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:i^>m^msmmamm
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i
EN
iHITMETICAL PBOBIEHS
SUITABLE FOR
SENIOR CLASSES
■N THI PDBLIC SCHOOLS AND CANDIDATM
FOR THE
ENTRANCE EXAMINATIONS TO HIGH SCHOOLS
AND COLLEGIATE INSTITUTES.
PREPARED AND SELECTED
BY
G. H. ARMSTRONG,
First Assistant Master, WelUsUy School, Toronto.
TORONTO :
GRIP PRINTING & PUBLISHING CO.
-3 p\ I
ft '60^
MinK'o^^Suiufre b,**ihe'^0*.,p'p*''° P«"''>"«nt <" Canada in tho Office of the
the year olth'S^S^AV'un^a'da'^dSyf'''' '^"''''''''' ^°"''^'''^' ^°'--^°' '°
aid
claf
by,
sub_
any
free
PREFACE.
10 Office of the
NT, Toronto, In
T „, ,tt e b„„k „t ArithmotM Pr„W„„„ i. deigned to
»^ bu., toac,e„ ,„ search „, ,„,„H»»1 e„.ci,c, for the'r .=,u„,
la »e, ,n ,,„bl,c .cl,„.,l.. A largo ,.art of i. „a. „rigi„,„y ,, '"
by the proaont ,.„thori.od Public School Arithmetic
While part „t this „ork is original, .11 recont' work, „„ this
.ub^eot .„ E„gl„„d„„d A,„orioa have bee,, consulted, and wh eve
any h„,g « found sui.»bl„ for our Canadian schools, it has been
freely used, and the debt duo is as freely acknowledged.
To.o»TO, j„,,, ,sso. "• "• ARMSTRONQ.
romi
hs a
left
3
Willi
4
it in
it?
5
doit
alont
6,
do it
7.
alone
8.
in7 c
how ]
9.
hours
how 1
10.
they <
alone
1.
his Boi
togeth
I ARITHMETICAL PROBLEMS.
I.
of his money for a pair of skates and J of the
$2.10 left ; how much money had
He had
1. A boy gave j; _
remainder for a book,
ha at first ?
i.f.^Ju^ \^^"^'"^ «''^\" " "^ ''•'^ ni""ey for a liorso and liad $t\0 more
left than he spent ; how mucli had he before ho bought the horse ?
»nnf f^ri"^/^ * P'f^^ "^ '""'■^ '" "^ *^'*y»' I^ '» '^ 'I'-iya; how long
will It take botli working together to do it / J > ^ '""g
it in "r^,!^"^ ''T "^V ''*''■*''!? ^""'^ '" ^ ^'^y^ •■^"*l J"s father can do
It HI 5^ days ; how long will it take both working together to do
5. Two men can dig a certain ditch in 9 days, one of them can
do it^alone in 12 days ; how long will it take the other man to do /J
A ^/•'^'.PJ*"'* '^*'*" perform a certain work in 10 days A can
do It in 16 days, B in 23^ days ; how long will it take C to do it ?
aloJ; in 1^ a"^^ ?" ^? '^ '"''r.k in 8i days, one of them can do it
alone in 14 days ; how long will it take the other boy to do it ?
in 7 divs"'^Thr«/r'^ a certain field in 5 days, his son can mow it
in 7 days, fho son works at it for two days alone and then leaves •
how long will It take his father to finish it ? '
9. A can perform a certain job in 5 hours, B in U hours C in fl
hours. All work together at it for an hour when A and B leave
how long will It take C to finish it ? ^ '
10. A in 2 days can do as much work as B in 3 davs • to^ethpr
II.
1. A man can perform a certain amount of work in i of a ditxT
6
ARITIIMKTICAL I'liODMCMS.
I
„,, ?• .^''*-''"o 'ii" two iiipos rumiiii;^' into a cLstoni, (.110 of which can
fill it in 4 hours, thuothor in 5 hours ; tiioro is also a pipe running
out of it whicli can empty it in 8 hours. If tlic cistern is empty
and all the pipes are ojiencil at the same time, in how many hours
will it be full i ''
3. A can do a certain work in a day, B can do it in 3 of a day,
and C in I a day ; how long will it take all working together to do
the work i
4. A drover sold ^ of his flock to A, \ of the remainder to B
and the rest to C ; haw many had he at first, if C got 32 ?
5. It takes 87 yards of carpet 1| yards wide to cover a room ;
how many more yards will it take, if the width be | of a yard 'I
6. A and B can do a certain piece of work in 4 days, A and C in
5 days, B and C in G days ; how long will it take the three working
together to do it ?
7. A and B can finish a piece of work in 1^ days, A and C in 2
days, and B and C in 3 days. If $1.44 be paid for the piece of
work, what are a day's wages of each workman ?
8. A woman loses -j*i of her money through a hole in her
pocket ; she had $4.20 left; how much money did she lose?
9. What number must be added to ^ of 2} to give 3g ?
10. A and B can do a piece of work in G§ days, A and C in 5^
days, and A, B and C in 3| days , in how ' many days can A do it
alone ?
.43fe
III.
1. What will $350 amount to in 3 years at 8% per annum ?
2. Find the interest on $650 for 3^ years at 6% per annum ?
3. If I put $25 in the Savings Bank, which pays3i% per annum,
how much interest will be due me at the end of six rnonths ?
4. What sum should be paid for the use of $250 for three
months, if money is worth 8% per annum ?
5. If $000 amount to $744 in 3 years, what was the rate per
cent, per annum of interest ?
6. What sum will amount to $1,200 in 4 years at 5% per
annum ?
7. If $500 amount to $700 m a certain time at 5% per annum,
find the time ?
8. A sum of money was loaned for 5 years at 8% and amounted
to $70 ; what was the sum ?
SENIOR CLASSKS.
of which can
[>ipe running
oin is empty
k' many hours
u 3 t)f a clay,
ogetlier to do
lainder to B
ver a room ;
a yard 'i
I, A and C in
[iree working
A and C in 2
the piece of
hole in her
md C in 5^
can A do it
nnum ?
annum ?
per annum,
iths?
)0 for three
'.he rate per
at 5% per
per annum,
d amounted
9. In what time will a sum of money double itself at 8°/ per
annum ?
10. What is money worth if $50 amount to $54 in 292 days 1
IV.
1. In how many years will $560 amount to $756 at 7% interest
per annum ?
2. Find the interest on $250 from May 2 to July 14 at 47 per
annum ? j /o ^
3. On the 10th of May $730 was t at 5% per annum. In
what time had the interest amounted cy. <p8.20?
4 When money was worth G% per annum, I had to pay $19 14
for the use of $3(55. How many days had I the money ?
5. At what rate per cent, will the principal amount to H of
itself in 2 years 8 months ? ' °
6. At what rate percent, will $2,293.75 double itself in 25 years ?
7. Find the interest on $150 from June 1 to November 15 at
6% per annum ?
8. If the use of $1,000 for 2^ years costs me $162.50, how many
cents interest am I paying every year on each dollar ?
9. At what rate percent, will $325.25 amount to $393.55i- in 31
years ? * a
10. I borrowed from a banker $730 on the IGth of July, and on
the 30th of August repaid him iu full with $739,90 : what rate per
cent, per annum did he charge me ?
V.
oAof a '"«''°hanfc buys an article for $7.50 and sella it at a gain of
20% ; fand the selling price of the article ?
2. By selling cloth at $2.50 a yard a merchant gains 257 : find
the cost of the cloth per yard ? a /o . •«
1 ^•o-^o/T'^r ^!"' * flo'lk of «heep at $4.00 each, and by so doing
loses 20% ; find the cost of the sheep per head ? ^
411 J" ^ "f ."• ^"^.^ * ^""^^^ f'''' ^^^' *"^ immediately after sells it for
$117 ; find his gain per cent.?
no ^lI^ »i *""f f sulphur are required to make 31J tons of gun-
powder, wh.ar. IS tho per cent, of sulphur in the gunpowder i
6. Teas at 60 cents 87 cents and 96 cents a pound are mixed
in equal quantities, and sold at 90 cents a pound ; find the gain
per cent. ? r > « k"'"
8
ABITHMETICAr. PHORLEMS.
^y^^^l'&^J^^^^ P-«* ^ --hant clears 8800.
relLti^f^o^tPZ. '""^ ''^ '^ "^"^^ ^^^- -^^h^« 5 find the
VI.
.if -rV 4 '''^^°^^"<^ Ws 400 yards of silk for $384, and sells 300 v«r^«
at |1 32 a yard, and the rest, which is damaged at 48 cjn J» ^ /
find how much per cent, he gains or loses " ' * ^^"^ '
44 oertf^'^^J^T:^^:^^^-' fj- ^8 cents and
mixture in order tha? he maj W^^^T^n 'ris t^'?" ^"^^ ^^ *'-
barn vaYued a't feSoTt^f! ?" ' '"'""^ "' """"'"^ '^^ ^ ^«"««-^
-r.lA-^^ y ^^"'"^ * ''°'''« '^'"' ^40 I lose 20%, what should
sold him for so as to gain 10% ? snoulcl
5. If a tradesman gains $
what is his gain per cent. ?
on both ! '• ' "■' Siua or lost per cent.
a pLfiz^ii: tTz:\^'Zir''' ^-^ -"« "^- ^^ ^ -^»
ai4?'90 aSoTl2t^' H ^ '"\^^^^ ^^^5 B sold it to C for
1 A Tr u f, ^' ^""^ "'"''^ '^'^ *^he carriage cost A ?
lU. It by selhng an article for S9.50 I losa Ry f-^n u
Bhou'u I sell it so as to gain 5% ? ^' ^""^ ^""^ ™"°^
I have
1.32 on an article which he sells for $5.28,
VII.
SKNKlli CLASSES.
9
what could he
it clears $800,
)rice for cash,
eceives $7.12^
fhta J find the
lella 300 yards
cents a yard ;
38 cents and
g price of the
r a house and
lould I have
alls for $5. 28,
y weighs 15|
lem he gains
>ss per cent.
3m at 5 cents
it to C for
A?
how much
ong. How
around it ?
;oing at the
ho.\.'llH',™'„?ii?3" '?"" """■ ' "' "'• '"""-y- '-i '■-' W left,
gain in CanadiM currency.' "^ *""■ ''"' *""' J^""" ">?
day!' ,1"'S ' i;7iy°a 1:°'M" * ?' » ''»?;, B »■' *■ i' i" i of .
together to dj it? '^^ "°"' '""^^ "'" " <^^o a" woikinf-
rindmygainorlossptclS.olJbott'^ ^ " lo™ on both. (2)
whi-,^r"c:r:rrh:*rrftsct'"7,''cc-ra^-raf "• -^•
le» th?,; fafd Worrlttnc"' ■=' "• *" "^ "'»■" >"'™ »"»
ofte"; Sfitrl'e in'*l41-°!,rr'°'"" '"«'"' " ' "»' ^ "-
VIII.
50 Pou?ra?|7orrp?un1 m o'rdl^tr'^?r"^• "'"^^ I "- -*h
a pound without loss ? *° '^" '^'^ ""^t"''« ^^ ^0 cents
30 f;ar longl'sS'^tf ;Tdran?ST".r1' ^'^ ^^'-^-•"g '^ --
high. ^ ^"'^ ^^ ^^^^ J"gh ; wainscoting 4 feet
3. Telegraph poles are placed 8 rods anart anW « f •
one every 4i .eoond. ; how^.any nnlo/.So^r i," 'h^ tS gSI
. .<fu.r"eTet?"3"«::;SrSc,^L^-- ^ -^». 3» P»ohes. 30^::!,:
76 cen^ erh:"s'i;°th.T„rk:;'',T2^\"°'=':i"^ '- "■-' '■"'-
the number of each ? ^ * •^'' '""'^' "'"■ '"■■ »" »1W; find
ponnd,^ ""o bu'XtSl'S ^iT^^ '"? " '■»' °"» -"ightaS 600
He three meTagri tl.at aXSI ^1 " '"' " '"'°"' » P™"*
.Jt-he^rS^fd-Xn'r;;- ,^ ^f^^lf "^ tj^ ^ it
10
ARITHMETICAL PKODLEMS.
are7mi?:par '''""" ' '""^ '' '^^^ ^'^^ hands of a clock
n^i2'«f"KA^*^^'i '" ^^'^^Pt"" expends 8200 in Scranton coal • he
pays $4.50 per long ton for the coal in Scranton. The freight from
ton a"t $6 ^O^TP-'r ^' '? '^u'' ^ ^""^ '^""- ^e sells itIL BrZ
ton at $6.50 a short ton ; find his total gain. *■
IX.
1. Find the greatest number that will divide 392 and 257 leaving
as remamders 7 and 12 respectively. ' ^^^^'"8
2. Five-sevenths of | of a number is 75. What is the number ?
a. A farmer sold 24 dozens eirgs at 22A cents a rlr.y^n n.,ri io
pounds of butter at 27^ cents a pofnd. hI was paid in tea"at 87
cents a pound. How many pounds of tea should he receive ?
A^ fil ^ man engaged to work a year for $G00 and a suit of clothe,
ii^Lff^''^^■?TYf^'''' settlement was made by giving him
^390 and the suit of clothes. What was the value of the clo"hes ?
5. Divide 125| acres of land among A, B and C eivin^ P ^4-
acres more than B, and B 12| acres more th^n A ^ ^ ^^
t Jq/" ^*?^ ^ * "^^^^ ^°^ ^ "^"""^ than it cost him. B sold it to fi
for 836 which was J less than it cost him. What did A pay for^t ?
7. At what tmie between 4 and 5 o'clock will the hands of a
watch be exactly over each other ?
8. A man buys a carriage and a set of harness for $232 • for the
cosTof'e'ch^''' "'"" *"^" '^ ""'^^^ ^^ '"^ ''^« harnels Find the
9. A train leaves a certain station at 9.30 a.m., and eoes 27i
mies an hour. Another train leaves at 10.15 am , and goes 41
miles an hour. When will the latter overtake the former ? ^
fo/feoir F-rdlLlfi; fefcet ^•""^^'•^'^^^ thereafter sells it
X.
alwaysTetliVfo^rtJindr^^ "''^' "'^" '"'^'^''^ ^^ ^4 or 27
U, graveV4 miL?/'^' '" '^'^'^^ '' '^^^ "' '''''^^ ^^^ ^-^ will it cost
3 A hound in pursuit of a fox runs 9 rods while the fox runs 7
but the fox had a start of 70 rods. How far will the hou^d run
before he overtakes the fox ? "uunu run
SENIOU CLASSES.
11
w many may I
anda of a clock
nton coal ; he
le freight from
Is it in Branii. "
id 257, leaving
the number ?
dozen, and 12
I in tea at 87
Bceive ?
uit of clothes.
)y giving him
he clothes ?
?, giving C 7i
B sold it to C
A pay for it ?
e hands of a
232 ; for the
8. Find the
and goes 27^^
and goes 41
ler?
safter sells it
by 24 or 27
fi will it cost
I fox runs 7,
hound run
high-at''S?;e7i^' ' ^"^ ''' '''''^^'''^ ''' '''' ^-S -^ 6 f-*
6. In a certain school there are 40 pupils present on Monday
on Tuesday there are 42, on Wednesday 44, on Thursday 46 and
on Friday 34. Find the average daily attendance for Jhe Let
SuJdaf?"'" ™^"^ ''''"™ ^'"'"^ 10.15 a.m. Tuesday until 7.45 p.m.
8. A race course measures 1 furlong, 8 rods, 2 yards 2 feet How
often must one go around it to travel 5 miles ?
9. A man bought 34,750 pounds of hay at $15 a ton. and sold the
same at 85 cents a cwt. How much did he gain ?
10. Two trains respectively 210 feet and 180 feet in length are
gomgm opposite directions, the first at the rate of 24 miles oei
hour and the other at the rate of 27 miles per hour. F^id how
long they will take to pass each other. u . rina now
XI.
wil/JhtSin'g t^Ttt; dolhtr^,^ ^" '^ '^y^' - -^^t tim«
theLI'f^s'oTror''^"""^'* """'^^ ^'""^««'" ^-^^^ -'
3. If a wheel makes 260 revolutions in passing over 1 milfl 590
yards, 2 feet, what is its circumference ? ^ ' ^"
4. In one scale are 3* pounds troy, in the oDDoaite 'i nn„n^=
avoirdupois How many more grains i J'one scale t^n in the^oTerl
5. If f of a dollar buy jl- of a pound of tea, how much is the tea
per pound ? (Answer in cents.) ^^^
9.30'a.n°:£Te^Sf8'rt''r'™° '' "'"'-"^ "-» ^^^ 2** -»
8. I( a ma,, working 9} hour, per day finiahes a piece of work in
luTi:? lyl ""■" """''^ '" ""^ ""''h'" " « heC"S''^J
long will it take the three to saw a corj ? ^ ''°''"- ^'"'
thlUe'-TiSftil-eVZ': o^S; "" '""' o' *» "" " i "■" <"
12
AKITHMKTICAL PHOliLEMS.
xn.
il A 1 u "'^ ^''.-uu lett. -t ind his income for a vpar
mucliwill„ede„ri„ayear! ^ ^' '"""'"S <"" Sundays. How
thick ^^"!M.Ti^\IU?:j'Z\''r ' ""'!'" '■'«'■ -O * '-'
long and 16 feet 8 inchL wide ■ S.S o, ""T""* " "'"o"' I8J '"'
yard. How much meney wS^ iveT "'°''°' "'"" "' *" '""' "
.w„1i,u?dLd a'd'fhir'iL™;;^ aly '""tl »"" '"«"'»' ""'"on
ahJArSri^Lt^l-.-^tla'Sn'r/----
73 will g?ve 62™'""' '"°""""^ '''' ^^^ ""<' "■« result decreased by
inlo^wLtl^tarXZt'rA'/ "" 'ri.'?V«' ""<' » <""ded
«8.86 peryard » " °^ " ''"'™ 2.156 links in length at
xni.
one theusand and thirty ; tSisThi X/ "rbT^" " '"'""'■
will'fiIlVc'is'e';n1t:t'4!n°cts° t'/'J J'T -»">', ^"'""» »' wate^
foot IJ inches deep ! ' "^' ^ '""" * '""'"m broad and 1
maleo^tSrst'cwt IVtCtSlyf^ ^°"-'' - -«
mJ. fflfi tZ glif J? P'^ "*'' ' '"» ' ■" *e CO... What
55}
SENIOU CLASSKS.
13
stock, I of tlie
Fiiul his capital,
among a certain
t., 2 qra., IGlba.
k year a tax of 4
e for a year.
sells them at 2
Sundays. How
high and 4 feet
a room 18^ feet
le at 80 cents a
twenty million
he (juotent six
thousand eight
if the breadth
n a second and
: decreased by
and is divided
s in length at
hers and 270
Jrs is twenty-
Ions of water
broad and 1
unds can be
cost. What
XIV.
1.
A man invests | of his fortune in land, ^ in bank stocks, ^ in
fSunf''' ^''"''^ ^vas $8,000, in spJcSla
debentures and loses tu« lemamae
tion ; how much was his fortune ?
acres did he buy ? ^'^O.Oo an acre ; how many
and 2J inche, thick Ttal'^^H-lf * "'° ■"=','""». *i '"dies wide
aeeded ? " . >' Uie mortar tils uji ,■„ li„,v ,„»„y bricks ate
14
AIMTJIMKTIOAL I'KOHLKMS.
■;ih
for $1,976. which was 1304 more thJ^^ '^^^ i "^ the re.nainder
he buy ? ^ "'"'^^ '^"*" •'"St; how many barrels did
1 I?" ^ ^""^ "^^ '".°"®y '» divided among 4 uerson« Th^ r ^
h the second i, the third i and the fmTrfh f^?* ^^«. ^pt receives
found that the first receives $700 n ore tha^ It T'"!}"'^'^. ^^ "
Bum received by each. *" *"® fourth. Find the
XV,
carittt (l1 wLf c!rpy?7'in^t:i^^^^^^^ n" '' ^^ *«
carpet 45 inc^es wide and $1 25 a Jard ? * ^" ' ^^^ '''*^^
dollar of incoLe he may save Sf a year ^ '""'' ^* '"'"^ °" ^^^^
2 feet ?iilf &tnT2" :j"li\^^^'^^^^ ' feet 4 inches long,
inches are contained in a pint? ^'' deep,, how many cubi^
fcwolysranrtheTor;f\hemt' ^''''' ^^^ -- ^"^^^^er for
finiahtLfieldinTdavs. Lrfh wT l,""""^' «"^ *^« other two
at the end of the second'd!v wi T^' *'? ,"'" ^^° «^^««d ^°rk
field by himself ^ "^""^^ ^^"^^ *^^«" ^o mow the whole
rhe^,?;airUml?oB:tTe%atT 'fT T/-- 7 miles apart-
other walks from B to A at the r. Jn ^k''^? miles per hour. The
after starting wHUheytl^trh^w^lt:^^^^^^^ ^^^ ^^^
and'ihtbtti^ltlTi^Ci^s- wtrrti;:L^-^r^"°\^^'°'^'
leaf? (Answer in fractma of S inch) ^' ^^''^''''' "^ ^^^^
9. A drover bought a number of cattle for M 375 an,1 o^u
LT giilfi46j"lt^ ""^^^ ^- ^'-^ --' ^« -" theremainderTo
SENIOH CLASSK8.
15
'arrels of flour for
I of the remainder
many barrels did
The first receives
remainder. It ia
fourth. Find the
hat will it cost to
a yard j (2) with
w much he may
7^ mills on every
Jet 4 inches long,
how many cubic
now together for
d the other two
i^ho ceased work
' mow the whole
38 7 miles apart-
per hour. The
our. How long
3f an inch thick,
lickness of each
twice as much
the answer in
i one he gained
St price. Find
S75, and sold a
sum of S.3,G55,
le remainder so
is Jh Jtnilted mmi^^rrhre: r'^'. "' T ""-'^-^ -"^ 2,431
three. One of th^ iSVs ^ T^eS^^^^^^ -^'^^"^ '1'""''*"^ ^"'^
Bix. Find the other. ^ thousand three hundred and
XVI.
yardand'withcarpet^2finfhi;t :r|rA5\^;:?d"^'' ''^'''' '
2. "WoBraph posts arsplacoci 80 vardsaimrf «„J . .. ■
o„o every 4 .»„„d. ; h„w Zny muJl^lZf.T^^^S'Y'^''
What t SZC^tJlifl"- "" '"" ' "' "" ""'^ '°'»''2«'-
amounted .o S4M5 ; „h„t wa, tl,| value'^trck pS: /""" '''^'
muJh money ha™?/ °' "^ """""^ """'» * ""^ "'»« «3»0 ' how
d»l°"et'l';i wha'tTelh^e-L-l-er? " =»»■ """ <-'■•" '-eir
XVII.
ohantable 'purpose,. FinTthe"'anS:nr„^'hrpre"V° *''°*' ''
oats. Find the price ot ei^h pert„X7 " "■""" *"" '">^ *»
«lo'6o?r&\^ ."oT. lm°; *»•*'"'( •"■; -'0 - P^ of it ,„.
mnoh did I gain on e^ery acreZT? '""' ' '«""'W°S. «"-i how ,
fofthtrri»dL°fffs''4°„t^p:t^^:;[r°'n'^^
It ;'3 trdte''°'"ti"r'"'° "4i -"Fu tyTmortS;
half as muohJorras'the LnL'J'^'''''' S ''° 'V 8"™ ""» »«"?
much the man earned7er™y. ""' ^"'^ ««oriingly. Rnd hoj
I
IG
AUITIIMETICAL I'lioHLKMS.
do each day ? ^^ ' ^^''^'^ P^^^ t "f tlie work did tlio boy
6. Find the value of ? of i r.f o.,
•7 T 1. i. "" "^ I 01 ,*j ot an acre m square rods
^o^'^'^tZ}:S-i:^^^^'f '"f^ with :.rin,two
measuring the distance ? '^'" ^ ^'*^^ ^ Wly tlie string in
wear-nTnetJntltTr"; lir%l ^^^^5. ''^^^ ^^'^^ -d will
months ? ' "^ '^ P"^^^ *^'»at cost U.50 and will wear ten
of interest does he geffo; hirmoney ? ''"'* "'^""'^ ^'^ ' ^^^' ^'^^^
10. A merchant bouf^ht veIvfi^ Af •a-r - j
what ia his loss per cent"? ^^ * y*"''' ^"^^ «oW it at $6.50 ;
XVIII.
respoc^vet;. ttj t SesTkin'' t^ ^"'^ f^ ^^^^^ P^ P--^
one pound of the latterraa^^ell t,fp ^ T.P""'"'« "^ ^he former to
what does he gain or lo^e per c"? ? "'" ^' ^^ ^""^« «* P°»"d )
long wMttrkV3le;°::;.:rrwte7inol^^^^^^ ^" ^^?'^^«' ^-
3. A runs at the rate of 2rirr , ''"''"^ '^"''^ ^
of 275 yards a minutef w'nScrstt """"'^' ^"'^ ^ «* *'- ^^^e
as to win by a yard in a mire race ? ^^ ''"' ^^^^ *'^« ^^her so
and'i2iSe:tronLTdi:t:n'""'^°"^^"^ ^^^ ^'-^kes 1 hour
take rowing down ag^n ? "^ " "'"'' ' ^^°^^ ^""g ^i" he
tim^ii^i^LXL^^^^^^^^^^^ « days, find in what
6. What per cent, is 25 of 80 ?
ho. ™oh oofte,. Mvr&tStr:ii?E* f '■■-»'«- ■
pound, of bSw tl'l buv s'n?' ,?' T'"'' "' ^ P^'n^s of beef, .„<I 4
&h "ill pounds ofTua'CvV """"" ' ''"" """'^ "■>"""->'
.ilk". }S * "' * "' ' >"»"- f- ! of a foot of .ilk , what „a, th.
I'ork in 4 days ; the
te work did tlio boy
ire rods.
with a string two
ipply t]ie string in
'St $3.50 and will
nd will wear ten
fc at $10 a month.
i'8 $7 ; what rate
sold it at $6.50 ;
cents per pound
^)f tlie former to
) cents a pound ;
in 20 days, how
18 work ?
id B at the rate
ive the other so
ar takes 1 hour
iw long will he
^8, find in what
1 are torn out
lany pages are
unds and then
f the mixture j
of beef, and 4
iny pounds of
what was thq
SKNIOK Cr.A,S.SE,S.
XIX.
17
K !»• -^St'St'crcVoSiV^^^^^^^^^ what had.
All have UO ; how „»„,, /,„ S;", ^ave had Ij timea what B had.
u.L°i »iSr 'te* ifiAt pi, J?' ^"« ■' ^» '-' >°ns and th,
XX.
they cort, find l,i,„.|„^,„„^V™™^M'8 renumder loat J „, „h„t
«.d ihL"; w7|3S*'whl?;L7h ** "'J"'«t W.S due hta,
• ^^ "^^ was the sum due ?
18
AIUTHMETIOAF. PKOHI.KMS.
H.o^' ^^'l'^*" "T* ^"^ ^''''^" l'^"'" ^'"'■^ ^'"* carpot 27 inelies wide that
6. A man hadlfiOacrosoflftiul. Hekid if cnM-nfr^finni , m
BtreoU toc.k up i of the whole land ^Tho o a Je o'S dl oJ^Jn
acre ,...re or less. How iPuch n.oro or less tlmn [ ^re theyV
7. Ihe flum of three numbera is 24 : and six tiino« fV,« i«f +1,
8. If Somngea buys lomons and 2 lemons huy 7 „„nT„ ,,„i
how many bushels of rye did it contain ? mixture ,
TK^^" ''^iV^l,"^^" t»"ght iJ*!. 585 worth of land at $1.75 per acre
They sold 100 acres at |2 per acre ; IGO acres at $4. and tlfe rest at
such a price per acre as whonld make the whole receipts omal fouJ
l"?as^ i; ?'" '"^^'="'' ""•"• ^' w'-t price peracr'^^'Sid hey se,
XXI.
1. What is the least number that must be added to five million-
to make the sum exactly divisible by seven thousand and ninetee,!;"
,« ^' ^ il^'i''!'^?*^ T^^ ^"^ ^- $1,039.84 and to B $012.80: if A
receives $357. 44|, what will B receive ? '
3. A clock gains 3} minutes in 15 seconds less than 24 hours • at
noon It 18 2 minutes too slow ; when will it indicate true time? '
4 A person expended $55.92 in tea at 87^ cents per pound coffee
at 18| cents per pound and sugar at 10} centl.buyin? vZZli quan-
tity of each ; how many pounds of each did he buy ',
5. $90 90 is shared amon- i men, 5 women and H . '.iM,..,n so
as to give to each man twice as much as to each wo , a l . each
woman three times as much as to a child. What do the women
6. A man bought sheep to the value of $9,000 and after keepins
tnem4 weeks and paying 50 cents each for their pasture duS
^vat time, sold the whole for $14,000 and thereby cleared $2 00 on
"■ ■■• low many sheep did he buy ?
Fmr> If ^" "^ *'*'".^ ""^ '^^^^ ^""^ ^^^' '^^'"^'^ ^^ ^ ™°^® than cost.
inclioa wide, tlmt
i iiichus broad tuny
into 600 lots. The
foro called j of an
J wore they ?
ino8 tho Ist, three
esult. Find tho
uy 7 apples, and
ivill 1^ busliels of
ey, 39 bushels of
8 of tho mixture ;
$1.75 per acre.
, and the reat at
ceipta o(jual four
acre did they sell
i to fivemillioni
i and nineteen ?
■' $012.80; if A
lan 24 hours ;at
3 true time ?
lerpound, coffee
'{ an equal quan-
id 6 (hiMnm so
•ii a L > each
do the women
id after keeping
pasture during
eared $2.00 on
more than cost.
I
I
KKNIOIt CI ASSKs.
19
8. A omt.rn is ^ ful ; one pipe runs out an.l two run in Th„
first p.pc. an on.p ty ,t ,n « hou.H, tho s.con.l can fill it in 2 h. u^^
Hud tho Inrd .an hi it in Id hours. Thuro is al«o a iLk h as
huyr as the bboou.I p.po ; in how many hours will the cLtem bo hal!
9. ^!owesB 5? of what B owes A B trivoH P «r; * ,. l\
accour.ts between^heu. all Btnn.ht ^Vh^t fs iS c?e.ft to A T ''"
fJn f" T^-^^ f'"' "^ i"''"^'^^' '"'^'"W ^"'^ eartrid.ros t-aoh, A fires
XXII.
1. How many times will a carriage wheel 4 foot 2 ,-nM.„= ;
diameter turn in going 1 mile, 1 furlo.ig. 1 peVeh ?
4. 10 men can do a piece of work in ^9 Anr,„ Aft ^i ,
one boy in 2 days ? ^^ P*"'* "^ ^^''^ ^""'^ '« done by
fallin/and'H'^oJth ^f ' '" '""""* ^^"« ^'•°'^^" ^"^0 two pieces by
^k:i:li^^:^^::,^'^^^ -« -l-l to ^ of the Shorter!
i2bt4rutt;>ir"te"sl'°^oT;f""^^M"^r^^^^
gained on them $40. Ho "m:;;;;^t\>l'did''he' b^^^ '"'^ *'''' ^"^
first'20^j;rb;i^n'^;arTh:lTte'^'o7'2l^^^ and travelled the
walked the remaining 32 mTles S f of th^ '. ^'"' a'I""'"^ ^« ''''^»
did he arrive ? o -^-^ ""' s at jj^ of that rate. At what o'clock
take'; i^Z^l!:^S^':^!l^^^r'^'-^^ ^^^ breadth,
carpet will it require / '^^ ^°"'' ^^^^ 5 ^"^ inuch
day'irit^elSf io'^:'!:;r ?11^^ ?^''™'"^- «" ^^«dnes-
11. How nfuch n.t,M,.\^,.:'^ "£«*•; ^^ ,7'^«" /he other strikes
together ni tlie ev, „i„g 7 P"*^ "" ^'^'^^ they may strike y
5% perli^unTr "' """'^ "'" '^'""""'^ *" ^^'^'2.50 in 15 months at
20
AniTHMETK.'AL PUOULKMS.
iiji.li
XXIII.
1. A merchant buys 2 butts of wine, one for 8120 and one for
SllO, he also buys a third, and, after mixing the three, retails the
wme at $9 per dozen bottles, making 12^% on his outlay ; supposing
the number of dozens in a butt to be 52," lind the price of the third
butt.
2. A plate of copper 2 feet 9 inches wide, 3 feet long and f of
an inch thick, is rolled into a sheet 1^ inches wide and 18 inches
long. Find its thickness.
3. How long will it take to walk round a square field containing
13 acres, 81 yards at the rate of 3^ miles an hour ? °
4. Find the price of digging a cellar 41 feet 3 inches long, 24 feet
wide and 6 feet deep at 20 cents per cubic yard.
5. Find the total cost of 1,G50 pounds of hay at $8 per ton, and
2,675 feet of lumber at f 10 per thousand feet,
6. If 3 men and 1 boy can do a piece of work in 6 days, and If 1
man and 2 boys can do the same work in 9 days, how long would 6
men and 7 boys recjuire to do the work ?
7. The price of 2 turkeys and 9 geese is 80.00, and the price of 5
turkeys and 2 geese is $4.75 ; find the price of ? turkey.
8. At what price must I mark cloth which cost me $2.40 a yard,
so that after throwing off i of the marked price I may sell it at i
more than the cost price ?
9. Find the interest on $7,300 at 33% for 120 days,
10. A bankrupt owes $2,085, of which $235 is due to A, $325
to B, $525 to C and the rest to D. How much must he pay in
the dollar so that D may receive as much as is due to C ?
XXIV.
1. A house built for $2,656 is sold for $3,320 ; find the gain per
cent.
2. For what sum would the life of a person aged 23 be insured
by the annual payment of $45.60, the premium for that age being
$2.40 per cent. ?
3. If 6 men can dig a trench 30 yards long and 8 yards broad in
6 days of 16 hours each, in how many days of 12 hours each can 8
men dig a trench 40 yards long and 16 yards broad ?
4. What is the interest on $757.60 for 4 years and 4 months
at 6^%.
6. A man sells a house for $437.50, and loses 12i% on what it
costs him ; what did it cost V
SENIOR CLASSES.
21
5120 and one for
three, retails the
3Utlay ; supposing
price of the third
eet long and f of
de and 18 inches
e field containing
iches long, 24 feet
it $8 per ton, and
1 6 days, and If 1
low long would G
vnd the price of 5
rkey.
me f2.40 a yard,
I may sell it at J
.ays,
due to A, $325
must he pay in
lue to C ?
find the gain per
id 23 be insured
ir that age being
8 yards broad in
lours each can 8
?
3 and 4 months
12|% on what it
6. If tea be bought at 75 cents per pound and sold at 68 cents
per pound, find the loss per cent.
7. Divide 480 into two parts, one of which is three-fifths of
the other.
8. A car is exactly filled by barrows that hold 9 hundredweight
each and emptied by sacks that hold 5 hundred-weight each ; given
that It holds between 8 and 10 tons, find the exact amount.
9. A speculator gave $18,810 for horses, and sold a certain num-
ber of them for $7,990, at $85 each, losing thereby $10 each; for
how much each must he sell the remainder so as to gain $2,180 on
the whole ?
i^;o^'^®i^"'" °^ ^^^^ '^ *° ^® divided among 24 men, 36 women
and 72 chddren, so that the shares of two men will be equal to that
of three women, and each woman's share equal to that of two chil-
dren ; what will be the share of each ?
XXV.
^u ^"t^^ ^ ^"y ^^^^^ ^* ^^-^^ ^ y^*"^' ^^^^ n^usfc I ask for it a yard
that I may be able to throw ofi" 10% from my asking price and yet
make 25% profit ? j s i- j
?^' I ^"'''■o^^ed $250 on the Ist October, 1875, and paid back $268
on the 24th February, 1876 ; what rate of interest per annum had 1
been charged ?
3. A clock marks the true time on Sunday morning at 6 o'clock,
^"11 u" i"®8*^^y »•= """" (true time) it has gained 24 minutes ; what
will be the true time when i^. shows 1 o'clock on Saturday after-
noon ? ■'
4. A certain piece of work was to be done by 25 men in 16 days;
after 4 days 15 men go away ; how long will it take the rest of the
men to finish the work ?
. ^' r^. f^®*^^^^ ^^^^^^ °" ^^^ ^- T- R., which travels at the uniform
""f fnn ^, ^^^^ "'o* ^P?"'^' *^^^^« Belleville for Toronto, a distance
ot lUJ miles, at 8 o clock a.m. ; at what time will the train reach
loronto ?
6. How many minutes must a boy who runs 6 miles an hour
start before another boy who runs 7* miles an hour in order that
they may be together at the end of 10 miles ?
7. A man on the average walks 10 feet 8 inches in 4 steps ; what
number of steps will he take between two places a dist.ann« of 1 n.iU
1,Z80 yards apart?
8. A bankrupt pays 59 cents on the dollar ; what will a man lose
to whom he owes $13,675 ?
22
ARITHMETICAL PROBLEMS.
tl.^^v/"'" ^°^' ^^V'^^ "' V''''^ '^"'^ •'"'^ "f tliom gains 5 feet upon
XXVI.
1. A can do | of a piece of work in 1 hour, B can do | of the
remamder m 1 hour and C can finish it in 20 minutes ; how W
will It take A, B and C together to do the work ? ^
on J' J^y f "^"S.tea at 90 cents a pound, a merchant gains I of the
on everv ii'^'f'^ ^'".^'t '".f ^"^^ * ?""'"' ' what does he clear
on every |,8.40 of his outlay by the latter price ?
an ^" ^ ^.^'''^^ '■",''^' /^ l'''"^ ^ ^^'''^^«' B ^=1'^ 3 loaves, and C had
ZZT: *'^«yf'^lti*^"^"''^^■'^^^^"•'>^' ^"^1 C divided the morey
fairly between A and B ; how much money did eacii receive ?
fK; t" ^uZ ""^"^ •^'' w^ ^ ^"^^^^ ^°"«' *2 inches broad and 4 inches
tt ck ,T h^nf"!"''"^ f" '" ^f f f««fclonK, 20 feet high and 4 fee
thick if the mortar make up ^'^ of the entire wall ?
5. If it costs 170.40 to carj)eta room 24 feet lono-with carnefc 2i
feet wide at $1.10 per yard, tind the width of the room ^ *
»n/p f„*=^" build 7 rods of fencing in a day, B can build 9 rods,
numWof'fnV.r ^'^'y-lf'^' quantity of fencing would afford a
number of full days work for any one of the three ?
7. A boy spent f of his money for a pair of skates and had 57
cents more left than he spent ; how much money had he at first ?
8 A quantity of tea was sold for $1 a pound, the gain being
^ of the cost price; the total gain was $57.00. How much
tea was sold i
9. A merchant sells 60 pounds of tea and coffee for |43. 50-the
tea at 90 cents and the coffee at 40 cents per pound. How manv
pounds of each did he sell? ^ ^"^
10 The fore wheel of a wagon is 8 feet round, and the hind
ir 1 i hT."''''"^ ^r'* ^'^" ^'^'^ ^^^g°" ^'■a^^l over before
each wheel shall have made a number of complete turns ?
XXVII.
1. Make out the following bill :
1,.344 feet of lumber at $1.62i per C ;
48,480 cubic feet of timber, at $59.^71 per 1\I •
7,400 cedar rails, at $7.75 per C ;
8,400 fence-pickets, at $15 per M ;
9,050 brick, at $3 per C ;
5,080 pounds of hay, at $12.50 per ton.
SENIOR CLASSES.
23
lu gains 5 feet upon
have gained at the
>% above cash price,
irked $26 ?
, B can do | of the
minutes ; how long
'i ^
hant gains ^ of the
what does he clear
loaves, and C had
divided the money
lach receive ?
broad and 4 inches
eet high and 4 feet
?
ongwith carpet 2J
i room.
J can build 9 rods,
ing would afford a
36?
ikates and had 57
had he at first ?
1, the gain being
.(30. How much
e for S43.50— the
ind. How many
id, and the hind
ivel over before
turns ?
ir M
2 Find tlie cost of diggin;,' a cellar 30 feet long, 24 feet wide
and feet deep, at 24 cents per cubic yard.
3. Wiiat is the least number which when divided by 24 or 39
leaves 2 for remainder ?
. ,/-^,'"^^^""|'^t^\frt''iin number of cows for $1,080; he sold
half of them for $810, thereby gaming $15 on each one sold. What
did each cost hnn ?
5. If a person spends in 4 months as much as he earns in 3
how much can he lay by annually, supposing that he earns 8420
every b months ? = v
t -J^^n^ '\*" '■'"''^'''f ^]-^^ ^ '^^y ^^«^y *^ay ^^ ^orks, and to for-
feit 80 cents every day he is idle. At the end of 76 days his wages
amount to $09.15. How many days was he idle ?
7. A clock which loses 4 minutes in 12 hours, is 10 minutes fast
at midnight on Sunday. What o'clock will it indicate at o'clock
on Wednesday evening ?
8. Find the interest on $050 for 4J years at 5h% per annum.
9. The Centre Road from Brampton to Orangeville is 4 rods
wide and contains 176 acres. How many miles from Brampton to
Orangeville, by way of tlie Centre Road ?
10 Out of a purse I take $100 more than J of the whole sum
ril ''^on^''"'^ ' u ''^", ^^P '""^^ ^^^"^ 5 °f ^^hat then remained,
and then $20 more than | of what then remained ; after this
remained. What did the purse contain at tirst ?
XXVIII.
1. A certain piece of work can be done in 18 days by 4 men 7
women or 9 boys ; how long will the same work occupy 5 men' 4
women and 2 boys ? ^ -^ '
2. The hour and minute hands of a watch are together at 12
o'clock, when will they next bo together ? & >■ au x^
3. A hare pursued by a greyiround was 130 yards before him
at starting ; while the hare ran 5 yards the dog ran 7 yards ; W
far had the hare gone when she was caught by the greyhound ?
4. A dealer in cattle gave $0,400 for a certain number and soM
a part of them for $3 000 at $18 each, and by so SgTost $2 " ^
will"i5"'2oS le^ ^.oVs"™ "'"' •' ^^''^' ^« *^^^" ^^- ---•i-
24
ARITHMETICAL PHOBLEMS.
6. By what number must the product of the sum and difference
of 8,370 and 5,(584 be increased so that the result may be exactly
divisible by 7,850 ? j j
7. A merchant failed and his goods were worth 17,770. Out of
this he can pay his creditors 37 cents on tlie dollar. Find the mer-
chant's indebtedness.
8. A farmer sold 28 bushels of oats and 39 bushels of corn for
$36.04. He received for the corn 34 cents more per bushel than
for the oats. What was the price of each per bushel ?
9. How many pickets, each 3 inches wide, placed 3 inches
apart, will be required to fence a lot 14 rods long and G rods wide
and what will be their cost at $2.75 per C ? '
10. A school clock which gains 3 sec(jnds in 5 hours was set cor-
rectly at 9 a.m. on Monday. How much too fast will it be at 4
p.m. on Friday ?
XXIX.
1. The sum of two numbers is 9,650, and their difference is
5,798. What are the numbers ?
2. By selling a horse for $128 I lost $40. What would I have
gained had I sold him for $200 ?
3. If 5 tons of coal are equal to 9 cords of wood, and a family
burns 27 cords of wood in a year, how much will it save by changing
from wood to coal, when wood is $4.25 a cord and coal is $0.80 a
ton?
4. The product of two numbers is 1,270,374, and half of one of
them is 3,129. What is the other?
5. A can dig 36 post-holes in a day, B can dig 32 and C 30 in
the same time. What is the smallest number which will furnish
exact days' labor, either for each working alone or for all workinL'
together ? ^
6. Find the greatest number which will divide 10,974 and 15,336
leaving as remainders respectively 54 and 36. '
7. A ship and her cargo are valued at $00,000, and f of the
value of the ship is equal to | of the value of the cargo. Find the
value of each.
^ 8. What number must be taken from 17 J so that it may contain
3f an exact number of times ?
9. Divide $8,888 among A, B and C, so that A may receive $88
less than 3 times B's share, and C $170 more than one-half of A and
B'a shares togetJier.
10. How many bushels of oats would be required to sow a field
32 rods long and 30 rods wide, sowing 2 bushels 1 peck to an acre ?
SENIOR CLASSES.
25
B sum and difference
isult may be exactly
>rth $7,770. Out of
liar. Find the mer-
bushels of corn for
re per bushel than
mshel ?
:le, placed 3 inches
ng and G rods wide,
> hours was set cor-
'ast will it be at 4
i their difference is
What would I have
ivood, and a family
1 it save by changing
and coal is $6.80 a.
and half of one of
lig 32 and C 30 in
wliich will furnish
or for all working
J 10,974 and 15,.33G,
000, and § of the
e cargo. Find the
that it may contain
A may receive $88
n one-half of A and
red to sow a field
1 peck to an acre ?
XXX.
1. Four geese and 5 turkeys cost $7.50. If 2 geese are worth
as much as 5 chickens, and 4 turkeys worth as much as 12 chickens,
nnd the cost of 5 pairs of chickens.
2. How many cords of wood can be piled in a shed 15 feet long.
12 feet wide, 9 feet high ? ^'
3. A mason charges 20 cents a square yard for plastering the walls
and ceilnigs of 3 rooms. The first room is 10 feet lon<', 8 feet
wide ; the second, 12 feet long, 10 feet wide ; the third, ] 8 feet long,
14 feet wide. Each room is 9 feet high. Find the total cost.
4. A farmer employed 6 men 20 davs to do some ditching.
After workmg 5 days he concluded to have the remainder finished
in 10 days. How many additional men must he employ ?
5. What is the least number which, if divided by either 8, 17,
20, 25 or 35, will leave as remainder 5 in each case ?
6. Find the cost of wire, at 8 cents for 5 yards, for a barbed wire
fence 6 wires high, to enclose a field 42 rods long and 35 rods
wide.
7. Find the cost of tlie posts for a fence around a garden 250
yards by 220 yards, if the posts are placed G feet apart and cost 10
cents each.
. ^- ^"^ "^*"y ^^^^ of lumber are required for the upright board-
ing, if a close board fence 4 feet high above the 14-inch base is
placed around the garden in No. 7 ?
9. One-fourth of I of the length of a pole is in the mud ; S
of the remainder is in the water and there are 5i feet in the
air. What is the length of the pole ?
10. John spent $80 less than | of his money at one time, and at
another $40 more than -j of the remainder, and now has $40 left
How much had he at first ?
XXXI.
1. How many 2-inch piakets placed 2 inches apart are required
for a fence 40 rods long ?
2. A farm laborer, who is to receive $1.35 a day, begins work
on Saturday, July 2ith, and works until the evening of November
0th. How much should he receive ?
3. How far will the horses travel in reaping a square 10-acre
held with a reaper that cuts a 4-foot swath ?
4. The estimated value of a school district is $450,000. How
many mills on the dollar will have to be levied to raise a tax suffi-
cient for $1,200 school expenses ?
26
AUrniMETlC'AL I'UoliLKMS.
fy,« f^ lAr"" f""? '""^ \^;^'''® ^^^^^'- ^"« '« 80 rods long and
the other 100 rods long. How many more yards of wire fence will
be ^required for one than tlie other, the fence to be live wires
which ^7803?^""' '^''^ '"^ ^ ^'l"^''^ ''^™' ^^^^ ^•'^^ «f
^•u^i^u^^-7^^^^^^,"^*^^"''^^^^^'"^'^'' to fence five miles of rail-
way, both sides, with 6 6- inch boards at $8 jter M ?
8. A man bought a horse for $125 cash. He traded it for a yoke
£e?nlH f\ fJ^ f^l^i"" *t^ ^^''"■'^■"- ^^"« ^'f the oxen died, and
trlnsactiJn? ° ^'^ '"""'' "^''^ ^'^ ^""'^ °" *^® «"t^^®
fK f-^W. lives with a farmer for three years upon condition
that he receives $1 the first month, $1.75 ;ie second, $2.50 the
third, and so on until the end of his time. How much will his
three years amount to ?
10. A binder receives $151 25 for working a certain number of
S^^^" ,_• , ., ^" worked 11 days more he would have earned $165
r ind his daily wages.
XXXII.
1. A ton of coal lasts a family 14 days. If coal is worth $6 25
Qi^^^c^o"^ • '^ Y'"- ^^'f"" ''''^^ ^'^^'^ f^°>" October 1, 1885, until March
ol, 18ob, inclusive ?
2. A farmer's horses, cattle and sheep together number 192
He has three times as many cattle as horses, and four times as
many sheep as cattle. How many of each has he ?
3. How many feet of lumber are required for a 12-inch base
board around a field 40 rods by 30 rods '^
4 Find the value of a pile of 12-foot lumber 8 feet high bv 4
feet 7 inches wide, at $21.30 per M. ^
6 If a street 5 miles long contains 30 iff acres, what is its
width ? ...J >
6. How many bricks 9 inches long and U inches wide will be
required to pave a space 18 feet long by 12| feet wide ?
*o L^"^^® *'°^*^ °^ ^ ^°"^® ^"'^ f'^''"^ ^a» $18,750; the farm cost
*J,300 more than the house. Find the cost of each.
8. Make out the following bill :— 1,020 pounds oats at 63 cents a
bushel ; 432 pounds barley at 70 cents a bushel ; 40 pounds sugar
at 8 pounds for $1 ; 27 pounds tea at 4 pounds for $2.60.
9. A piece of land is 300 rods long and 484 yards wide. How
many acres in the piece ?
US.
SENIOR CLASSKS.
27
i is 80 rods long and
ii'ds of wire fence will
ance to be five wires
farm, each side of
ice five miles of rail-
srM?
le traded it for a yoke
of the oxen died, and
le lose on the entire
'ears upon condition
le second, $2.50 the
liow much will hia
a certain number of
Id have earned $166.
coal 13 worth $6.25
1, 1885, until March
gether number 192.
, and four times as
he?
for a 12-inch base
er 8 feet high by 4
g acres, what is its
inches wide will be
it wide ?
750 ; the farm cost
each.
nds oats at 63 cents a
I ; 40 pounds sugar
for $2.60.
yards wide. How
I
' 10. Ill 25 days a man travelled 472 miles, 7 furlongs, 12 rods,
travelling the same distance each day. How far did he travel in
one day ?
XXXIII.
1. How many posts are required to enclose a i-acre lot of
()6 feet frontage, if the posts are placed U feet apart ?
2 How many feet of lumber in a tight board fence 5 feet high
round a rectangular lot 132 feet by 66 feet ?
3. Find the cost of 245 pounds of flour at $6.00 per barrel.
S o^J"*^ ^^^ expense of carpeting a room 15 feet inches long
and 13 feet 4 inches wide, with carpet 27 inches wide at 95 cents a
yard.
.5. At the rate of 124^ rods a minute, how many hours will a
tram be m going from Boston to Buffalo, a distance of 498 miles ?
6. What nuniber must be added to 1,000,000 to make it exactly
divisible by 492 ? '
^^J^-j^^hat number divided by 379 gives a quotient 9,734 and a
8. If I start on a bicycle for a place at 15 miles an hour, 1
am one hour too soon ; but if I drive at 10 miles an hour I ani 1
hour too late. How far is it ?
9. If a clock gains 2^ minutes a day, and it was exactly correct
at 2 p.m. on October 16th, what time will it indicate at noon on
l/hristmas day ?
*^.^^^' ^uZ "'^''y- ^''l''}^ ^ "^'''^^^ ^°"g' 4* inches wide and 4 inches
IZZ "" M • ^^'i"^':^.^ ^"5 a ^all 60 feet long, 17 feet high and 4 feet
thick, allowing nothing for mortar ?
XXXIV.
it L\lT ^*=^«^/"" °f '"ilk I draw out i of it and fill
It up with water ; I draw out J of this and again fill it ud
with water ; I do this altogether 4 times. If thelilk now were
separated from the water, how much of the cask would it fillT
2. What length of road 36 feet wide will contain an acre ?
;o A^' '^i^ P''??"" oS^ '^'■^^ numbers is 443,398, one of tho numbers
18 47 and another 89. What is the third nimber ? ""moers
+atf ■ f!^''"i "^^F ^"*^^', ^^""^ ^ ^^^^ ^ i"'^''«a '^y 10 inches, will it
take to sod a i acre plot? ' ^"'^^^
5. Of what number is 17 ten less than its half ?
28
AniTHMETICAL PROBLEMS.
C. A quantity of coffee lias cliicory addod to it, so that chicory is
}, of the whole mixture. If tlio mixture bo worth 4,S cents a pound,
and the chicory 8 cents a pound, wliat ia the exact value of a pound
of pure coffee ?
7. A man owning a farm of 108 acres divided it into 14 equal'
parts, 11 of which he sold ; he then divided wiiat he had left
into 9 equal parts, 5 of which he sold. Find the value of what he
still owns at $50 an acre.
, A ^ ^'^y S'l^e 75 cents more tlian ? of his money for a book and
had $2.40 left. How much had he at first ?
9. A watch gains as much as a clock loses, and 1,799 hours by
the clock are equivalent to 1,801 hours by the watch. Find how
much the watch gains and the clock loses per hour.
10. A train passes a telegraph post every 15 seconds ; tlie posts
are 20 rods apart. How many miles an hour is the train running ?
XXXV.
1. A dealer in horses gave $5,920 for a certain number, and sold
a part of them for $2,700 at $75 each, thus losing $5 on each. For
how much each must he sell the remainder to gain $428 on tlio
whole transaction ?
2. A and B ran a race which lasted 5 nninates,B had a start cif
20 yards; but A ran 3 yards while B was running 2 and won by
30 yards. Find the length of the course.
3. If 8 gold coins and 9 silver coins are worth as much as C
gold coins and 19 silver ones, express a gold coin in terms of a silver
coin.
4. How much per dozen is 87| cents per pair.
5. A field of hay 40 rods long and 20 rods wide averages 1 ton
1,400 pounds to the acre. What is the hay worth at $9.60 a ton ?
6. A drover bought cattle, hogs and sheep ; the hogs cost on the
average half as much as the cattle and four times as much as the
sheep. He paid $36.75 for 7 sheep. Find the total cost of 7 Bheep,
23 cattle and 48 hogs.
7. A pile of 4-foot wood is 33 feet long and 5 feet high. How
much is it worth at $3.84 per cord ?
8. The sum of two numbers is 1,415 ; the greater one of the tve
is 817 ; divide the product of these two numbers (that, added
together, make 1,415) by their differuncu.
9. From what number must I take 8 more than its half to
leave 30 ?
1
sidiii
2
he ci
it. :
3
rema
quoti
4.
at3i
walk
5,
6.
steps
7.
der 1
8.
he so
his gf
9.
10.
galloi
tiian :
left, A
KMS.
SEXIOR CLASSES.
29
srtain number, and soW
ising ^5 on each. For
r to gain §428 on tho
tinutes, B had a startdf
unning 2 and won by
worth as much aa G
3oin in terms of a silver
pair.
i wide averages 1 ton
worth at $9. GO a ton?
3 ; tho hogs cost on tlio
inies aa much aa tlic
le total cost of 7 sheeii,
d 5 feet high. Hou
greater one of the tw"
lumbers (that, added
more than its half to
I to it, so that cliicory is
wuvth 4S cents a pound,
1 exact value of a pound
vided it into 14 equal
ided what he liad left
1 the value of what he
3 money for a book and
?
is, and 1,79!) hours by
the watcli. Find how
r hour.
15 seconds ; tlie posts
• is the train running ?
10. A person bought a certain number of eggs, half of them at 2
! P^"y '^"^ i^^'f "f tl^«'» at 3 a penny. He sold tliem again at the
fate of 6 for two pence, and lost a penny by the transaction. What
was the number of eggs ?
XXXVI.
,.^' How many feet of lumber are there in 100 nieces of 14 foot
■iding 6 niches wide ?
2. A man rows 30 miles and back in 12 hours, and he finds that
he can row 5 miles with the stream in the same time as 3 against
U. J.' md the time of rowing up and down.
3. 689 is contained in a certain dividend 487 times and leaves a
remainder of 409. If 090 be added to the dividend what will the
quotient and remainder then be ?
,. o:-^^ ^ \^^^ *'^ a train, I am I of an hour too late ; but if I ride
at 6 times the rate, I am 5 minutes too soon. How far is it, if I can
walk o miles an hour ?
5. Of what number is 14 greater by 3 than its third ?
6. How many miles an hour does a person walk who takes 2
•teps a second and 1,800 steps a mile ?
7. Find the largest number that will divide 3,791 with a remain-
der 17, and b,232 with a remainder 15.
8. A fruit merchant expended $523.00 in purchasing apples ;
he sold them at $4.92 a barrel, gaining $1.07 per barrel. What was
Ais gain on this transaction ?
9. Find a number whose j^^ part is 7 greater than its }.
10. If I take from a cask 1 gallon less than i, and then 1
gallon less than ^ of what remains, and, lastly, 1 gallon less
than i of what remains, and find that I have still 12i gallons
left, what did it contain at first ? t b »
XXXVII.
^htu -^ oi""^", ''^^ ''u'^ ^ "l"^*"^ ^" ^""'' ^g^""fc a stream, the rate of
Ttream ? "' *" ' ^^"^ ^'^^ ^''' """"^ "' ^^ ^""'"^ ^'^^ ^^^^
2. With what quantity ofspirits, worth $3. GO a gallon, must 3^
gallons of water be mixed to reduce tho price per gallon to $3.20? ^
v«ri 1^^""" many Ijoards 12 feet long will it take to fence a field GO
yards long and 40 yards wide, supposing the fence to be 5 boards
30
ARITHMETICAL PHOHLEMS.
4 A farmer sold 50 bushels of wheat, and -. ;h 5 oi the pnce of
it blmctht 6 bu8hel8 of timothy seed at $2 a bush, 4 bushels clover
LtSa bushe 4 pounds tea at 0;5i cents a pound and 60 yards
^otLl 10 Ss aVard. How much did he .et for Ins wheat ?
5. How many apples must be cut up to give 20 boys 5 «? '^'^
'^t How many 2-inch pickets, placed 2 inches apart, wdl fence a
i-acre lot of 06 feet frontage 'i
' 7 . A man bought 03 sheep, and sold f, of them at a prot.t of 15
"l!lf 8 horses plough 11'^ acres in 2 days, in how many days
$1.20 a pound so as to form a mixture 01 j.o y i
value of the different teas is equal ( . ^, , „ „„. :„ o
10 Divide 17 into two parts so that 6 bmes the grea- ." part is 2
less than 7 times the smaller part.
XXXVIII.
"■ 3 Fi^ 1 olof feeding 14 acre, of oat, at 40 eent, a bu.M,
if "TPi nnunds are sown to theacre. .
Cat%L"irp*ce;»t'a<ra.t,»othe„. Find tKe ga.n per
cent.
6. Two- foot w
ood is piled to the height of 6 feet. How long
be to contain 3 cords ?
must the pile
7. A man sells a piece o
an acre, b
ho receive
throws off
213
of land 8 rods long and rods wide at $120
of the price for cash. How much should
SENIOR CLASSES.
31
o. 3 horsos aro worth as much an 10 cowh, and ;j cows as much
as x4 sliuop. If a slioep l.o worth 87.50, fuul tlio v.vluo of 2 horses,
4 cows and (» slieop.
9. A owes I? a bill of ^42.80. Flo i)ay8 the debt partly with
wood and partly witli cash. Tho wood is twenty-oight feet Ioiil' 5
feet high, and 4 feet long, and ir. worth ^2.(32.1? a cord. What sun;
in cash will settle tho bill ?
10. A haro is 200 of her own i)acos in front of a --eyhGund. If
2 of the greyhound's paces aro eijual to 3 of the h.ire's, and she
only takes 3 while tho greyhound takes 4, in how many of tho
hare a paces will he overtake her i
XXXIX.
^- ,^"^Y ^°"g ^^^^ '*^ take a man to walk round a square fi.dd, the
area of which is 5^ acres, at the rate of a milo in IO5 minutes ?
2. A footpath goes up the side and then along the end of a
rectangular field, 2JU yards long and 195 broad ; what distance will
be saved by cutting across in the direction of the diagonal ?
3. 2 cwt., 3 (jrs., 15 lbs., is taken G times from a certain num-
ber, and the remainder contains 2 qrs., 1 lb., 7 times. Find the
number in pounds.
4. What is the least number added to 7, 869, 450, that will make
it exactly divisible by 8,975?
. ^' FJ^r.^ certain country, farms of 200 acres have a road fron-
tage of 220 yards, how far back do they extend ?
6. The area of a county containing 100,000 acres covers 5 sciuare
inches on a map. What is the scale by which the map is drawn ?
1:^0?*'''^^''"''^,''^ "" ^"^'^ ^^ ^*'^5' expense of the sale 6%
profit 24% ; what is the retail price ?
8. A and B walk a race of 25 miles ; A gives B 45 minutes start;
f'^n •,"" °i'"'y a mile in 11 minutes, and catches B at the end
ot M miles ; find B's rate, and by how much he lost in space.
9. A and B receive $1 .37i for digging a garden. They work at
It together for 4i hours ; B then left, and A finished the work in
cs^ hours. How should the pay be divided ?
10. In how many years will $320 double itself, a. 7i% per
annum, simple interest 'i ^ ^
XL.
1. A watch which gains 3 minutes 12 seconds a day is nut rieht
at noon on Monday ; what time will it indicate at 3 p.m. on the
lollowmgTuefday ?
33
AUITHMRTUiAr. I'KOHl.KMS.
2. 2,.'170 iiion Iiiivu provisions for 57 <liiys, and aftor 17 daya 120
men f,'() away ; how long will tho remaining provi8it)n8 last tho men
who are left 'i
3. Tho wages of A and B together for 22| days amount to the
same sum as the wages of A alone for iiHi days. For how many
daya will this sum pay the wages of li alone ?
4. A cistern is fed by a spout which can lill it in 4 hours ; how
long would it take to fill it, if tho cistern has a leak which would
empty it in 17 h(jurs ?
5. A person spends jj of his money for dry goods, ? of the
remainder for groceries, and has $15 left. How much had ho at first?
G. In rolling a grass plot 24 yards long and containing 400 sq.
yards, lii)w many times must a roller 3 ft. 4 in. wide bo drawn over
it lengthwise so that tho whole may be rolled ?
7. How many sods, each 2 feet 3i inches long, and 8] inches
broad would be rei^uired to turf an acre of ground ?
8. A can beat B by 20 yards in a mile race, B can beat C by 20
yards in a mile race ; how many yard's start can A give C that there
may be a dead heat ?
9. A train going 25 miles an hour leaves Bristol at 1 p.m. for
London (120 miles), another, going 30 miles an hour, leaves London
for Bristol at 2.12 p.m. ; when and where will they meet ?
10. A and B working together do a piece of work in 7 days ; B
alone can do it in 13 days ; supposing B works at it for 3 days, in
how many days could A alone finish it.
XLI.
1 . After a certain number of men had been employed on a cer-
tain work for 24 days and had half finished it. 10 more were put on,
and the remaining half was completed in IG days ; how many men
were employed at first ?
2. One vessel contains 24 gallons of water, another 12 gallons of
wine ; one gallon is taken from each and then poured into the other;
this is done twice ; how much wine and how much water will the
vessels then contain ?
3. Divide 8111 among A, B and C, so that A may have U less
than B, and twice as much as C.
4. A and B have equal sums of money, A gains $250, B loses
^95, and then A has twice .aa much as li.. How nmch had each at
5. In a division tho majority was 108, which was ^-^ of the whole
number of votes, how many voted on each side ?
SENtOIl CrAHRICH.
33
Find .!:;'«l::ri';,fr„^"f:;,: -"" «i',.«o „„.» .h„, ,., „, i,
coach, ancl waE the laHt'Z'Z':^. "''">"' " '^^ '''" '^"'"i'HUT by
vcu uio last J inilL'H ; lum J„i,g wuh thu jouri.ov ?
wii.o„„„, t,..„^:XirLi;;:;,'7i',,f ;«,,.!;■?«'''"• ''™ """»
camp in tin,., .^Ikh.riVth:.! ^^ 6"3er.nl„L'; T'"" "" '"»
XLII.
time will C l^ke to do ii / " ""' " ""'" '" = """• ^5 sec, „l,at
take to do the whole wol tf < *• "'""''' "'" """«■ '""" "lone
f.»^;;l,a,rsi;s:r;,L';T.th*°r.;ttf;""°'»'' '-• -™ "3%
eni -:^:;^^-- -St-St^-^^U ^ee ^.et hi.,
^•.iil"!:?^''"^?;^^ feet lon«, is cut into 2 pieces so that ^
piece.
«,ual to A of .„. ,:„,,, K„d tlJelen^th Ztl
10. A lawn which is tw
y.z. Ft„7iSetgrh'.Tb;:i: - " " --^ '=™'"-' «»*
sq.
34
ARITHMETICAL PliOHLKMS.
XLIII.
1. In a battle 8% of the army were killed and 10% of the re-
mainder mortally wounded ; the difference between killed and
wounded was 9.15. How many were there in the army ?
2. A man lost j^jj of his capital in a certain speculation, after
which he gained $550 he then had $6,885 ; how much did he lose ?
3. A boy hired with a farmer for 40 weeks for $40, and a suit of
clothes, at the end of 24 weeks he gave up his situation and received
$18 and the suit. Find the value of the suit.
4. A'man rows 10 miles in 2J hours against the stream, the rate
of which is 3 miles an hour ; how long will he be in rowing 5 miles
w'th the stream?
5. Three men working all day can plant a field in 10 days , but
one of them having other employment can work only half time ; how
long will it take them to complete the work ?
6. A man would lose, 17^% by selling a house for $5,776 ; what
price must he ask in order to gain 15% ?
7. On a certain line of railway the telegraph posts are placed 58
yards apart, and a passenger counts as he passes 37 posts in 2 min-
utes ; at what rate is the train moving »
8. A man walks to town at the rate of 3| miles per hour, rests
there ^ an hour, and rides back at the rate of 7} miles an hour ;
how far has he walked, the whole time occupied being 4 hours 10
minutes?
9. A square grass field whose side is 123 yards has a gravel path
4^ feet wide round the edge and inside the field ; find the area of
the grass.
10. A starts to walk 30 miles at the rate of 4 miles an hour ; B
follows from the same place half an hour afterwards and cornea in
at the same moment ; at what pace does B walk ?
XLIV.
1. A merchant bought a number of barrels of choice apples for
$3,000 ; he sets aside 40 barrels for his own use, and for g of the
remainder he receives $1,794 whijh was $138 more than their cost ;
how many barrels did he buy ?
2. If 32 eggs be sold for 40 cents, and the gain at this rate be
^ of the cost, find the cost price per dozen.
3. What is the value of a farm 150 rods long, and 94 rods wide,
at $40 per acre i
SENlOn CLASSES.
'i of the re-
. killed and
T'i
lation, after
did he lose ?
and a suit of
and received
sam, the rate
i^iiig 6 miles
) days , but
If time ; how
6,775 ; what
re placed 58
ts in 2 miu-
hour, rests
iS an hour ;
4 hours 10
gravel path
the area of
an hour ; B
id comes in
I apples for
or I of the
their cost ;
:hi3 rate be
rods wide,
I
peryarlTaftTispret\r'^^^^^^^ -hat did it cost hi.
make a profit of 33>T? ^''' ^ ''^^^"""t of 207, Td still
5. Water which vveitrhs 1 onn^
0. A sets out walkintf at f>i ..,:i V
and «,h«n he has gone 8 mlA? „?"!'''"'' "'""g a straWitroad
-ou^r; when .„<, Ihere wSlt^.e'Shtr, '"" =' '^ »"" I-
his weaght by SOOpounds S his ti^t^'"''''" *^^"" ^^'^'^^ times
XLV.
1. A roller is 10 feet lonor anrl 19 f„ <. • •
muse I sell him^o gain 50/?' ^^'' ^ '"^^ ^^^^^ ^or how much
30 feet'lSnl IfluLl ^' fe^.^^' T,^ '\ ^'^^ — ^ -om
Pnce per yard ^ ""' ^^^« length <>f the carpet and the
aa ^"*1„"T„?-;,tt">': i'r,*t'"ti*ff -O'toy-. do A
together? ' ^^"^^ time can they do it working
7- The price of butter nor nonnrl ,'« i„ ^ ^ , , ,
per ao,e,i and it costs $3.78 to W 14 i"'*^ ^'""^^^ ^he price of egsys
butter. Find the aelliiig pSce of eachf '^^'' "'"'^ ^* Poundaif
36
ARITHMETICAL PROBLEMS.
8. A telegraph line, measuring from the first pole to the last
one, is 27 miles 5 furltmg, 187 yards long ; the poles are 09 yards
apart ; how many are there ?
9. A borrows 8:5,205 on the 3rd of May, and on the 15tli July
the interest due is $'.)(). 15. At what rate did he borrow ?
10. A stock of goods cost $300, and freight 5% additional. If
40% of the goods be sold at a profit of 27% and the remainder at 25%,
what is the gain ?
XLVI.
1. A spirit merchant buys 75 gallons at $3.25 a gallon, and
drawing off 10 gallons, sells the remainder so as to gain 5% on the
whole. What is the selling price per gallon ?
2. Coffee is bought at 25 cents a pound, and chicory at 10 cents a
pound ; in what ])i-oporti on must they be mixed that 10% may be
gained by selling the mixture a'^ 15 cents a pound ?
3. A telegraph pole is 22 feet long and the part in the ground is
^( of the whole length. How far is the top of the pole from the
ground ?
4. How many yards of silk § of a yard wide will be required to
line 24 yards of satin | of a yard wide ?
5. At what price per pound must a grocer sell sugar which cost
him $15.40 per hundred weight, so that on every $44 of outlay he
may gain the cost price of 80 pounds ?
G. If eggs sold at the rate of 35 for 48 cents, and the gain at this
rate is -^ of the outlay, find at what rate per dozen they were pur-
chased.
7. How many gallons of water must be added to 63 gallons of
alcohol, worth $4.40 a gallon, in order that it may be sold at $3. GO
a gallon without loss 'I
8. A can do a piece of work in 5 days, B in 0, and C in 8. If A
and B work at it two days each, how long will it take B and C to
finish it (
9. If it costs $48 to carpet a floor 24 feet long by 18 feet wide
with carpet 27 inches wide, find the price of the carpet per yard.
10. The dividend decreased by 13 is equal to 33 times the
ro!!iait>,<lrr ; t]>ft difference between the remainder and divisor is 9 •
the quotient is 21. Find the divisor, dividend and remainder.
■•:
rf
SENIOR CLASSES.
37
to the last
09 yards
15th July
tional. If
ierat25%,
allon, and
5% on the
10 cents a
% may be
1 ground is
I from the
■equired to
which cost
outlay he
;ain at this
were pur-
gallons of
d at $3.60
in 8. If A
and C to
i feet wide
er yard.
times the
visor is 9 '
lainder.
XLVII.
*».80, hnd the cost and credit prices arcicie is
t.n,e when ib marks the end „t the week ! ""^ '^"'^'^
o.i,\^^jzihi^^;r;^^^^^^^^^^
7. If 10 men can do a piece of work in 19 /1o,t„ u
be,i„„i„, ■»-' ".ey be joLa b/ 3 l^^sfaBtf intlTthZojf f^
.oM'k?r°Se%',red';oS'r''°''^«- What must I have
XLVIII.
1 ^" • A^°^ P*^^ ^ ^^^^^ ®^°h for oranges and had 9 cents 1«ff • h.A
he paid 3^ cents he would have been 9 cents short F,nd If ' ^^'^
her of oranges bought -"^ '""^ ^^^ """^-
U J. 3^pL"„^^-p^S"^ V'ifS'Se^ - -n W'
^. A drover bought a certain number of «h«en f<.r c^ofin - ^'^ "
38
AIM! lIMKllCAr, PUOHLKMS.
4. A book is 'iil inclies thick. Each cover is f„ of an inch thick,
and the book contains 1»04 pages. What is the thickness of each
leaf?
5. A grocer mixes 40 pounds of tea at 60 cents per pound with
66 pounds at 72 cents per pound. At what price per pound must
he sell the mixture to gain 25% of the cost ?
6. How much water must be mixed with 100 gallons of vinegar
at 60 cents a gallon, to reduce the value to 50 cents a gallon ?
7. A customer bought what he supi)osed was $48 worth of tea,
but a false weight having been used, ho got only .^42 worth. How
many ounces* were given for a pound ?
8. A and B run a race of 200 yards, and A wins by 3 yards.
A and C run over the same course and C wins by 2 yards. What
start can C afford to give B in a 200 yards race ?
9. I bought 10 pounds of tea and 12 pounds of coffee for $8.40.
The twv was 40 cents dearer a pound than the coffee. Find the price of
each per pound.
10. By selling 175 yards of cloth at $1.50 a yard, a merchant gains
$10.50 more than twice as much as he would have lost had he sold it
for $1.20 a yard. Find the cost price per yard.
XLIX.
1. A merchant bought a piece of cloth for $72. He kept 25
yards for his own use, and sold the rest at an advance of 10% on
cost, receiving for it $57.20. What did the cloth cost him per
yard ?
2. A farm contains 120 acres ; its width is| of itslength ; find its
length in yards.
3. A piece of cloth would be worth $65 if it were -^\y longer. If
the price of a yard be $1.25, how many yards in the piece ?
4. How far may a person ride in a carriage going at the rate of
8 miles per hour s) that if he walked back at the rate of 3 miles per
hour he may be gose 6^ hours ?
6. Walking 4} miles an hour, I start after a friend whose pace
is Smiles an hour, how long shall I be in overtaking him if he has
a start of 2 hours ?
6. Bought a piece of cloth for $12.96.
yards in the piece as it cost cents per yard.
I buy?
7. A can run 8 yards while B runs 7|.
should be given to B in a quarter mile race in order that neither
may win ?
There were as many
How many yards did
How much of a start
SENIOR CI.ASSKS.
39
8. Tlie wages of A and B together for 7h davs will ,mi, +l,o
wage, of A alone for 20 days. For how nm^y "day/ wiT tl sMm
pay the wages of B alone ? ^ " """"
9. A sold B a carriage which cost him $150 at 12A7 nrofit B
Bold It to C at a profit of 10%. What would have been^I^ prolS
per cent if he had sold to C for the price C paid ? ^
cenfs ^FinH "fi ^^''^ "i^'^^^^ '' S'''''^'' ^^^*^'^^« ^3 cents instead of 32
cents. J^ uid the number of ounces in his false pound.
L.
1. A man has $260, he spends a certain sum and afterwards
ho's^ent ' ^ '' '" 'P'"'' ^' '^'^" ^'^ ^*^^- Find fowTuch
2 A grocer bought a quantity of potatoes for $250 ; he sold half
o t em for $150, gaimng 8 cents a bushel on what he sold. What
did the potatoes cost him per bushel.
wor^h^7?5''"Tf fl^'^''' T'^ ^T^ \^^ ^«'gh'"g 16 pounds is
worth $7. / 5. If the proportions of each are interchanged the mix-
FinVI. b«.^°''f,f -45. The black tea is worth 40 cfnts a pom d
* ind the price of the green tea. puuim.
f..l' f "i^n bought 80 barrels of flour for $427.50, pavinc $5 40
equal to the profit on $G0 outlay. ^
6. A train 120 yards long, moving at the rate of 40 miles an
and ;.T'''>^"f .f ' *^rain moving at thi rate of 30 miles an hour?
and passes it in G^ seconds. Find the length of the last train
mJh nf fr""*"- f "*^^^"« ^^Pa'-fcs alcohol to 3 parts of water. How
much of the mixture must be drawn off and replaced by water that
the new mixture may be half and half ? ^
more tHn B S^?.""""^ ^' ^i ""'^n^' »° '^^' ^ "^^ ^ave $30
more tn.m a, and d times as much as C.
ofw^od "'H«wf !T,*^^^''^"^^■•'^^•' ^«««^^« ^156 and 7 cords
th^^ A ^-^i^t^ ^^^ ^"^ ^^ ^ '""»*^^8 and received $83.50 and
the wood. Find the price of the wood per cord.
fl,f ?■ ^ ^r oif "'^'''y^ ^ ^^^ a"<l a ««''<^ain number of boys ; he pavs
the men $1.25 a day and the boys 76 cents a dav ; the am'rnETf
paiu to all was as much as if each had received $1.05 a day. How"
many boys were employed ? •v ^x^y. now
40
ARITHMETICAL pitOHLKMS.
LI.
1. What sum of money will amount to $426. 56 J in 6 years 3
months at 5% per annum ?
2. If a man can do a certain work in 1^ clays and a boy can do
it in 4 days, how much of the work will be left undone after both
have worked together at it for one-half of a day ?
3. A man divided a farm among three sons ; to the first he gave
80 acres, to the second ^ of the whole and to the third | as much
as to both the others. How many acres did the farm contain ?
4. Sold 20,900 feet of lumber for $331. 62i, gaining thereby
$78.37^. What did it cost per C ?
5. The cost of carpeting a floor lOj yards long with carpet 27
inches wide, and costing $1.35 a yard, was $93.15 ; find the width
of the room.
6. A grocer mixes 60 pounds of tea at 65 cents a pound with 80
pounds at 60 cents a ])ound ; at wiiat rate per pound must he sell
the mixture to gain 30% ?
7. A bankrupt owes four creditors as follows : A, $2,400 ; B,
B3,300 ; C, $4,200, and D, $4,000 ; his property is worth $10,500.
What does each creditor receive ?
8. Fi' .d the expense of plastering a room 20 feet long, 18J wide
and 11 J feet high at 18 cents a Sijuare yard.
9. If A can do a piece of work in f of an hour, and B in J of an
hour, how long will it take both workmg together t< do it ?
10. If by selling an article for $2 I gain 20%, for iiow much must
I seU it to gain 33^% ?
LU.
1. How much water must be mixed with 600 gallons wine, at
$2.50 a gallon, in order to make the mixture worth $2 per gallon ?
2. A railway company pays $24.76 per acre for a portion of
road 100 niles long and 94| feet wide, find the whole amount paid ?
3. A merchant bought 27 pieces of cloth, each containing 19i^
yards, at $4.31J a yard, and paid freight $9.G2i ; he sold so as to
gain $381. 87|. At what price per yard was the cloth sold ?
4. A sum of money amounts to $787.50 in 10 years at 7|%. In
how many years will it amount to $990 ?
5. A bankrupt can pay 40 cents on the $ ; if his assets were
$500 more he could pay 45 cents. Find his debts and his assets.
I
HKVIOK (;las.sk.s.
41
many Vy^^^U^' uZ Td''? V"'' ?' ^"^"^ ^'^ '^ ^^^^^ ' ^'^ h«-
times as grear? ^ ^ ^^^^^ ^'^ ^ P^«c« of work three
10. It costs $96.25 to carpet a room 99 f^^^ a- u i
carpet 27 i„„he. „iae at W./s a ^arTrfnV^hl t.'dt^f 'Z'C:
Lni.
$224 .re than^lf^^^L^^.^CStdt tv^ ^'^"'^ ^-
years 1^' "^''^ ''^'^ P^'' ^"^^- "'" ^^'"^O amount to |1.733.75 in 2^
co„L7of "c^rd'^/trdT' °' ^ '''^ ' ^'^^^ ^-^' ' ^-t high, to
of wmch is" miKn ?o"r "ho;?* hours against a stream, the rate
the stream ? ' ^""^ ^^"8 ^^" ^^ ^e rowing 6 miles with
posid t^KTlVoTdTfe'' H-''"'^^P°""? ^"^ ^h^t J^^ «»p-
annum*"' " "'^' '""« ^^^'^^ ->" double itself at 6f% per
9. A can run 10 yards to R'h Q tt^.„ ™ •. .
AgiveBtomakean'^evenracehxlOOyaTdsT"^ ^"'^' ''''' ™"«^
10. A merchant sells 90 pnun'l'" of fps Bn^ , "• ' -i*,. .
at 90 cents and the coffee t 40 Jn^^ ''° '^°'' *"*^' *^h® *«»
pounds of each did he selU ^^^ P*^""*^" ^ow many
42
AHITIIMETICAL PHOULEMS.
LIV.
1. A grocer in selling goods sells 15| ounces for a pound; how
much does he cheat a customer who buys to the amount of $40 ?
2. A crew can row down stream a distance of 4 miles in 30 min-
utes, and up stream the same distance in 34y minutes. Find the
rate of the stream.
3. I sold 250 yards of cloth for $345, receiving $1.30 a yard for
part of it, and $1.50 a yard for the remainder. How many yards
did I sell at each rate ?
4. The whole time occupied by a train 176 yards long, going at
the rate of 20 miles an hour in crossing a bridge is 25 seconds. Find
the length of the bridge.
6. Bought $64 worth of apples at 80 cents a bushel, part of
which, being damaged and rendered worthless, I sold the remainder
at an advance of 50%, receiving $76.80. How many bushels were
damaged ?
6. A and B together can do a piece of work in 61 daya ; A can
do it in 9 days. How long would it take B to do it I
7. Bought wheat at 96 cents a bushel, and «old it at $1.10 ;
find my gain per cent.
8. A ship with its cargo is worth $260,000 ; | of the cargo is
worth ^ of the ship. Find the value of the cargo.
9. A book was sold for 30% more than it cost. The sum of the
buying price and selling price is $4.60. Find the buying price.
10. A man spent 12% of his money, and had $76 more than 50%
of it left How much had he at first ?
LV.
1. A man sold a horse at a gain of 40%, and, with the money,
bought another horse, which he sold for $126, losing 10%. Find
the cost of the first horse.
2. At $2.25 a rod, what will it cost to fence a field 42^ rods Jong
and 137^ yards wide ?
3. If 7 pounds of flour are worth 10 pounds of pork, how much
are 10 barrels of pork worth, if the price of the Hour is $5.60 a
barrel ?
4. A certain sum of money for a given time at 8% per annum
amounts to $710.40, and at 6% for the same time to $652.80. Find
the principal and time.
5. By Belling goods at 40 cents a pound 20% is lost. What
advance must be made in the price to gain 33] % on the cost ?
SKNIOU Cr.ASSKS.
43
6. A rectangular field :iOO yards long and 150 broad is senar
afced into 4 equal parts by 2 bands c.f trees, 20 yards wide parallel
to the sides. How largo will each part beV Parallel
7 How many stones, each 2 feet long and 15i inches wido
would be required to pave a square courtyard whcU sTde is 124
I 8 What weight of water will a rectangular cistern contain the
length being 5 feet, the breadth 3.^ feet, and the doplh 12 feet ?
r.}J.l oi ^"u^'' 1''52 yards long and 18 feet wide is covered with
ofl^infZfTv,"^^*'!""'''^'^''*^"''"*"'*^^'^ mixed with m gallons
of wuie that the mixture may contain 17*^ of water ? "
LVI.
^n in ^ i"'i"i'^ 60 pounds of tea for $35 and sold it so as to gain
$5.20 ; had I purchased $105 worth of tea and sold it at the sime
price, what protit would I have made ?
w.ifi.A/fr^'"'''''^ ^ ^fl"^ °^ ^'^y ""^ ^14.00 a ton; the whole
3 -^t^ oon^ "^^^'^^ ^"/^ ^'^y ^^« 2,050 pounds ; the wa^on alone
weighed 900 pounds. How much did the farm'er recelvf ?or the
3. At what time are the hands of a clock exactiv S minnfo
spaces apart between 1 and 2 o'clock ? ^ ""*^
.o ^A^ '^'fo^™ ^"^^ ^ ^'P'^^ 5 the first will fill it in 8 hours the
second in 10 hours, and the third will empty it in 14 hours If all
are opened, in what time will the cistern bj full ?
5. Bought oranges at 15 cents a dozen and sold them at 3 for K
cen^^^ How much did I gain on 12 boxes, ;tVcontatfng''25
Mondayr ""^"^ "''""^'' ^'""^ ^"^^ P"™" ^^^"'^^^y """^ 8.43 a.m.
.■ha\-J4?i^tst"o¥tret'S^ '''^'' ' '"^^^'^^"^ ^^-" ^250,
8. A field containing 6 acres is 40 rods long. How many trees
16 feet apart, will bo required to plant it around ? ^ '
ounLrslrofa^otdT"^'^^'*^^^^^" ^^^ ^^"^- ^^ ^^^ ^^1
hiJcommTsin?o;sXn'.7"' ' ''^"^ '°^ ^'''"^ "^^ 2^^- ^^^^ "
44
AUrniMETlCAIi PKORLKMS.
LVII.
1. A ])late of brass 4 fetst h>n>^, 2\ foet wide, and h an inch
thick, is rolled int(j a sheet 7 fetft lung and 5 feet wide. Find its
thickness.
2. A bar of iron G feet h)ng and an inch square weighs 65
pounds. Find the weight of one the same length and 1^ inches
scjuare.
3 . Find the cost of a farm 1 mile long and 80 rods wide at $60
an acre.
4. A farmer bays a plough at f 14 from an agenc, who makes $4
by the sale. Find what rate per cent, of proht the agent has.
5. Five pounds of tea at 60 cents are mixed wi>;h 4 pounds at 50
cents. At %vhat price per pound must the mixture be sold to give
a gain of fr; of the outlay ?
6. A, B and C met. A had 3 loaves of bread, B 2 loaves, and
C 25 cents, The loaves were divided equally among the three ;
how should the money be divided ?
7. TheC.P.R. Company pun.hase a road 4 rods wide at $75 an
acre across a man's farm, which is 80 rods wide. How much does
the man get for his land ?
8. What will it cost to insure a mill worth $18,000 for § of its
value at 1|;^?
9. A company charges $27.75 for insuring a house for $1,850.
What was the rate of insurance ?
10. How long must the side of a square lot be to contain d|
acres ?
LVIII.
1. What is the premium for insuring a cargo, valued at $15,500,
at 2i% ?
2. A trader gets 500 barrels of flour insured for 75% of its
cost at 21%, paying $80.85 premium. At what price per barrel did
he purchase the flour ?
3. What sum should be insured at 4%, on goods worth $2,940,
that the owner may receive, in case of loss, the value both of goods
and premium ?
4.. An estate assent sells 420 acres of land at $18. .50 an acres and
charges 2|% commission. What is his commission /
SEN'IOIt CI.ASSKS.
45
wah„f 7.,'.'!;'"^ ■■','"'"' """,W"'-"i" '« wiui™! I" cover the
walls .,f a roctiuigular n:„m i.f ordiiuu v liciolit ■>! 1,^, v,„ i a ( .
LIX.
rate^ftmli -"siotT''' ^''•'' ''^'' ^'^"«'=^'»« ^'^^S. What was his
price. What was his not gli.^j'I^r t^t. ? '"'" ^'^'^ "^' '"'^^'^^^
an/'then'*?^nK*' ^ "^ '>«V'"f ^^^ '" ^"^'"8 ^i'^ at 81.40 a yard
am tnen ^ ot the reniainder for a hat • shn li.»l «t;ii i f^ Z on
Hr>w many yards of silk did slio buy ? ' ^'^ ^*•^^•
4. By selling an article for $5.70 the owner loses 5°/ Fm- h
much must he sell it to gain 5 / ? /°" * "^ "°"'
ce„L,tit!I-?:iL"S.fr;,trre'cLitt: ""^ ™^ ""°''« "»
7. Two pounds of tea and G pounds of su^ar cocf -PiP 9n n.,.
^A^^^^^ interest of a certain sum of
en. 90. Find the
sum,
money for 2^ years at 7%
IS
46
ARITIIMETICAIi THOHI-KMS.
n. A man ai^reed to work for ^1.00 por clay, anil to forfeit 25
cents every day he was idle. At the end of 'M days his wages
amounted to $25. How many days was he idle ?
10. The premium for insurinf; a schitol-house at 1|/^ was $^G.
For what sum was it insured l
LX.
1. Find the interest on 8375 from June 5th to August 17th, at
6% per annum.
2. Find the cost of digging a cellar 3() feet, long, 22 feet wide
and 6| feet deep at $1.50 a cubic yard.
3. A grocer sells 55 pounds of tea and sugar for $19.10— the
tea at 50 cents and the sugar at 8 cents per pound. How many
pounds of each did he sell ?
4. By selling tea at 72 cents a pound, a merchant gains I of the
cost ; he then raises the price to 85 cents a pound ; what does
he gain on every $42 of his outlay by the latter price ?
5. At what price must I mark cloth which cost me $3.00 a yardi
sa that after throwing oflf 20% of the marked price I may sell it
at a gain of 25 ^ ?
6. Four men can do a piece of work in 8 days. After they have
worked 2 days three boys join them in the work and the whole is
djne in 6 days. What part of the whole work is dono by the
boys ?
7. The ice on a pond, whose area is | of an acre, is 9 inches
thick. How many tons of ice may be taken from the pond, if a cubic
foot of ice weighs 56 pounds ?
8. A grocer mixed 25 pounds of tea worth 30 cents a pound,
with 35 pounds of another kind, and thon had a mixture worth 37
cents a pound. Find the price of the second tea per pound,
9. If a boy buys oranges at 6 for 4 cents and sells them at 3 for
Scents, how many must he buy and sell to gain $5.25 ?
10. A bought #3 of a certain property for $1,700, B bought ^^ of
the same property at a rate 10% higher. What does B's part
cost him ?
SENIOR n.ASSKM.
47
ONTARIO EDUCATION DEPARTMENT EXAMINATION
TAPERS.
ADMISSION TO Jll(;n SCHOOLS.
July, 1880.
and four hundred and 8oventoon Fvni ' ^u "^ ^'""^red thous-
ducb is removed one jlce to the left ' " ^^^ '*'^ ^'''''^^ ^'-
meL?f"" """"'■'^' •^"'"""'^ "-*-'•«. and .jreatest common,
Find the G. C. M. of 153,517, and 7,389,601,522
3. SIiow that ij = ^,1.
Simplify ; "
-lli^^Lll!^ , ^l±m 12354
^Ai-, „^^^■^o~^ 9?-3,-V!j—l2365:
«. A brick wall la to bo blIiI^ 'tc ' „ 1^T r , . . .
feet thick leach brick . 9 hicl o ' ii i?' "■?"' ^}^^ «"<> *
thick. How „,a„y brick, willbe 4iit;dT " """ ^* '""'"»
IherorjSt? ?i'^' ^" '^ ^"^^^ ^^^ cents!^fi„tthe'amount of
of eg.sl'eadi conSninl SSnuff'"^ ^'^' ^''' ' '^^^^ ^^-'^
price of 14-85 cen 3 ?,er dnZ aT^- ' ^^ '^''^'^'^'^ '■^» *^«'-age
13-5 cents per dS"f, Ld tlrentire nr^rf 't' ''"I' '" ''^^^ ^'^«»
find the nu'„.ber of e^s pa^t dt 3? barrd '^'^ '^"^ *' '^•^^'
incL.'^ird'irdSyTs^^^S^^^ f« -«^- by 32
of Yonffft Sfr««f ..ii.i, r„ :v-,°"''3" ""^ ^' ®^ ' ^'""^ many miles
with ten weeks"is8ue? " ^ ^ '^ '""' ^^•^''' '^'^ht be covered
48
ARITHMETICAL PBOBLEMS.
9. A flag-staff 120 feet Iiigh was broken off by the wind and it
was found that 70 of the longer part was ^% of 9| times the shorter
part. Find the length of each part.
10. A and B together can do a p-.ece of work in | of a day, B and
C in ^xi of a day, and A and C in i;| of a day. In what time could
all working together do the work ?
December, 1880.
1. Define— Number, Numeration, Notation, Addend, Minuend.
2. Find the G. C. M. of sixty-eight million five hundred and
ninety thousand one hundred and forty-two, and eighty-five mil-
lion forty-four thousand and fifty-nino.
3. For a voyage of 17 weeks a ship takes provisions to the
amount of 48 tons 4 hundredweight 2 quarters 20 pounds 9 ounces.
Supposing that there are 73 men aboard, how much may be
allowed each man per day ?
4. Find the amount of the following bill : 14| pounds beef at 10
cents ; 12| pounds pork at 9^ cents ; 3 turkeys, weighing in all
35| pounds, at 12^ cents per pound ; 12 pounds 10 ounces lard at
15 cents a pound ; 5 geese, weighing in all 45 pounds 12 ounces, at
10 cents per pound.
5. Simplify :
of of ,3^ + 3 -3 of 2-]| £19 163. 7|d.
5)
of
£20 iGs. 8|d.
j^ of (2-045
6. What is the weight of a block of stone 12 feet 6 inches long.
6 feet 6 inches broad, and 4 feet 1^ inches thick, when a block of
the same kind of stone 2 feet inches long, 3 feet 9 inches broad,
and 1 foot 3 inches thick, weighs 1 ,875 pounds ?
7. A man, after paying an income tax of l^ mills on the dollar,
and spending $3.37^ a day, is able to save 11,230.871 a year. Find
his gross income.
Jnly, 1881.
1. Define Subtrahend, Multiplicand, Quotient. Explain the
statement—' ' The multiplier must always be regarded as an abstract
number."
Divide 2,000,000,018,760,081 by sixty-three millicm, two hun-
dred and forty-five thousand five hundred and fifty-three.
2. Define Prime Number, Prime Factors. How do you resolve
a number into its prime factors ? Resolve 132,288, and 107,328 into
their prime factor."?, and find the least common miiltiplo of these
numbers,
SENIOB CLASSES.
49
vind and it
the shorter
day, B and
time could
Minuend.
ndred and
ty-five mil-
iona to the
s 9 ounces,
ch may be
I beef at 10
linor in all
!es lard at
ouiices, at
iches long,
a block of
lea broad,
;he dollar,
ar. Find
plain the
n abstract
two hun-
)U resolve
7,328 into
of theae
3. How many minutes are there in 19, of a vear nfi5 f]».,.\ ^ i
of a week + ^^ of 3^ days } ' ^ ^ ^^^^^ + si
4. Simplify :
ii+^\ 9+U
iF^ ~ 2?2^ + l'7«lA-l,«50iei.
bus^elfaS|i/S^;!^LSL;^^Se1t:!^t^^^^^
quantity at 97 cents ner hiwhul a I , ''o^' "^^- > "^ sold 4 of the
December, 18R1,
yard, tt 2.. ?d ;"84 A St: M ° f/trlTS %t- X ^ "'
Stair rods at 53 Gd •"•, <^ yaras at Js. «d.; 10 dozen
th^yhain c„.ti„, X6.. „d.. .„d the .opr.SglliJSt^kt/S:
6. By selling tweed at $2.60 a yard, it was found that f of fK
cost was gamed; what selling pric'e w^uld have gained' I o1 tt
an
g. Find its thiikne ' "^'^'^" ' "^"^ ' "^^^'^^^ -^^^^ «"d 6 feet
long. Find its thickness
4
60
ARITHMETICAL PKOBLEMS.
8. How many bricks 9 inches long, 4i inches wide and 4 inches
thick, will be reciuired for a wall (iO feet long, 17 feet high and 4
feet thick, allowing that the mortar increases the bulk of each
brick ^\ ?
0. A grocer gained 20% by selling 10 pounds of sugar for $1-
Afterwards he increased his price, giving only 9 pounds for $1.
How much per cent, did he make at the increased price ?
June, 1882.
1. Define Greatest Common Measure. State the principle on
which the rule for finding the G.C.M. of two numbers depends.
Find the G.C.M. of 68,590,142, and 85,054,059.
2 A dealer bought 8 carloads of lumber, each containing 9,870
feet, at $13.50 per M. He retailed it at $1.43 per 100 feet. ^'="-'
his gain on the whole lot.
3. Show that » = ^, and that § -^ t = Ig.
Simplify :
263-U3
Find
•if
of
65<
6ii
l + lJ-^^ofU^of I-
4. Prove that 2-3 x '04= '092.
Add together 154 2125, '5421, -0001235, 741-206, -03, and 4567
■0004.
Reduce 75 0125 cwt. to ounces.
5. A steamer makes a nautical mile (6,072 feet) in 3 minutes 50
seconds. Find her rate per hour in statute (common) miles.
6. There is a solid pile of bricks which is 36 feet long, 16 feet 6
inches wide and 14 feet 6 inches high, and contains 122,496 bricks
of uniform size ; each brick is 9 inches long and 4^ wide. Find
its thickness.
7. A London merchant transmits £250 10s. through Paris to New
York; if £1 = 24 francs, and 6 francs =$1.14 American currency,
what sum in American currency will the merchant realize ?
8. In a map of a country the scale is ^ of an inch to a mile (i.e. ,
^^ of an inch represents a mile), and a township is represented on
this map by a square whose side is half an inch. How many acres
in a township ?
9. If 4 men or 6 boys can do a work in 8 days, how long will it
t«ke 8 men and 4 boys to do such a piece of work '{
SENIOR CLASSES.
51
iris to New
%7m«l"t "C:„r'',SS' w'/'""'"" '"/^ constituency „t
persons did not vote ? ""tjoricy ot lUU. How many
December, 1882.
stop.- '''''" "^^ "i" S^". ^-Pl-tai-S clearly tl,o reason for each
f- -"^'"ti the amount of the followino- Kill . Qr , „'
beef at IG cents ; 10 p,mnds lOn r " .. 30 pounds 8 ounces
12 ounces pork c^.p^^ 2 cen 15 Znl'r ' ^ '""' ' / '"""^^«
cents ; 4 pounds lO^ounce^ suet .i 10 cTts """'"' '"''^'^^ ^^ ^^
3. Find the 1 M, of 11, 14. 28. 7. 56, 42.81 ; and theG.C.M.
of 40,505, and
4. Prove t
Simplify :
■J.
n = iof3.
tf of*
VtT + ]
of 3]
■'(^ "f Si-i)
Jof ^ + .3of5
6. Prove that 1 025- 05 = 205
•O70S ore' °' ■'"'' '' ''' '^"""^« -'g-' -J-n 1 pound cost
0. Reduce 45.740,108 square inches to acres.
/. The bottom of a cistern is 7 feet inches bv "^ f^^f 9 • 1
*irl,tp^-t°„Kl';'* » -^j™c;„2»<. I.;, speea been .
A s speed to B's. ''^ y^ras. i-md the ratio of
30 ,„in„te, :n „,i,at tone --U.' t rj n^ll^Sf, ^ X' l^ri"
»hJltS';?„?r^a'': 2SV' '■°"'"' ' «'""" '--^°%- ^Vhat
Jime, 1883.
1. What is the object of Division? VVrito down fl. i .-
connectuig tile Div'sor Dividpi.rl n,", f '^"^^ ?own the relation
Divido'l08.419,71.i;00n:y V^748;oot ""'' I^->«'»der.
52
AKlTllMPynCAI, PK0131-EMS.
2. Find, h castinjj out the nines, whether the following is cor-
rect :— 34.>,75i X 28, 037 = 10, 015, 819, 397.
Find the weight of 500,000 bricks at 4 pounds 2 ounces each,
and tlio cost in dcdlars and cents, at 27s. Od. each, allownig 4s, 2d.
to make a dollar,
3. A merchant received from England the following invoice in
sterling : —
375 tons iron plates, at £8 15s, 6d.
107| tons bar iron, at £11 148.
10 tons bulb iron, at £10 lOs.
48 tons steel, at £18 7s. Od.
15 tons rivets, at i,'ll Is.
17 tons T iron, at £15 10s,
Find the amount of this invoice in Canadian currency, allowing
the shilling sterling to be eiiual to 24^- cents.
4. At 31.75 a rod, what will it cost to fence a piece of land 63-5
rods long and 27 '75 rods wide ?
5. Simplify :
4,-0 + 5.81— 2;5
I-Hu^-.HIo + tS^?. ; and ^^^ ^^ 32 of 45.
6. Gunpowder is composed of nitre, charcoal and sulphur, in
the proportion of 15, 3 and 2, A certain quantity of gunpowder
is known to ccmtain 20 hundredweight of charcoal ; find its weight,
and also the weight of nitre and of suli)hur it contains,
7 Bought 3()0 gallons of wine at $2.(iO a gallon ; paid for car-
riage, .r!17 20, and for duties S8(i.50. If ^ of it be lost by leakage,
at wiiat price must the remainder be sold to gain $50 on lUb whole
transaction 'I
8. Find the i.iterest on a note for $257.81, dated January 3,
1883, and paid April 0, 1883, at 8% per annum,
9. The length of a second's pendulum is 39'37079 inches ; if M
French metres'are e(iual to 70 yards, by what decimal of an inch
will the length of a second's pendulum differ from one metre ?
10. At what time between 4 and 5 o'clock are the hands of a
clock (1) coincident, (2) at right angles i
December, 1883.
1. Multiply the sum of 59,404 and 47,675 by their difference,
and divide the" product hy 7 x 13 x 19,
SENIOU CLASSES.
53
cents a dozen, and sold
How much did I <'ain
2. Bought oranges at the rate of 10
hen. at the rate of 5 oranges for 11 cents.
on u boxes, each containing 20 dozen ^
wide! ltyTnTtt"£'at'lt'>:r^%S "" ''^' '""^ ^y 25 rods
fenced at the r ite of «f ^n a^ ^^^^ ^'^"^ ''•=''«' '''"^ t'^«» l^^^l it
exactlytn\^irs^?l'etel.rftce'^^°^^^'^^^ ''"'' ^""
.o.tt?i:;i%Sirsihi'^2? "' - ''-' ^ -^ ^-^ ^^^
betwe^l^S sllTi of !:f^ '^' '^ ^' ^^ ^^ ^h« '^'^--e
bv ^OO^^ln!^^'?^']' \?^^' ^'^^^^ ^"^ 4'093. Multiply the sum
fractions to L ^ /-"'^ ^•''°^".'=*^ ^^ '*0<^->- d^ecinials, not vulZ
aUowed.) "" ^"'"2 '^" ^°'^^' "^^^••^i^^ "o ™ark8 to^be
w.,!i .^^J""^"" ^"''^ * ^"^-^ of hay at $16.25 per ton ; the whole
8. A can run a mile race in 5 minutes, B in 6 minutes TTn«r
n.any yards st.rt should A allow B in ord^r to make theL chancel
9. Three men can dig a certain drain in 8 days. Thev work at
he;orkTn'5"d:r;r'^'r '^"^ ^1'' '"^^^ '^ otherLnnisI^'
man7o before heTell";;?' ''•^" '"'"^' "^ '''' --^^ ^id the first
10. Find the interest on 1^275.80 for 91 days at 7% per a.mum.
June, 1,^84.
1. The quoti^ent is 12,434, the remainder 2743, and the dividpnrl
thel ■c;:"M"':f Voo^an'd ^M"' ''• ''• ^- ''■ '""'• ''' ■ -"•
of a .idereal day <''-'"«^" "'"'we.,, u,„ t„„ to the decimal
64
AKITIIMETIOAL PKOBLEMS.
Simplify :
(1).
(2).
^ of a guinea — ,-. of a £.
8s. lOi'd.
5. A grain dealer bought G4 l)ag3 of oats, weighing (including
bags) 3,GU) pounds. The bags averaged 1 pound 12 ouTices each.
The dealer paid 34 cents a bushel for the oats and sold them at
42^ cents a bushel. How much was his gain ?
6. A plate of metal h inch thick was burnished on one side for
lis. 6id, at 2|d per square inch Find the weight of the plate, sup-
posinga cubic foot of the metal to weigh G2i pounds.
7. A, B and C do a work in 12 hours ; A and B can do it in 16
hours, and A and C in 18 hours. In what time can each do it
separately ?
8. An army, in its first engagement, lost 1 in 10 in killed and
wounded, and in its second engagement 3 in 25 of the remainder ;
there ware then 3,000 men left. How many men went into the
first engagement ?
9. Find the duty on 8 hogsheads of sugar, each weighing 1,200
pounds gross, at 1§ cents per pound, 16% being allowed for tare.
10. (1) Find the interest on 8225.40 for 16 months at 8% per
annum.
(2) The amount of a certain principal was $307.20 for 3^ years,
and $312 for 3| years. Find the principal and the rate.
December, 1881^.
1 Of what number is 8,967 both ilivisor and dividend ?
2. Find the greatest number that will divide 11,067 and35,602 ;
leaving as remainders respectively 17 and 21.
3. Find the amount of the following bill : — 12^ yards cassimere
at $2.75 per yard ; 18,^ yards silk at $1.17 ; 23| "yards flannel at
37^ cents ; 112 yards print at 9|\ cents ; 56 yards shirting at 17^
cents ; 37^ yards tweed at $1.12.
4. Simplify :
(a)5i + 2i^ll|x7i +
$18.64
$1.16i^
(b) <; I X i\ X 0-02 X 0.456 )■ -^|f of |.
8ENI0K CLASSES.
65
6. A boy can do a piece of work in 42 flava o»,;i
Hllt-^fh'^"^ f^ simple interest ca $275.60 from 18th July 1883
till 13th September, 1884, at 0% per annum. ^' '
9. At what time are the hands of a clock exacMv 9 m,-r,.,^
spaces apart between 4 and 5 o'clock ? exactly 2 minute
June, 1885
CLXXXr'' '" ^'''^' =-i708%53-006904, $705-637 and MDCC
2. Simplify :_j7(3| + 9X3)^ 4 ^f &1^5jd^
^ '"* 10s, 2d.
3. Find the value of 17 -654 + 4 -835 + 6 -408.
4. Make out a bill of the following cronrlo ■ 9Q , j
iJ^Tard^L^eratlS^l^lff^^
cloth at I4 50. ^^^^•^^' 12^ yards serge at$1.75; fi^yardsbroad-
5. A merchant purchases sugar at 17. 50 per hundrpdwpml.f. „f
what price per pound must he sell it in order^?o gaTn 10 % ?
perti' *'" "™P'^ '"'^^^^"^ °" ^^«7 f- 3 y--. 9 months, at 7%
intlesu''^'' '™' """^ '"^ '""^ °^ '"''"^y '^''"bl^ ifc««". «*t 6% simpk
8 f 1,200 is to be divided between two nersonn A an,! Ti o^ *■!, *
A'B share is to B's share, as 2 to 7. Find tfe shSe ofeach " ^'^'^
y. At what two times between 3 and 4 o'clock arp tli« hn«,q= r.t
watch equally distant from the figure 111*''''^°^'' "^ the hands of a
^.}^- ,\,"^«" ^'^^ing ^720 spends a part of it. and affc^nwoH-
mTch did L^'eUV"""' " '^ 'P^"' ' '^^ '•^^^ had $1,305." "How
56
ARITHMETICAL IMIOHLKMS.
December, 1.885.
1. Define the following terms :— Factor, Prime number, Multi-
plication. Write down all the prime factors of 2,310.
2. (a) Reduce to simplest form : — v'/fJrt^-
(b) What is the loast number from which 1,224 and 1,G56 may
each be taken an exact number of times 1
3. A man who lost ^ of his fortune in i ae year, and if of the
remainder the next year, had $900 left. Find the amount of his
fortune at first.
4. What quantity taken from 169} will make it exactly divisible
by 12f 1
5. Express 3 '74976 minutes as the decimal of a week.
6. What will 11,750 feet of lumber cost at $27.50 per thousand ?
7. Name the units of length, time, and sterling money.
8. Find the simple interest on $800 for 3 years at 5|%.
9. A cistern has three pipes ; the first will till it in 10 hours, the
second in 12 hours, and the third in 15 hours. In what time will
they together fill the cistern ? ^
July, 1886.
1. (a) Multiply the sum of forty-eight thousand, six hundred and
thirty-nine, and thirty-nine thousand five hundred and thirty-seven
by their difference and divide the product by sixty-four.
(b) The product of four numbers is 827 658,432 ; the first
number is 12, the product of the second and third is 144. Find the
fourth.
2. Make out a bill of the following articles : —
28| yards flannel, at 68 cents ;
36 yards calico, at 15 cents ;
3| dozen pairs of stockings, at $2.10 ;
7 pairs of gloves, at 90 cents ;
12i yards linen, at $1.12 ;
4 pairs of muslin curtains, at $4.20,
3. What will it cost to fence a lot 49 feet front and 180 feet
depth at $1.15 a foot?
4. (a) A horse worth $170 and 3 cows worth $36 each were
exchanged for 14 calves and $82. Fnd the value of a calf.
SENIOR CLASSES.
57
• \'/l^'^ ^^?^ '^*" "^^ ^ *^®''^'^'" piece of work in 20 days • after wort
December, 1886.
corL^^i^^^"^^^ '^^ «"'* ^^^ "'-y t™es the result is
an/'o^s''"^' '^^ P'"'^"°' "^' "^^^ ^"^ "^25 by the sum of -9. -02
acre^a ?^^ ^ '"'"'^ '' ^ '°'*' ''^^'' ^"^ ^^^^ "^^^«« "^ ^^ will make 10
.^J\^ ^".'/^^ H^^. ^'"?^ ^""^ ^^ fee* wide to be surrounded bv .
5. A farmer bought a number of horses and cows for #2 000
There were three times as many cows as horses, and a horse cos^
twice as much as a cow. If each horao o^at &a(\\ ..
he buy ? * ""^w many cows did
Tf I,!' ^ "^^"|}a« a salary of $400 a year and has $500 in the bank
If he spends $500 ayear, in what time will his mLey be allgone ?
annum ^ ^"'°""' *^ ^" ^ ^^^^^^ 219 days at 7^% per
8 A man borrows $900, for the use of w.uch he has to nav «^ a
price ^'Stjivl'^redlo",*'-""-^^
58
ARITHMETICAL PKOBLKMS
10. How can you tell, without actualdiviHion, whether a number
can be divided by 9 without leaving a remainder?
11. If a cow gives 12 quarts 1 i)int of milk every day, and 1 pound
8 ounces of butter can be made from 25 (juarfa of milk, how many
pounds of butter can be made in one week from the milk of 16 cows /
12. A man bought a quantity cf tea supposed to be done np Iri
packages of 1 pound each, for which In- '.<. m to jiay $G4 ; on weiyliing
them, however, it was found that each package was 1 ounce too light
How much should he pay for the tea ?
Jidy, 1887.
1. What multiple of 695 divided by 595 gives as quotient 595 ?
2. Find the least common multiple of $2, $3, $4, $5, $10, $20,
$50 and $100.
3. A man owns f of f of -J^ of an investment , on selling ^ of his
share he finds himself worth $100 less than before. What is the value
of the whole investment i
4
4. Change i^gOf^ +
3 + J
to a simple fraction.
in 5 years at 4J% ?
6. What principal will amount to I
6. If 1 pound of thread makes 3 yards of linen 1| yards
wide, how many pounds would make 45 yards of linen 1 yard wide <
7. A man sold two farms for $3,000 each ; on one he gained 20%
and on the other he lost 20%. Did he gain or lose on the whole, and
how much ?
8. If a garrison of 1,000 men have provisions for 12 months,how
long will the provisions last if at the end of 2 moiiths they be rein-
forced by 500 men ?
9. A merchant sold a piece of cloth for $24 and thereby lost
25%. What per cent, would have been the gain had he sold it for
$34?
December, 1887.
1. Ten cents will buy 3 oranges, 4 lemons or 5 apples. How
many apples are worth as much as 5 dozen oranges and 7 dozen
lemons ?
2. A man can run 100 yards in 10 seconds. How many miles
will a steamboi^t go in 5^ days at the same rat« i
SENIOR tlLAHHEH.
59
3. Find the interest on ifloO from the 10th of July to tlie !»th of
Uecember, at 5% per annum.
4 A person borrows money for fi years at 3A%, and repays at
ho end of tlie tune as pruicipal and interest, $847. How much did
no borrow /
many
5. A map is drawn to the scale of * an inch tt) a mile. How
acres are represented by a scjuare inch on the map.
nn fi ^"|.,TnH."""' *','''''°^^ ^^-^^ f*^"" * day's work of 8 hours, and
another |.} 50 for a day s work of 9 hours. Which had I better
I'Miph.y, and how much shall I have to pay him for work that he
Clin do in a fortnight, working hours a day ?
■'^l Tllno '" freezing expands lOX. If a cubic foot of water
weighs 1,000 ounces, lind the weight of a cubic foot of ice.
8. A merchant bought 1,000 yards of carpet at 60 cents a yard
and sold g of It at a profit of 30%, one-half at a profit of 207, and
the rest at a loss of 20%. How much did he receive for the carpet ?
o f^'u'^J^f^ ^{ ^'■^",'^ '^ surrounded by a stone wall 8 feet higli and
J feet thick : the land inside the wall ia 100 feet long and 50 feet
wide How many cubic feet of stone d.^es the wall contain ?
10. A house and lot are together worth $2,100 ; J of the value of
the house 13 equal to J of the value of the lot. Find the value of
each.
•iV-\ t^J'^hl^} ^t!^""^''. }^ ^ f^®* ^^^P- How many gallons of water
will It hold if 277,274 cubic inches make a gallon i
July, 1888.
1. Prove the rules for division (1) of vulgar fractions, (2) of
decimals, using as examples f -^ f and '012 -f- -6.
2 A produce merchant exchanged 485 bushels of oats at 50? cents
per bushel, and 13^ barrels of ai)ples at $3. 85 a barrel for butter at
37^ cents a pound. How many i)ounds of butter did he receive ?
. ■ ^* A*oA'"^?^"^ ^^ ""'^^^ ^"^ ''""'■ »*»''t8 at 1 o'clock p.m. on a
trip of 280 miles ; another going 37 miles an hour starts for the
same place at 12 minutes past four o'clock p.m. ; when and where
will the former be overtaken ?
4 If in a certain town $3,09.3.75 was raised from a 17 tax
what was the value of the property in the town ? » <> »
5. By selling my cloth at $1.26 a vard T aain 11 cent° "lore «-han
Hose by selling it at $1.05 a yard. What would "l gain by selling 800
yards at $1.40 a yard ? => ^ &
60
vuithmktu;al imjohlkms.
6. How iiiftiiy thuUHfiiul Hhiiiglos 18 iiiuhus loiij,' hiuI 4 iiK^lics
wi(; , lyirif? .\ to the wciitlu r, (iro re(|uiri;cl to Bliiii<^le tho loof of a
building "4 foet long, with rafters 22 foot long, the first row of
shingles being douhlo?
7 A farmer eniployB a number of men and 8 boys ; he pays the
boys $ .(55 and tho men $1.10 i)er day. Tlie amount tliat ho paid
to all was as much as if each had received $.92 per day ; how many
men wore employed?
8. A field whoso length is to its width as 4 to 3, contains 2
acres, 2 roods, 32 rods ; what are its dimeasion.s ^
9. A man havinir lost 20' of his capital is worth exactly an much
as another who has just gained 15/ on his capital ; the cond
man's capital was originally $»9,000. What was tho lirat man's
capital ?
December, 1888.
1. Write down neatly the following statement of six weeks' cash
receipts ; add the amounts v-rtically and horizcmtally, and prove
the correctness of the work by adding your results: —
MON.
Ties.
«31.47
30.05
29.70
32.73
31.19
2G.07
Wed,
.S33.35
28 39
29.98
31.80
27.36
24.09
Tiuni.
Fri.
Sat.
TOTAU
Isb
2nd
$29.87
27.38
19.90
23.19
17.84
12.09
$35.00
34.83
30 10
37.91
35.55
31.87
.i<2G.10
27.07
25.49
27. 8 J
28.10
29.15
$48.17
49.99
3rd
47.30
60.00
63.94
4th
6th
()th
57.77
Totals.
2. If you buy 3 pimnds of butter at 28 cents a pound, 5 pounds
of tea at 50 cents a pound, 6 bars of soap at 17 cents a bar, 12 gal-
lons of oil at 27 cents a gallon, and 3 oranges at 40 cents a dozen,
and the merchant throws off 10 cents for each dollar's worth pur-
chased ; how much change would you get out of a $10 bill ?
3. Divide $82.00 among 27 men and 37 boys, so that each man
may have three times as much as each boy.
4. Find the interest on $387.56 from March 18th to Novem.ber
19th at 6% per annum.
SKNIOIl CLASNEH.
61
6. A bushel of potatoes weighs «iO poiuuls If -i „r„on,. i .,.
ton of potatoes for .*15 nud sdls tJ.om fo 15 centVu Sek f '
much per cent, will ho g,i,„ { *^"" '^ I'"*-"*' ""w
KrouncMOftT f/'"'' ^"Vl,a?1 '"'^ ^^'"'^ ^'<i« « built on a plot of
grounct 308 foot lon-r ,i„,l 204 feet wide. 'J'ho rest of th« , W
much w, I *J HH, „„„,„„t i„ j„ t|,,„„ „ „.,,^ ^j ,1^^ J^^;^^ _^^.^ Mo»-
J«?J/, 18f!9.
1. A bushel of wheat weighs «!0 nounds ind n Kn....„T * ^
..SZpcrit,;,'""'''""'"^'"-'*"''"''^-"' =* ■""""■•. 12 .lays
4. The circumference of a wheel is >" of its di-mmt,... . <;. i n
dun>eter of a wagon wheel which n.kes^ 300 r:vlSi^n gig ^
for q vti^'"""' T''!"'' P^pi'l'-ition was 10,000, increased 10% everv year
for 3 years ; what was its population at the end of that period ?^
6. The map of Ontario recently issued by the Crown T md*
Depavt.nent is drawn on a scale of 8 miles to an inch. ( '?his ma,
the township of Scott measures 1 ^, inches in length and U in wid S^
how many acres does it contain ? ^ ^ ^^'^ '
7. If for $7 I can have the use nt $35 for 3 years 4 monfh-
how much a month shall 1 have to pay L the use S S'tSoT '
8 It 18 required to build a sidewalk a (juarter of a mile in lenL'th
V::^^^t:^.:^^^^^^^-^Vovt.a \ 3 continuous'ViS'of
thousand flet ? ' '''' ' "^"'^ ^"'^ '^" ^"•"^«'- «^'«^ ^* ^^^ per
62
ARITHMETICAL PROBLEMS
9, Write down neatly the following statement of six weeks' cash
receipts ; add the amounts vertically and horizontally, and prove
the correctness of the work by adding your results :—
Mox.
TUES.
Wkd.
Turn.
Ist
$28.79
$34.71135.33
$30.10
2nd
23.87
30.03 29.38
33.84
3rd
1G.99
27.09
28.77
30.16
4th
29.13
33.72
30.81
39.17
5th
18.47
32.29
2G.73
34.45
6th
19.02
27.06
29.04
29.89
Totals.
Fri.
$27.97
26.77
24 95
28.47
28.88
29.51
Sat.
$47.81
48.77
43.07
50 05
54,39
61.93
TOTAL.
December, 1SS9.
1. A fruit merchant bought a quantity of apples for $144 ; he
sold half of them for $82.80, thereby gaining 12 cents a bushel on
what he sold. What did the apples cost him per bushel ?
2. Find the interest on $84.25 from April 16, 1888, to Novem-
ber 4, 1889 at 7% per annum, (year =365 days).
3. A pint contains 9,000 grainu of barley and each grain is J of
an inch long. How far would the grains in 17 bushels, 3 pecks, 1
gallon, 1 quart, 1 pint, reach if placed one after another ?
4. An orchard is 24| rods long, and 15^ rods wide. At If cents
per cubic foot what will it cost to dig a ditch around it 3 feet 9
inches wide and 4 feet deep ?
5. A sold a town lot to B and gained 12^% . B sold it to C for
$306 and lost 15%. How much did the lot cost A ?
6. In a room 26 feet, 6 inches long, 16 feet, 8 inches wide, and
12 feet, 3 inches high, there are 3 windows each 5^ feet high and 3
feet wide, and two doors each 7 feet high and 3^ feet wide. The
baseboard is 9 inches wide. How much paper, | of a yard wide, will
be required to cover the walls and ceiling ?
7. A farmer sells to a merchant 3,015 pounds of hay at $16 a ton,
and takes in payment 6 pounds of tea at 80 cents a pound ; 22^
pounds of coffee at 26 cents a pound ; 33 pounds of sugar at 12
pounds for a dollar ; 32| pounds of raisins at 18f cents a pound ; 14
pounds, 13 ounces f bacon at 16 centB a pound ; and the balance
in cash. How much cash does tho farmer receive ?
SENIOR CLASSES.
63
my farm is uncleared ? ""ciearea bush. What per cenu of
rece^iL^nHH f^" ^''' following statement of six weeks' cash
receipts , add the amounts vertically and hormmtJlJ^T a
the correctness of the work by adding y "ur resets :-^' "^ P'"""
Alofj. TuES. I Wkd.
1st
2nd
3rd
4th
5th
6th
Totals.
$95.05^89.24 359.79
Tfll'R.
71.58
58.47
G9.29
45.81
63.42
65.41
57.99
80.07
93.56
77.68
67.24
50. (iO
91.87
82.54
79.18,
$78.04
62.49
71.08
93.74
57.90
80.00
Fri.
Sat.
$59 37198.16
67.02| 51.42
82.91
03.36
72.12)
87.31
76.89
90,21
67.96
82.75
TOTAL.
July, 1S90.
recJiptr;id^drhramitt:traV^^
correctness of the work by adding your resuUs"^ ^ ^'""^ ^^^
Ist
2nd
3rd
4th
5th
6th
$65.95l$24.89
Total
58.71
47.58i
29.09
8145
42.63
41.05
99 57
70.80
50.93
68.77
$79.79|$40.78
24.671 94 26
50.00
87.91
54 82
81.79
80.71
74.93
96.57
60 80
$37.59
70 20
91.82
30.03
12.72
31.87
TOTAL.
$89.61
42.51
89.76
21.90
90.67
76.82,
J^o marks vnU be allowed for this quest
correctly done.
wt,, Unless all the Work is
64
ARITHMETICAL PROULEMS.
I;
2. A boy's age now is } of his father's. In (5 years it will be ^
his father's present age. How old is he ?
3. Some Atlantic liners consume 200 tons of coal per day. They
average 8 days out and 8 back. In case of accidents they carry a
supply for four days extra. How many cubic yards of the hold of
such a steamer will be occupied with coal for her round trip if each
ton is 33 cubic feet ?
4. In a factory 12 men, 16 women and 30 boys are employed.
At the end of a week they receive $330. A man is paid as much
as two women, and a woman as much as three boys. What is the
share of each ?
5. A farmer whose property is assessed at '$9,600, pays on the
dollar, 13 mills for township rates ; 1^ for county rates ; 1^ for
railway bonus ; and 2^ for school rate. How much does he pav in
all ? ^ ^
6. On June 29, 1890, I borrow $16.50 to be returned April
30, 1892. With interest at 6^ per cent, what amount must I
then pay ?
7. In what time would a field 80 by 60 rods, pay for underdrain-
ing lengthwise at 2 cents per foot, if the field yield 2 bushels, at 66
cents per acre more than before draining ? The drains are 4 rods
apart and the first drain runs down the centre of the field,
8. If 18 men do ^ cf a piece of work in 30 days of 10 hours, in
what time should 15 men do the whole, working 9 hours a day ?
9. Two men start from the same point at the same time to walk
in the same direction around a block of land IJ mile on each side.
A goes at the rate of 4 miles and B 3 miles an hour. How far will
A walk before he overtakes B ?
will be s
ANSWEKS.
65
ay. They
3y carry a
le hold of
■ip if each
employed.
as much
lat ia the
ANSWERS.
ya on the
8 ; 1^ for
he pay in
led April
)t must I
iderdrain-
els, at 66
re 4 rods
hours, in
day?
5 to walk
ach side.
' far will
Exercise 1.
1. $5.40.
2. $2.40.
3. 2/j days.
4. 3^1 days.
1. -T of a day.
2. 3^3 hours.
3. 'i oi a, day.
4. 60.
1. $434.
2. $146.25.
3. 43| cents.
4. ttpO.
6. 36 days.
«. 16rVo days.
7. 21/1 days.
8. 3# days.
5.
6.
7.
Exercise 2.
58 yards.
337 days.
A 60 cents, B 36
cents, C 12 cents.
Exercise 3.
•'5. 8%.
6. $1,000.
7. 8 years,
8. $.50.
9. a/ydays.
10 23^ days.
8. $2.40.
9- 23^f.
10. ]5if.
9. 12^ years.
10. 10%.
1. 5 years.
2. $2.00.
3. 31st July.
4. 319 days.
Exercise 4.
5. 5%.
7. »4.12.
^' 6J cents.
9. 6%.
10. 11%.
«9.00.
$2.00.
«.<) 00
30%. '
6
Exercise 5.
5. 12'/.
2- io?n.
V. lu/;.
8. »6,400.
9. $7.50.
\0. 14? oz.
66
ARITHMETICAL PliOBLEMS,
1. WrA gain.
2. 47j'V cents.
3. $20.25.
4. $55.
Exercise 6.
5. 33J%.
6. mx.
7. 6i% loss.
8. 28%.
9. $150.
10. $10.50.
1. 165.
2. 264 seconds,
3. $11.52.
1. $36.46i.
1. 100.
2. $60.
8. 20.
4. 0.
1. 35.
2. 210.
3. 10 lbs.
4. $30.
Exercise 7.
6. tV of a clay. 8. A, $360; B, $260;
6. (1) $12.50 loss, (2) C, $220
4% lose. 9. 480.
7. 40%. 10. 3j^ days.
Exercise 8.
6 58 turkeys, 42 geese. 8. 25.
6. A 5,\ cents, B4if 9. 41i''r and 56^^ af-
cents. ter 9 o'clock.
7. 2i days. 10. $91.20.
Exercise 9.
6. A 30}^ ac , B 43|,
ac, C 50{^ ac.
6. $40.
7. 21^r after 4 o'clock.
8. $203, $29.
9. 11,45 a.m.
10. 15%.
Exercise 10.
1. 220.
5. $39.37i.
9. $84.75.
2. $3,080.
6. 41.
10. 6^*8^.
3. 315 rods.
7. 129i hours.
4. IQoi'jj acres.
8. 33 times.
Exercise 11.
1. 2^\ days.
5. 11 7f cents.
9. SrVr hours.
. 2. $256,960.
6. 29,\i^ bushels
10 $3,000, $600.
3. 26 ft., .S4J in.
7= 146.7S0 minutes.
4. 840 grains.
8. 7^ days.
- -
1. i
2. 4
3. «
4. 1
1. $
2. 9i
3. ■!■
4. $;
ANSWERS.
67
1. $40,000.
2. 154.
3. 87,500.
4. $69.38 J.
Exercise 12.
5. $2.16 + .
6. 200,563.
7. 8A? yards.
8. 44,000 feet.
9. 473.
10. $4,787.23 + .
1. 476.
2. 81 gallons.
3. 1.346f.
4. $3.85.
Exercise 13.
5. 13,840.
6. $90.78.
7. 270 times.
8. 800.
9. $16,200.
10. 77ifJ.
1. $60,000.
2. 102.
3. 1 44,451 U^i acres.
4. 10,208 yards.
Exercise 14.
5. 15/j.
6. 50i%
8- 5,413+ bricks.
9. 400 barrels.
10. $2,000, $1,500,
$1,200, $1,300.
1. $131,25, r6.25.
2. 4-80.
3. 34§ cubic inches.
4. 14 days.
Exercise 15.
6. i^ hour, 3rV miles. 8. $80.
o- TsJ!Tw inches. 9, ©45
7. $1.219.58S, 10 14 7SQ
$609.79f. ^'^^^•
1. $12.80.
2. 40H miles.
3. $5,040.
4. Hi feet
Exercise 16.
a. 3J feet.
6. $18.02, $15,018.
$12.01J.
7. $4,750.
8 $10.50.
9. $520,
10 450 J 250.
». $36,000.
2. 90 cents, 65 cent.s.
3. -10 acres, $(j.
4. $3.36.
Exorcise 17.
6. 12.
7 52S.
I ft 710/
8 The pair worth $3. 50.
68
ARITHMETICAL I'HOBLEMS.
1 . $5 gain per cwt.
3. 52 yards, 1 foot.
4. 51 f minutes.
Exeruse 18.
6. 4 days.
6. .Sl.i/.
7. 280.
8. 90; 24.
9. Tjtlbs.
10. $7.36.
Exercise £9.
>.38.V
1. \45, B90. ,'-,. $1
2. «!5(H», $1,500, »2,(HX), 6. 40 .
3. Hf inohes. 7. Sm. 54i,
4. s*?] 59.681. f '2 men.
•10.
Eixc rcise 20.
9. 98 yards.
10. S^eet.
1
1. 276.
2. $36, $60, $57.60,
3. $34/^ loss.
4. $481.'68.
5. $2,98iH.
6. ,V.
7. 4, 8, 12.
8. 77f oranges
Exercise 21.
9. HtVi. 15
10. $8.51 iV,.
1. 4,547.
5. $.S0..S0.
9. $12.50
2. $210.65
6. 2,000.
10. 5i.
■i. 14 hrs., 46 min.
7. 4 cents.
4. 48 lbs.
8. 8 hours.
1. -
3. .
4. 5
1. 454 J J times.
2. 100 acres.
3. 206A lbs.
4. ■/*.
Exercise 22.
5.
56 feet, 84 feet. 8
6,
120. 9.
7.
34', 271^3" past 6 10.
o'clock p.m.
37 g square yards.
13|^J minutes.
$520.
Exercise 23.
1. $1,018.
2. 2 feet, 9 inches.
3. 10', 16iii".
4. m.
5. $33.35.
6. 2 days.
7. 75 cents,
8. S-3.60.
9. .$90.
10. 52 J cents.
AXSWEltS.
C>0
1. 25%.
2. 1,900.
3 IB days.
^ $213.39i'j.
Exercise 24.
5. $500.
7. 300, 180.
8. 9 tons.
9. $125.
10. $4 ; $2.66§ ; $l.3^.
1. $5.
2. 18%.
3. 11 hrs., 53^ J min.
4. 30 days.
Exercise 25.
-^- 11 hrs., 38 mill,
tj. 20 minutes.
7. 3,420 steps.
8. $5,606.75.
9. 26 yards, 2 feet.
10, $21,663.
I 48 minutes,
2. $2.10.
3. A .S5 cts., B6 cts,
4. 24,000.
Exercise 26.
5. 18 feet.
6. 252.
7. $1.3.3.
8.
633f lbs.
9. 39 ; 21.
10. 56 feet.
1. $3,907.02,
2. $46.08.
3. 314.
4. $30.
Exercise 27.
5. $210.
6. 12 days.
7. 5 hours, 48 min.
8. $160.87i.
9. 22 miles.
10. $375,
1. 8Mf days.
2. 5j»f' past 1 o'clock.
3. 325 yards.
4. $30.
Exercise 28.
6. 31,2.39.
6. 7,283.
7. $21,000.
8. 68 cents. 34 cents.
9 1,320; $34.
10. 1 mill., 1*^ sees.
1. 7,724; 1,926.
2. $32.
3. $12.75 a year.
4. 203.
Exercise 29.
5. 70,560.
6. 60.
7. Ship .$24,000, cargo
$36,000.
8. I?.
9. A $4,334, B $1,474.
C $3,080.
10. 13i bushels.
70
AKITIIMETK'AL PliOHLKMS.
w-
1. $3.00.
2. 12HcordB.
3. $38.84$.
4. 9 men.
1. 1,980 pickets.
2. ail8.80.
3. 20| miles.
4. 28 mills.
1. $81.25.
2. 12 horses, 36 cattle,
144 sheep.
3. 2,310 feet.
Exercise 30.
6. 23,805.
6. $81. 3U.
7. $47.
8. 11,280 feet.
Exercise 31.
5. 880 yards.
6. 70 fields.
7. $1,267.20.
8. $64.
Exercise 32.
4. $112.06.
5. 50 feet.
6. 816 bricks.
7. $8,225 ; $10,525.
9. 18 feet.
IC. $180.
9. $508.50.
10. $1.25.
8. $47.75.
9. 165 acres.
10. 18 miles, 7 furlonga,
13^ rods.
1. 78 posts.
2. 1,980.
3. ,p8.25.
4. »29.55t.
1 -A^
2. 1,210 feet.
3. 1,061.
4. 7,841 rods.
Exercise 33.
5. 21 J hours.
6. 236.
7. 3,689,243.
8. 60 miles.
Exercise 34.
5. 54.
6. 53 cents.
7. $800.
8. $5.25.
Exercise 35.
I- ?P6. 4. $5.25.
-. 150 yards. 5. $81.60.
A 1 gold coin = 5 silver 6. $2,010.75.
coins. 7. 819.80.
9. 2 hours, 54 minutes,
47 i seconds.
10. 43,520.
9. 2 seconds.
10. 15 miles.
8. Quotient 2,230;
remainder 196.
9. 76.
10. 60 eggs.
2
3
4
1.
2.
ANSWERS.
71
1. 700 feet.
2. 4i hours with the
stream, 7i hours
against.
Exercise 36.
3. Quot. 4.S8 ; rem. 470.
4. ] J miles.
5. 33.
6. 4 miles.
7. HI.
8. $145.52.
9. 294.
10. 40 gallons.
1. 28 miles.
2. 28 gallons.
3. 125.
4. $51.06.
Exercise 37.
6. 1 4 apples.
6. 1,386 pickets.
7. $534.
8. 4 days.
9. 80 lbs. ; ICO lbs.
10. 9 and 8.
furlongs,
1. 288 time «.
2. 2 o'clock,
a. $12.35A.
$65.
4.
Exercise 38.
5. 7%.
6. 32 feet.
7. $34.20.
8. $418.33J.
9.
10.
$31.31iV.
1,600.
minutes,
tds.
1.
2.
3.
4.
6.
4 minutes .
120 yards.
2,097 lbs.
1,619.
2i miles.
Exercise 39.
6. 28-28 mis. to the in.
7. »6.17i
8. B walks a mile in
13i minutes; ||
of a mile.
9. A 88 cents ; B 49J
10.
cents.
13i years.
1. 3 hours, 3 minutes,
36 seconds.
2. 42iV days.
3. 64 days.
4. 5^j hours.
Exercise 40.
5. »42.
6. 15 times.
7. 27,648.
8. 39i| yards.
9. Ij'j hours after de-
parture last train ;
49rV miles from L.
10. 6r*jdays.
230;
■ 196.
32 men.
22^ giU. water; IJ
wine; 10^ gals.
wine ; 1 J water.
Exercise 41.
3. $44; $ 5; $22.
4 $440.
•^ ;00 ; 402.
•> 3il ,045.44.
7. 4 min., 47 sec.
8. 42 miles.
9. 45 minutes.
10. 16§ miles.
72
ARITHMFTIOAL PPORLEMS.
i
1- 114 days.
2. A, «656 ; B, ?287.
* o min., 30 sec.
4. 26fdays.
1. 76,250.
5J. $2,715.
3. $15.
4. 30mmuteB,
1. 500 barrels.
2. 13 cents.
3. $3,553. 12i.
4. 81.56.
1. $400 loss.
2. 21-216.
3. $210.
4. 120 yds.; 83 J cents.
Exercise 42.
5. 45 miles.
«; $100.80.
7. r.o lbs.
8- $10,093.76.
Exercise 43.
6. 12 days.
6. $8,050.
7. 36|^ miles per hour.
8. 9 miles, IK) yards.
Exercise 44.
9. 80 feet ; 6.3 feet.
10. 20i yds. by 41 yds.
9.
10.
2 acres, 3 roods, 36
perches, 1 yard.
4f miles per hour.
750 tons.
i„ c 1 r. ^ 88 yards.
- in 8 hours ; 26 miles P. $36 50
7. 9daTs.'*"'' ''' ^«^"lb«-
Exercise 45.
5. 120 yds.; 83 J cents.
o. 3J days.
7. 18 cents; 9 cents.
8. 494.
9. 1S%.
10. $81.27.
1. $3.93|.
2. 8 lbs. coflfee to 25
lbs. chicory.
3. 18 feet
E> .ciae :6,
4. 28J yards.
S- 19i«i^'5 cen':?,
6. 13fcer..,.
7. 14 gallons.
8.
9.
10.
II of a day.
75 cents.
25 : 641 ; 16.
1. 80 feet.
2. $9.24.
3. 17f I? minutes to 12
Saturday night
Exercise 47.
4. 450 miles. ,_ « ^
5' 2ifir days. i
5: .?.■£.»• ^'^^•^•■''■'-'^"S hour.
ANSWERS.
73
Exercise 48.
1. 36.
2. 57J rods.
3. 120 sheep.
4- rii7 of an inch.
1. 80 cents.
2. 880 yards.
3. 48 yards.
4. 12inUe«.
5. 84f cents.
6- 20 gallons.
7. 14 oz.
Exercise 49.
«. 4 hours, 48 minutes.
D. db yards.
7- 27i yards.
o. 1'2 days.
9.
10.
4 yards; 4-97 yards
^oi'ld make theii-
ch/inces equal.
60 cents; 20 cents.
fl.32.
9. 23f%.
10. 15iJ ounces.
1. ?29.
2. ».: cents.
4. 3G ..reU.
Exercise 50.
5 8 cents a vard.
6. 90 yards. '
7. i
8. »870 ; $840 ; $290.
9. ?4.50.
10. 6 boys.
1. $325.
3. 630 acres.
^- «1-21AV.
Exercise 51,
5- m yards. o -„. „,„
6. 80H cents. y" P^^^L
7. \.81 87'i' R «o .iTc ,^' «">a'ihour.
CA
i 150 gallons.
^- $28,350.
3- «5.06i.
4. 16 years.
Exercise 52.
5. $10,000 ; $4,000.
o. 5 hours.
7. 150 feet.
8. $506.88.
,9- 22J days.
iO. lOifeet.
1. $16,800.
2. 300 barrels.
3. 6| ,
*• 7i acres.
Exercise 53.
5. 4 feet.
6. 30 minutes.
/. |4.0o.
8. 15 years.
l^^^^fSi^pP'^
74
ARITHMETICAL PROBLEMS.
Exercise 54.
1. 62i cents.
2. ^ mile an hour.
3. 150 ; 100.
4. 68t yarda.
6. 16 bushela.
6. 19} I days
8. $118,1811^.
9. $2.00.
10. $200.
Exercise 55.
1. $100.
2. m3.75.
3. $20.
4. $480 ; 6 yeara.
5. 26^ cents a pounda.
6. 9,100 H(juaie yarda.
7. 5,952 stones.
8. etona, 1,125 Iba.
9. $.'{29. 67.
10. 6ii gallont.
Exercise 66.
Ill
1. «15.60.
2. $12.25.
3. 8i\ minutea
1 o'clock.
1 . 4^ of an inch.
'2. lOlji-jlba.
3. $9,600.
4.
8. 132treea.
10. $215.
4. 6JJ houra.
5. $15.
after 6. 2,528.
7. $1,666§.
Exercise 57.
5. 60 cents. 9. 1^%.
6. A, 20 cts. ; B, 5 eta. 10. 30 rods.
7. $150.
8. $210.
I
2
3
1. $387.60.
2. $9.80
3. $3,062.50.
4. $174.83.
Exercise 58.
5. $23.65.
6. $235.
7. Four milla on the $.
8. $109.44.
9.
10.
112 yards.
8 double-rolls.
1.
2.
3.
1. 1J%.
2. 4%.
3. 12 yards.
4. $6.30.
Exercise 59.
5. J of a day.
6. $4.96; $2.18.
7. 50cent8 ; 20 cents.
8.
9.
10.
4 days.
$2,400.
1.
2.
ANSWERS.
75
Exeroise 60.
1. 94 50. 4 j„7sp
i- E^f: ^ 6. $4.68f
3. 36 lbs. tea ; 20 lbs. 6 *
«"«"• 7. 686,Uton..
8. 42 cents.
9. 625.
10. f 1,618.
Is.
ADMISSION TO HIGH SCHOOLS.
July, 1880.
1. Book-work 4, 104.448 bricks
2. Book-work; 13. .5 81,1.34.34ft
3. Book-work; HS^f 3^. 6. 830,000.
10. A and B can do ]/i or I in 1 day.
AandC •' l/Hor|J •«
7. 70 dozen.
8- 43^,V miles.
9- 68f ft. and 51^ ft.
1. Book -work.
2. 9187.
3. 178 ounces nearly.
December, 1880.
4, $13,565.
6. 53,625 lbs.
7. $2,501.62-f.
J'uly, 1881.
1. Book-work; 3,162,277.
2. Bok-work; 2x2x2x2x2x
2x3x13x53; 2x2x2x2x
" ^^ ^^ ^ ^^^ ' "3. 948, 992.
3. 73.590 minutes.
6. «I-30fcJi
6. 61507-1- . »8«
7. 7.008,750 cu^o feet.
76
ARITHMETICAL PKOBLEMS.
^'l
December, 1881.
1. 351,526,239.2 +
2. 31 i.
3. i?35r).30J.
A certain mass of lead weighs
\\\ tiniea an equal bulk of
water ; tlie same mass of
platinum weighs 21 times an
equal bulk of water, .•. plati-
num is 21 ,,- ,.
-r-ri = li5 times the
weight of an equal bulk of
lead. Then a mass of platinum
the size of a mass of lead weigh-
ing 56 lbs., will weigh J J§ times
56 lbs. = 103A lbs.
5. 182s.
6. ?2.72.
7. ^\ of an inch.
8. 40.960.
9. 33i%.
June, 1882.
1. Book -work ; prime.
2. $63.16f
3. Book-work ; ^^^j.
4. Book-work.
5. 18 miles.
6. 3 inches.
7. $1,142.28.
8. 16,000 acres.
9. 3 days.
lOf 300.'
December, 1S82.
1. Book-work; 7,4851*4*.
2. $l2.60i.
49,896 ; prime.
Book work ; IJ.
Book-work.
7 acres, 1 rood, 6 perches, 21
yards, 7 feet, 20 square inches.
2U feet.
When A runs at % of his speed,
he runs 1,760 yards while B
runs 1,760 yards - 22 yards ^
3
4.
5,
6.
7.
8.
0.
10.
1,738 yards. But if ^ of his
rate=l,760 yards, his rate —
1,320 yards; for if | of it =
1,760 yards, then J ^^440 yards,
and I, or the whole=3 x 440
yard8= 1,320 yards, .•. A only
runs 1,320 yards while B runs
1,738 yards, or A'srate is to B's
as 660 is to 869.
2^11 hours.
90 cents.
June, 18SS.
1. Book-work.
2. Book -work,
3. $29,027. 84J.
4. ?319.37i.
6. 1.33i ; 100 ; 13J.
7. $3.5r,i.
8. $5.2o nearly.
9. -00421.
10. 21 iV after 4
K r. »
and SSrV' after 4.
ANSWERS.
'• Book-vork
2. $36.08.
4. r,08; $438; $254.
6. '0014863 + .
7. «14.56.
l^ecember, 188S.
8. Since it takf>n T? <; ^•
run fL 1 , " inmutea to
r n tlie wliole course, A mav
allow him] minute of ^starttn
time or ]_30 yards '"
1 = 293J
9 yard.s m distance.
iO, R81+.
I.
2.
3
4.
7,070.
149,688 ;
•00278 + .
'3a
119.
June, 188!,.
?8.76.
5,
6.
7. 28f; 36
8- 5,000.
1 J> ^ -I
IT I fig.
48.
9- $109.91}.
10. $24.04+ ; $240-
8%.
1- 80,407,089.
2. 221.
3- $I26.S0||.
December, I884.
■ (a)22[!J;
I'ii'li}'''-
7 days.
7.
25^
8. «1 9. 12 nearly.
9- 4 hours, 24 minutes.
1. Rook-work.
3. lS-;790i7927.
4. ?.SI8 39^.
5- 8.J cents!
«■ ?43.83|.
7. 16§ years.
8- !?266g ; $933i.
9- i6iVafter3;13H'after3.
June, 1885.
JO. $,20 less what he spends + 7A
30o I hen $720 together with
I .mes what hf, spends*;'
after 4.
1- 2, 3, .-5, 7, II.
2- ^^; 28,152.
3. $1,890.
4, 6f .
December, 1885.
5. 000372.
C- 1323.1 2^.
7. A yard ; a day ; a
sovereign.
«• ^132.
9' 4 hours.
78
ARITHMETICAL PROULEMS.
July, 1886.
1. l,380,505i; 478,969. 4.
2. $69.08. 6.
3. $526.70. 6.
$14 ; 30 of each.
$2,000 ; 8%.
$424 ; $364 ; $212.
7.
8. lOiJ yards.
1
December, 1886.
1.
2.
3.
4.
6.
52 times.
•0001.
1^ miles.
$37.50.
30 cows.
6.
7.
8.
5 years.
27 cents.
12i years.
1.
2.
3.
354,025.
$300.
$1,000.
1.
2.
3.
4.
205.
2,700 miles
$3.00.
$700.
9 $9.90.
10. A number is exactly divisible
by 9 if the sum of its digits
is divisible by 9 without
leaving a remainder.
11. 84 lbs.
12. $60.
JuLy, 1887.
4. \l.
5. $685.71 f
6. 12 pounds.
Decemler, 1887.
5. 2, 560 acres.
6. First man ; $27.
7. 900 ounces.
8. $720.
7. $250 loss.
8. 8S months.
9. 6i%.
9. 4,928 cubic feet.
10. $1,200 ; $900.
11. 779 01 gallons.
1
2
3,
July, 1888.
1. Book work.
2. 190^/,.
3. 10'62 p.m
miles.
246S
4. $412,500.
5. $240.
6. 14,580.
7. 12 men.
8. 24 r. by 18 r.
9. $12,937.50.
December, 1888.
1. $1,169.35.
2. $2.80.
6. $56.70 ; $25.90.
4. $15.67 + .
5. 334%.
6. 3,627 cords.
7. $17.50.
8. 307 S square yards.
ANSWERS.
79
1. 63Jf
2. «116.81f§.
3. 24 miles.
July, 1889.
4. 4Sfeet.
6. 13,310.
6. 60,800 acres.
7. $43.75.
8. 8448.80.
1. 80 cents.
2. $9.18 nearly.
3. 54HJ miles.
December, i88g.
4. $349. 71 A.
6. $320.
6. 169IJ yards.
7. $220.
July, iSgo.
2: f;ei?f • '' «SJ«' «10-60; 7. 10 years.
3. 4,i>88g cubic yards. 5. $67 20 n ^^ '^^y^'
6. $18."47V. 20 miles.