at a bank for 4 months and 9 days, at 9 per cent, it will
give $240 ?
225. A, B and C having equal shares of a ship, sell respective-
ly one-third, one-c|uarter, and one-fifth of their shares to 1), who
dies and leaves his share equally among them : If B's and C's
interest in the ship be now worth %l1,2PO, what is the value of
A's share ?
226. A farmer has 500 bushels of wheat ; he can sell it at
once for $1.20 a bushel ; by storing it for six months at a cost
of $20 paid in advance, he can realize $1.30 a bushel ; he adopts
the former course ; money being worth 8% per annum, determine
how much he has gained or lost l^y so doing.
227. Express the value of .83 of 8j. +.65 of 2 guineas +
1.8 of 5^.
228. A merchant bought a number of barrels of flour for
$1800 ; he used 20 bbls. and sold -i of the remainder for $1568,
which was $224 more than cost. How many barrels did he
buy ?
229. When gold is quoted at 133^, what is the gold value of
a $10 greenback ?
230.. What is the area of a circle whose diameter is i foot I
inch ?
2 ''I, Mow menv Dencils may be bought for $1.00, so that
20% may be gained l)y selling them 4 for i cent ?
I
24
PROBLEMS IN
232. A l)oy hired to a mechanic for 20 weeks for $20 and a
coat, at the end of 12 weeks the boy quit work and was paid $9
and the coat. Find vakie of coat.
233. At what discount must I buy stocks so that by seHing at
2% premium I may gain 20% on my investment ?
234. What number is that, fV and % of which being multi-
plied together will produce the number itself?
235. A and B can build a wall in 4 days, B and C in 6 days,
A and C in 5 days ; required the time, if they work together?
236. A makes B a present of $100 on condition that he shall
expend it in cows, sheep, and geese ; cows at $10, sheep at $1,
and geese at idy^, cents, so as to have just a hundred in the
whole. How many must he purchase of each ?
237. A, B and C start from the same point to travel round an
island in the same direction, 'J2> miles in circumference; A at the
rate of 6, B 10, and C 16 miler, per day, in what time will they
be met together ?
238. By selling at 2,1 cents a pound, twice as much is gained
as by selling at 29 cents a pound, what per cent is gained by
selling at 32 cents a pound ?
239. A house that cost $8250 rents for $750 a year, the
insurance is tV%, and repairs >^% every year. What rate of
interest does it pay ?
240. A box, with cover, made of board an inch thick,
measures on the outside, 20 inches long, 14 inches wide, and 8
inches deep ; tind the cubic contents of the interior, and the cost
of painting the outside at 18 cents per square foot,
241. I can obtain $6 more per annum by investing a certain
sum in 5 per cents at I2S>4 than in the 3 per cents at 81 ; wiiat
is the sum ?
ARITHMETIC
25
ANSWERS
I. %% of 8.2 ; greatest \ of
23.
' 9^.
24.
2. 40] ? niiles.
25-
3. 2 feet 9f inches.
26.
4. 114 yards.
27.
5- 82H;
28.
6. 37.2748839. .0625.
29.
7. iiX feet.
30.
8. 88 perches.
31-
9. $2,080.
10. 15 acres.
32.
II. 2% mills.
ZZ-
12. $958.30,
34.
13. $156.81^
35
14. 1040 feet.
36.
15. $4.77.
n
16. $86.40.
38
17. $14.30.
39
18. $3240.
40
19. $17.50.
41
20. $1170.
42
21. 5760 feet.
22. sYl-
• «
576.
/600.
48 guineas.
3 inches.
;^8,400.
;^2,40o; ^1,200; ^200.
36 minutes.
I day 4 hours after C
joined A and B.
.009984 ;"9Ttwa^ ^%(i9 ^^
£12 los. i}4(i.
£S40.
£8 2s.
•555555-
;^86 8s.
4^% hours.
3 days.
5480 yards.
10 feet.
15 acres, 155 square rods,
23 sejuarc yards, I square
foot, 24 square inches.
26
43.
44.
45.
46.
47.
48.
49.
5o.
51.
52.
53
54.
55.
56.
57.
58.
59.
6o.
6i.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
PROnr.EMS IN
2 weeks, 6 days, 5 hours,
52 minutes, 14 seconds.
18 miles, 230 rods, 8 feet,
10 inches.
I s
"So"
3 rods, 2 feet, li^^^i in.
100; o.oi.
1
2.045.
0.02 i 35 ; 6.056.
609,840.
25 gallons.
3.
80 rods, 22 yards.
57.8948. , ^
3,564 yards. J.f^
$4,905. ^*-j
13 feet.
10 yards, 11 inches.
T¥T.
20542.5.
524.16231.
0.7003005.
".fiw75v^
37026 feet?
1015487/
16.01 16S.
24 lbs.
74.
75.
76.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93-
94.
95.
96.
97.
98.
99
100,
lOI.
102.
103.
104.
105.
^tt3^ per cent.
$137.50.
A, ])y 7^ minutes.
136^ yards.
$0.07^. ,
6,199. ^ f
176 yards.
3 years.
44 square yards, 5 scjuare
feet.
165 men.
3,000 men.
$600.
15 days.
(iain 3 U per cent.
\T,% inoies.
4 horses.
208 A.
0.008.
I.
I.
$5.25.
40.2175.
0.000999.
685?.
0.080026
$551.25.
$2,000.
48 cents.
ARITHMETIC
27
juare
106.
7 hours.
136.
0.4427.
107.
74 cents.
137.
18 horses.
108.
$47.76.
138.
12^4 per cent nearly. j
109.
3 days.
139.
248,832. '
no.
120,000.
140,
$S9.i5t^. 7/-^-^--
III.
2340 lbs.
141.
^n^.^
112.
3 feet, 9 inches.
142.
4 hours.
113.
3 years, 6 months.
143.
$2.89^^
114.
5 men.
144.
;^4I0 8j'.
115-
1834^ per cent gain.
145-
;^900.
116.
26 acres, 126 square
rods,
146.
^227 \os.
29 square yards,
&c.
147.
/6930.
117.
45 men.
148.
^4^. 1
118.
'A-
149.
^4860.
119.
9 men.
150.
^3200.
120.
5% g^in-
151.
/3.
121.
400.
152.
;^ 20,000.
122.
45816. 1 1479.
153-
^211 i8.^ 5r%y.
;^i73 18.V. SM
123.
121. ^/
154.
124.
$36.^. 6 /^^
155-
;^76oo.
125.
24.
156.
^^645 y. 2nd,
126.
1320 yards.
157.
£'j los. gain.
127.
0.00071.
158,
^2141 lis. 7\md'
128.
4 quarts.
159.
y/2 per cents.
129.
$945.
160.
^112 I5.y. 7i^jV.
130.
27 men.
161.
A 282^ ; B 351 ; C 26^
131,
iS men.
162.
40 head.
132.
855^ per cent.
163.
$97.9 + .
ni-
59t?.
164.
49
T51T'
134-
42 square rods, 22 square
165.
50: 53.
yards, 6 square
feet,
166.
tHs-.
nt;.
2'7 cn\]n».f; inches.
14 days.
— / •
168.
6000 Stock.
28
PROBLEMS IN
169.
$20.
206.
$8.76.
170.
$118.08. $134.40.
207.
$250.
171.
$744-
20S.
$412.32;^.
172.
6,\.
209.
/3 I7A-. lO^r/.
^11'
$1349.891%.
210.
$11.80 $17.70.
174.
$400.
211.
<i7
1 tl (T .
•75.
200.
212.
58 cents.
176.
96 bushels.
213.
$748oi!}.
177.
10 (lays.
-14.
30 miles.
178.
80 lbs. tea, 10 lbs. coffee.
215.
A$9-37K ; l^$7-5o; ^
179.
62)^ cents.
$8.I2>^.
180.
7-
216.
$593.70.
181.
7^'5.
217.
6 oxen ; 15 cows ; 75
182.
=^$1209.30.
sheej").
183.
= C()st C $360; W $384;
218.
$39. 94a •
A $400.
219.
4/2%.
184.
A'sgain $3570; B-s'gain
220.
$5-49.
$3520.
221.
240. 144. 90.
185.
$26666^^.
222.
1 ti 4 ;t -2
•J!J1 4!..
186.
c^M '-^t
223.
I dozen each, $2.397.5,
187.
:; '2 r, ^
$4-79^6, $9.58'''-.'
188.
;['-; of a day.
224.
$247,998.
189.
$10140.
225.
$16700.
190.
6^:^ cents.
226.
Loss $5.
191.
227.
17^. 9iV/.
192.
^■3078 stock.
228.
300 barrels.
193-
$50,000.
229.
$7.50.
194-
$41662.^.
230.
132.7326 scjuare inches.
195-
4% 5%.
231.
480.
196.
$40. 20.
232.
$7.50.
197.
ifff, of furlong.
233.
15%.
198.
^iva-
234-
20.
199.
$19,512.
235-
3:^V ^i^ys.
200.
$4000.
236.
5 cows, 41 sheep, 54 geese
201.
ix.
237.
36^ days.
202.
$11056.10.
238.
28%.
203.
(ifi feet.
239.
8%.
204.
4} -4 yards.
240.
1296 cubic inches, $1.38.
205.
Soii.
241.
$3078.
I
Sci
anc
it a
tioi
are
anc
nu]
«
i
ex]
ref
thi
ARITHMETIC
29
APPENDIX
1. Define Arithmetic as a Science and as an Art. As a
Science, it logically investigates and philosophically classifies
and arranges the principles and rules of the subject ; as an Art
it applies these principles to the practical affairs of life.
2. Upon what is Arithmetic founded, and how are its opera-
tions carried on ? It is founded on notation, and its operations
are carried on by means of addition, subtraction, multiplication
and division.
3. What is a Unit ? One, or a single thing.
4. What is a number ? A unit or a collection of units.
5. W'hat is an integer ? A whole number.
6. What is notation ? A method of counting or expressing
numbers by characters.
7. What is numeration ? A method of reading numbers
expressed by characters.
8. What is an abstract number ? A number used without
reference to any particular thing.
9. Concrete number ? One that has reference to a particular
thing.
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30
PROBLEMS IN
10. I low are nuniltcrs classified ? They are classified as
follows : as even and odd, prime and composite, integral and
fractional, abstract and concrete, simple and compound, like and
unlike.
11. What is the minuend? The number to be subtracted
from.
12. What is the subtrahend? The number which is sub-
tracted.
13. What is factoring? The process of separating numbers
into factors.
14. What is a prime number? One that cannot be resolved
into factors.
15. When are numbers prime to each other? When the"
have no common divisjr.
16. What is a common divisor ? One that will divide two or
more num])ers without a remainder.
17. The greatest common factor ? Is the greatest factor that
will divide two or more numbers without a remainder,
18. What is a least common multiple? Is the least number
that is exactly divisible by two or more given numbers.
19. What is a vulgar fraction ? A part of a unit.
20. What is a decimal fraction ? A fraction whose denom-
inator is increased or decreased in ten fold ratio.
21. Upon what does the value of a decimal depend? Its
place from the decimal point.
22. What arc circulating decimals ? A decimal in which a
figure or set of figures are continually repeating.
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1
ARITIIMETJC I
23. What is the difference l)ctvveen decimal fra* u , id
common fractions? The first has a denominator u tood,
showing that a unit is divided into ten equal parts, or sub-
divided into a ten-fold ratio ; the second has a denominator
shewing that a unit is divided into any number of equal parts.
24. What is currency ? The medium of circulatitjn.
25. From what was the sign % derived ? From the initial
letters of the United States. U. S. joined together as a
monogram.
26. What is a standard unit ? A unit of measure from whicli
the other units of the same kind may be derived.
27. What is the standard unit of value ? Money is the
standard unit of value and is of two kinds, coin and paper
money. In Canada and the United States the standard unit is
the dollar. In English money it is the pound.
28. What is the standard unit of weight ? Troy pound.
29. What is the standard unit of length ? Yard, &c.
30. VVhat is the standard unit of surface ? Square yard for
ordinary measurement, and acre for land.
31. What is the standard unit of volume? Cubic yard for
ordinarv measurement, and cord for wood.
32. What is the standard unit of capacity ? Gallon for fluids
and bushel for dry measure.
33. What is the standard unit of time ? Day, this is deter-
mined by revolution of the earth.
34. What is the difference between a lb. Troy and a lb.
Avoirdupois ? Troy has 5760 grains, Avoirdupois has '^OOCi
grains.
32
PROBLEMS IN
35. What is linen r measure ? That which is used in measur-
ing lines or distances.
36. What is a s(|uare ? A figure having four cfjual sides and
four e(|ual angles.
yj. What is a cube ? A figure having six equal sides.
38. IIovv many inches in a wine gallon? 231 cubic inches.
39. 1 hnv many inches in a beer gallon ? 282 cubic inches.
40. How many inches in a bushel? 2,150.4 cubic inches.
41. What is commission? Per centage allowed an agent or
commission merchant.
42. What is brokerage ? The fee paid a broker for the trms-
uction of business.
43. What is insurance ? Security on property guaranteed by
one party to another, for a stipulated sum, against the loss of
that property by any casualty.
44. What is a policy ? A written contract between the
parties.
45. What is a premium ? Sum paid for insurance.
46. W^liat is interest ? A sum paid for the use of money.
47. W' hat is usury ? Illegal interest.
48. What is the difference between simple and compound
interest ? Simple interest is the interest on the principal only.
Compound interest is the interest on the amount.
49. What is discount ? An allowance made for the payment
of a debt before it is due.
50. W- hat is the present worth of a debt ? The present worth
of a debt is such a sum which, 'oeing put ai. legal interest would
amount to the debt when due.
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