IMAGE EVALUATION
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1
2
3
12 3
4 5 6
V7J660 0V32. 9ocito ^00^00
IMiiiii UfiWi i iiw i i wymu ii , n ^
«*'4fc
fM¥ S^$ f^4 4 4^^
"j^i^P^^Wnji
V
4 It; i V
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Mb
7
KEY
TO
ELEMENTARY ARITHMETIC,
#
FOR
^1
CAITADIA.i SCHOOLS,
BT
REV. BARNARD SMITH, M.A.,
BT. PktBR's COIiLEOIl, Cambridos,
ARCHIBALD McMUROHY, M.A.,
f University College, Toronto.
TORONTO:
COPP, CLARE <fe CO., KING STREET EAST.
187 1,
6 8 3^?7 4'<3 ^'^9V67>»9
£•
— *■
Entered-icoordiiig to Act of the Parli^ent of Canada in
the ye«. One Thousand Eight Hnndred and Seven yle"
by CoPP, Clabk * Co., Toronto, in the Office of the
Minister of Agrioultare.
^%i o9S 7*.
f » / % 3 ♦'vT
i ^ T t 7 6 i-V
V
''■•4-6
KEY TO
ELEMENTARY ARITHMETIC.
i
6 + 1= 7
7 + 3= 9
Ex. vr. (p. 17.)
2
3 -f- 2 = 4
4-+-2= 6
29 boys.
A's 2
B's 6
C's 7
D'a 9
23
12 ycai*8.
If C had bought *7 more.
80 total.
17 + 19
30+ 9
Ex. VII. (p. 19.)
?9^ J^'^
- X2 ^^^52= »7 women.
-_45 83 + 07 = 129 youths.
iftrt„,«.ui 29mfante.
287
(38)
65D 1st
657 + 231= 888 2(1
2437 + 11 r. ^448 tx\x
4885 5th
0770 total.
#■
KEY.
(39)
$9080 wife's share.
$11788 two younger sons* share.
$10600 eldest son^s share.
$10800 three daughters' share.
$42068
[Elem. AniTif:
(40)
589 1st
2154-589= 804 2d
197+589 = 786 3d
589+780 = 1875 4th
3554
i
«
(21)
24916
51954
27499
87750
44720
186889
Ex. VIIL (p. 21.)
(22)
15499
6824
29620
20325 .
72268
(23)
44821
90323
19096
14669
13743
11555
194307
II
i
(14)
44 sheep.
85 cattle.
15 pigs.
6 horses.
100 animals. —
Ex. IX. (p. 22.)
(15)
623 bii. wheat.
120 " oats.
64 *' peas.
237 " potiitoes.
38 " turnips.
982 total.
(17)
25211
32050
31183
28590
23780
24088
(16)
$1650
160
575
200
600
$3185
105802
i
11
Ex. X, xi.J
$560
300
KEY.
Ex. X. (p. 35.)
11
(80)
$300
260
75
(31)
47
28
$260 wU of carriage. $ 40
(33)
49 + 65+ 19 = 133
167-133= 34
05- 34=1 31
28
47 No. of boys. 19
(33)
6 + 4 = 10
0-4= 3
10-3= 8
(34)
10 + 3 + 8 + 5 + 3 + 4
40-33 = 7.
38.
II
(33)
Ex. XI. (p. 26.)
9377- 1383= 7994 3d In.
9377+ 7994 = 17371
23257-17271= 5980
(34)
1869
1819
50 the age of the queen no2o.
1841
60
.23047
175
23222
868
22854
495
33349
133
(33)
10000
8406-
1594
704
890
7305
8195
33317
the difference is
1891 when the prince's v..x.^*ctxv;c is
1801 1S10 4«^ = t^^e q"e6n's 23317-81£5=15033.
18 Jl - 1819=73 years, the queen's age then.
07
(25)
jj - 20 = 68 Hei!ry's marbles.
08 - 35 = 140 Cliarles' mar])les..
13'
KEY.
(26)
84
135
39
88
89+58= 97
804
(27)
45-16=29
89-f- 7=36
86-10=26
26+ 2=28
28+ 4=32
82-11=21
^1217 80- 7=23
$1217-$1000=|217mdebt23- 5=18
18+ 8=26th from top.
45 - 26= 19th from bottom.
(28)
63 — 6 = 58 children. 1769
^25 ~ ?§ = iT able-bodied. 1262 - 73 = 1189 nuts.
. , (29)
1696 = 73 eggs.
70 -4 47 = 23 infirm.
6 cfficere.
(30)
117986
72268
73 + 1189 = 1262
176^-1262= 507 oranges
1189- 607= 682
(31)
45008008
87906703
4.5718
7096305
(32)
Since miunend = sum of subtrahend and remainder
.-. mm. = 56312300 + 77313 = 56289013 '
(33)
Since subtrahend = difference bet. min. and remaind.'r
.-. sub. 66304000 - 12586 = 66291414.
(34)
Gained $1 per head.
Total gain $305.
.*. Actual gain = |305 - $45
= $260.
(35)
$43054836
34717248
$8337588
Ex. xn, xiir.J
KEY
13
3 = 111;
7 = VII;
11 = XI;
9 = IX;
12 = XII;
16 = XVI ;
190 =
C51 =
1204 =
III
VIII
XV
XX
LXXXI
CXI
DCV
VII
MC
MM
DCCXLIX
3VIDCCCLXV
Ex. XII. (p. 28.)
(1)
18 = XVIII; 59 = LIX-
25 = XXV; C2 = LXII.
.2?= XXVIII; 77 = LikVlI:
37 = XXXVII; 84 = LXXXI V;
^ = }'^i 103 = cm ; •
53 = LIII; 157 = CLVII;
-f^n?i 200 = CC;
: MPniir . Z®^ = I>CLXXXIII ;
-MCCIV; 1527 = MDXXVII •
1805 = MDCCCLX V '
= three or 3; W=i^ix,6;
= ei^ht, or 8 ; XIH = ^bi^te^n. or 13 •
= fifen, or 15; XVII = seventeen, or 17-
= twenty, or 20 ; LIV = fifty-four, otH-
- eighty-one, or 81 ; * '
= one hundred and eleven, or 111 ;
= SIX hundred and five, or 605 ;
= five thousand and two, or 5002 ;
" ""^lOOOOO^ """^ ^"""^^'^ thousand, or
= two thousand, or 2000;
= seven hundred and forty-nine, or 749-
(45)
39xll=429bu.
429 X 6 = 2574 s.
(47)
11x23 = 253 cents.
jJ3x a = 297cenb.
397—253 = 44 ccms.
#■
Ex. XIII. (p. 31.)
(46)
21x12= 253 pence.
252x 3= 756. once
2j2x 7 = 1764 pence.'
252 X 12 = 3024 pence.
(48)
12x12+ 8 = 152.
8x12 + 12 = 108.
152- 108= 44.
u
.-f^.
KEY.
(49)
[ELE>r. AniTii.
1?I^^o'^.?"= 680 B's share.
9^0 "" J? "^ ^^ = ^'^^'^ ^'^ share.
Ex. XIV. (p. 83.)
(18) 1st travels 93 miles per Jav and 9ri '-a ♦;
fore, in one day he ffaing q/Ziq^'^a •, *^ " ^"^'"6-
Ex. XV. (p. 34.)
34050
1485
183150
(23)
904
803
735913
(20)
. C90
480
65300
2760
3313C0
(24)
8359
497
£13813
29331
13086
1619733
(21)
417
730
8753
1261
2919
308163
(23)
378
900
350300
(25)
15900
3300
477^
477
53470000
Ex. XV.]
KEY.
15
*
m)
50738
9706
304428
mmm
4r)oa43
492403028
(20)
C8:9(,
206.J
140645085
<32)
92035
8007
614245
736280
536J2424.5
(27)
8«370
90900
77733
77738
7851033000
'am
860^53
85344(^773
m)
84009
7898
672072
756081
672072
588068
663503082
(35)
90058
90009
810522
S10522
47«72
6120
285083
95344
47673
338860
244866673
568^$
(S049
011S92
,:&27652,
' nil - I I »| iin
844115513
<34V
678000
876000
40€8
4746
5434
593928000000
^106030522
.<36)
80108
7770
560756
560756
560756
022439100
•J
%.
7039
4709
63351
49273
28156
33J 16651
87900
9006
5274
Ml
KEY.
(37)
[Ei>EM. Akitii.
3910
350000
^.955
1173
1368500000
7008005
400703
21024015
49056035
28032020
(W)
8SP128627515
{') 973
63
2919
5838
61299
973
8
2919
3
8757
I.
C1299
(39)
J93:^
m4
808
148672 product.
(') 33000
1560
198~
165
38
33000
13
99
33
51480000
429000
5
2145000'
4
8580000
G
51480000 ^
■I.
iniTir.
■r
JjX. XVI.J
KEY
(40)
,-
1263
3
5613
2
11226
3
96732
3
67628
2
3789
2
290196
4
135256
4
7578
6
33678
9
1160784
6
. 541024
8
45468
303102
mmoi
'*f> '•■^:
17
4328102
''4
$'
i%
(1)
78689
547
550823
314756
393445
43043883
(4)
46481
936
278886
189443
418329
4350621G
Ex. XVt, (p
.)
1
19
1103S2$
13129608^ :
(5)
40980
779
86837
28651
28651
31884470
m
729817
C7o6
4^78903
^iao«5i
51087'^
491^604731^
(6)
^264397
9584
37a57588
.. 74116176 i
4632198.5
88379573
13
(7)
6707986
9878
58668488
46955553
53663488
60371434
66260991808
6835675
2689
KEY.
6078908
6725
30394540
12157816
42552356
86478448
40880656300
(11)
27088679
8709
61521075
54681400
41014050
136713110 .
18381180075
(13)
' 8523725
25BS
!38189800
10571175-^^
17018625
7047450
■1*.
8125108^^
fl4)
0778588
0867
19450116
16671528
22228704
^50072^2
8943214050 27416327790
(16)
i . 79094451
. • ' 764095
395472255
711850059
816377804
474566706
[Elea;. Arith.
(9) '
708670567
97806
4252023402
56G9364536
4960693969
6378035103
69312233476002
(12)
25058612
6289
225527508
200468896
50117224
150351672
157593610868
, (15)
79068025
1886
494408150
632544200
237204075
79068025
109588282650
, (17)
6076812
97613
■ -"* -^^ •
15230483
6076812
80460873
85537684
45091808
60-135674.536845
;* (■:
J, lij
4&d565849756
Ex. XVII.]
(18)
0507340
7071
950734
0655138
G655138
67326401140
KEY.
(19)
12481630
150a
11233467
6240815
1248163
18884779670
19
■■|: i'i
12) 800709 Divfeor^^ aivideM -^ rem'f 4- qitotient
.-. dirtsof -1^ Si!:^ B •<r 9 = 9.
66725 -S Dividend = ^^^^ x quotient + rem'r.
^.xo.o.«w •*• dividends Mxl4d+ 7 x: 1618.
11)218581 :
19871 .
(It
Cost of fowls 11 X 36 =i8#^<5ts. /- T
Selling price 396 cts:>t- 108 cts. := 694J cts.
Selling price per fbi^?ltel?.tt-i^?S4 cts.
(16)
9)214
23—7 rcm'r,
(17)
Greater Ko. = 4568 - 9 = 4554.
.-. qiioticut = 4554 -*- 9 = 500.
40687
503
JL2206^
m
11)93710562
851&143
20465501 .-. diff. = 20465561 - 8519142 = 11946419.
hf^
I
^"'^^'- [Elkm. Anrrn.
(iO)
Suppose cook'8 Hlinro t"i n'lli^ T^? '"^^^ ^0 = 48.
Housekeeper's slairo »• 4 S^ "^ ^ ^ = 4.
r^|^l = cook'8 share
▼ ui X 4 - f SS44, Iiou8ekeei)er'8 sUuix*.
007057
0000000
....^^ ^442343
(Sft)
0)5442047442342
004705271871-3
5442347442343
(22) '
. ^, 2^a~280 = 52.
• • J>o. ot oranges = 52 •+. 2 rr 20.
^ost of penholders 4x12x10- 4«a .
|g> of cjnyelopos 25 x 20 .' iSoT ''' ^^^^•
^o. of penkuivea = 500 h- 10 = a^.
«««)|g3.(34r 308)n^3,.e„' ,o.)3anr6(»oo4
j203
1024
1702
i J iT-w
1540
2125
1848
2772
2772
077
ma
i 4 O
410
ITU,
12.
Kx. xvni.J
829)058720(1087
829
8347
2061
2083
280i
2308
000)8180181(0000
. 8181
KEY.
(8)
608)8577026(7071
8342
8502
8542
500
500
di
884)542100(660
5004
4170
4170
m
f-l^) 4040820 (iMStt
888)843004(888
' 2040
8181
8181
mm
2080
2285
4470
4470
7770
:4 7064
7064
7064
(10)
805) 7848000 (3 1508 678) 3880100 (8450
730 ociiiA
730
548
805
1880
1825
ItOO
2084
3051
?713
8890
.•]8no
r37) 90626(124
727
1792
1454
888<>
3908
477
[Elem. Aritji.
22
KEY.
478)27291888(57096 ^^^^
!^ 397)30387310(76542''^^^i^f«S».5
8846 t:;;:! 46io
4588
4302
2868
2868
2597
2382
2153
1985
1^
1588
794
4218
3926
3515
~4118
3515
603
136
843) 87|24792 (103044
02)
3324
2529
Im
7587
8709
3372
3373
337^
■ ''513)90373189(175971
609)53006751-7039 ^^
4872
4286
4263
2375
1827
5481
5481
3897
3591
3063
2565
4981
4617
3648
3591
579
513
(^ontinned on next
pnoro)
m
^niTir,
(4655
Ex. XVI 1 1, j
009) 5300G751 (87039
4873 ..
KEY.
(12 continned.)
23
4380
4303
3375
1837
5481
5481
358)30073074(84003
3804
1433
1433
lp74
1074
•71
053) 630703540981 S67437310
5808
4398
3913
4842
450*
278^
2008
1774
1304
I I ..
4700
4504
1309
1304
058
053
01
*
SI
2731)510387043(190183
24028
24579
4970
2731
22394
■ 21848
5463
54G2
307«)15«m0(50801
KEY.
925$
9328
8076
8076
■^»
1^4)2015039(3007
3008
04)
7039
7038
1
[Kr.KM. Ativrn.
2185)10101255(463-^
8740
13613.
18110
6025
4870 .
6555
0555
7343)682708014(87366
57944
53358
60701
26570
21729
48411
43458
49534
43458
6076
6487)131686100(30300
13974
19461
19461
(Continued on npxt page.)
'^M. AfJITll.
>J255(4623
[0
13.
10
[)25
m
1555
(555
(87360
Ex. xviir.]
KEY.
sa
(14 continued.) .
6007) 3954946Pr5 (65880 1017) 60696184 (81853
4851
86042
85074
80035
50398
48056
28437
18031
54065
54063
2
3186
1617
5691
4851
Bm
r-6085
m4.
8284
6008) 4519559744 (903468
45072
(i5)
12359
10016
(30300
23437
20033
84054
30048
mm
. 400^
9306) 16332858 (1754
9806
m
70168
65143
mm
50365
46530
87858
87324
*
fl
12»
(Continued on next page.)
86
^^^>23ei7102000(14967000
7827
6813
15111
14S11
KEY.
(15 ccmtiuued.)
[Elim. Ap.its.
2735)2106144185(770071
9000
7895
19164
19145
11053
11063
19418
19145
1 ,
2735
2735
8^2)142997430(37810
11346
m
29587
26471
30634
30256
3782
3782
^0^«)J^gW07200(3250450
16067
. 12032
30350
30080
27072
24064
30080
8008O
#1
tContinuetr on next
Dft2?e.\
iism^
J5 (770071 ♦
Ex. XVIIT.j
KEY.
87
(16 continued.)
38706) 2828882701578 (73086413
119463
116118
834470
309648
i>
48221
23223G
159865
154824
50317
88700
(18)
116118
116118
(17)
.-. No. of pairs stoqkings == 1 1880
-*- 66 = 180.
(19)
80984051 -^ 288 = 107583 ; rem'r 147
.'. JNo. to be added = 288 - 147 = 141.
274+108 = 382.^^^^
274 - 108 = 166.
382 X 166 = 63412.
6341 2 -h 176 = 360 ; rem'r 52
(31)
75x$4 = |300 ,
94 X $3 = $282 ^ = $794
106 X $2 = $212 f ^
He wishfis tn reoii-^n <k'yf^i
$941 -^ 275 (whole
i_ AH Jft _ _^ AA ...
ot sheep) =$3Hg.
«l- - ■
88
I
k
KEY
[Klj.:m. Aritut.
(82) Gain,* 1267
' (23) 10e+ 29 + 267 = 890
699 -H 19 = 2t ^^^•
^ 21 X 57 = 1107
1107-197=: low.
(24)
1 lamb is ^orth 16 -i- 8-40 o^>iao ^^^^
1 sheep i8 wcrth 60 -<- 15 - If IZ^^ ~ ^'"^^ = ^'^048.
840 lambs cost 840 1 $2 =1^680 ^^^^ "^ ^^^ = ^^-
ANo.ofsheep = |i6|oH-4™0
(26)
154970553 ^ 4t« = 872647. 470C32 - fo- 4796,2
(38) 479013^28= mil
- 1WW -f. ^y _ 110 = gam per buUSck.
(4)
Ex. XIX. (p. 43.)
81393
73536
88572
81603
69694
63469
62355
54402
— «U-_
(5)
70602)6137090G6(8678WgiJ
I.
653186
494214
589726
56481G
24910
Ex. xix.J
KEY.
(6)
896)60^ 05«a6 (66970 iil
5076
6245
6876
8698
8064
6343
6272
716
i'T)
9986)70867509(7096 8941
69902 ^
96550
89874
66769
59916
685a
mm
868) 8673456954 (9992461 |§f
8614
7812
8025
7813
2136
1736
4009
8472
5375
5208
' 1674
868
M
93256) 200006783^2144 f t|i|
186512
184947
98256
416918
373024
438943
873024
65919
806
30
14609
719
181481
14G0D
103203
10503871
KEY.
[Ei^M. Arith.
(10)
8067) 10503871 (1303 em
8067 *•
34368
24201
16771
16134
637
m. I
Ex. XX. (1x51.)
W JO 8
i.
ft
^-ja
17®360d
4 ;
681440 g.
(2)
mis. fur.
• 17 1
8
137 fur.
.' 40
5480 poles.
4 27400 '
: 3740
. 30140 yds.
i 3 -
90433ft.
12 ,
ft.
3
^
1085070 in.
in.
Arith.
3 8¥d^
in.
Ex, XX.]
KEY.
81
(8)
tons, cwt
8 2
20
qrs.
3
lbs.
5
-
162 cwt
4
^ ■
651 qrs.
25
•
8260
1302
16280 lbs.
16
ac. r.
612 2
sq.p.
Q
S.Td.
97680
16280
260480 oz.
40
*
—
16
0ft»Oa
•
*
1562880
260480
29400371
£4500
4167680 drs.
•
■.
2964527iyds.
9
' 26680747i lOt
144
106722988
106722988
26680747
3842027668
7S>.
•3842037640
^M'
W
mk fUr. pp. yds. a in. j^
.40
8405p.
H
17080
17001.
ii^iyds.
60197* #7^
13 ^'; ■
674875 ftr Ak
13
^Oft8605inr'&^
[Elem. Abit^.^
(6)
*?• r- Pjr. yds.
4
20r.
40
808 p.
80f
24119
200f
»48i9|yd8.
y
218877* a
144
^ 876508
875508
218877
81618288
108
31618896
t (.
(7)
40&hrs.
60
■'■■■??'
■ii^.f
Abit^>
Ex. XX.]
KEY.
83
■r ^-
(8)
lbs. oz. drs.
2 11
12
85 oz.
8
280 drs.
3
840 scr.
20
scr. grs.
20
16820 grs.
cub.yds. ft.
23
1000
, (0)
lea. mis.
2 2
8
8 mis.
8
71 Air.
40
.2840 per.
♦ 5i
14200
1420
15620 ydd.
27
161
46
ill)
galls, qts.
18 8
4
621 ft.
1728
55 qts.
2
5968
1242
4347
621
(13)
220 bush.
4
llOpts.
4
440 gills.
1074088 in.
880 pks.
2
•
1760 galls.
#
fur.
7
7040 qts.
TV
Si
(13)
yra. dys,
15
18
9
1095
315
1410 dys.
24
5640
28;a[)
38840 hw.
60
2030400
min.
KEV.
PElem . Akith,
(14)
it t
12
329 oz.
20
6696 dwt
24
26384
13192
158304
dwt
16
grs.
lbs.
47
12
575 oz.
8
4606 drs.
3
iisiosc. '
20
(15)
o«. drs.
11 6
sc.
276400
J?i.
£
200
20
4017^.
12
2
17
8i
Irith.
wt
16
Ex. XX.]
KEY.
35
(17)
ac. r.
219 2
4
878 ro.
40
per.
16
(18)
yds. qrs.
218 2
4
874 qrs.
4
3499 Ills.
Ills.
3
35136 per.
80i
1054080
8784
■
1062864 yds.
. (19)
£ B.
2376 19
20
d.
8i -
(30)
cwt. qrs.
216 2
i 866 qrs.
I 25
4347
1732
47539 s.
12
lbs.
17 /
570476 d
4
22819062'.
21667 lbs.
(21)
25* 36'
60 ^
1536'
I
921.60"
86
I?,
I
KEY.
T 'r- '7. yds.
[Elem. Arith.^
8
8
8
40
2680 per.
5J
13404
1340
14744 yds.
3
44232ft
12 "
580784 in.
£
312,
20
6257 a
12
75090 d.
4
(33)
8.
17
300362
9-
(25)
26
_£ .
180 qiB,
4
(24)
12.
mooz,
2a
«^2Q0dwt.
84
lOOSOO'
50400
520 nis.
604800 gi^.
Fr.efls.
lbs. oz.
287 6
12
sSooz.
8
27600 drs.
3
2^qw.
£
576
20
11340 a
12
136086 <f.
4
(27)
a.
6i
*
(M4345.
£ (80)
200 /» 4
82800
sc.
(29) ^
pipes.
8
2
378ga]Js.
4019 a
12
48234d
4
192938 />
Ex. XXI. 1
KEY.
87
Ex. XXI. (p. 58.)
(1) ' (2)
4)123290 '?W^*^ 24)18172 ^^^'^^^^
12) 30822 -i(?.
2i3l)256^"«. 6d
20) 548-20 gra,
12)27-8 dwt
2 lbs. 8oz. 8dwt.20grs.
£128 8 8. Qi d.
2)18191 ^>-4
(4) ^riA^M 4) 9095-1 pt.
12) 76787568
8)6398964
6i)2132988-yds.
2 2
2273 g^9, 8 qts. 1 pt
11)4265976
40)387816
8) 9695 -16 poles.
3) 1211-7 fur.
403 lea. 2 mis. 7 fur. 16 poles. .
(5) ,<!p<*-
16)2007008 ^
16) 125438
25)7839-14 oz.
4) 313-14 lbs.
20)78-1 qr.
i4j3()9382Jf
V.
4) 2845 r.- 27 per.
586 a. 1 r. 27 per.
3 tons. 18 cwt. 1 qr. 14 lbs. 14 oz.
88
'\
[Elbm.
AniT^.
(8)
KEY.
(7)
24)167813 4^^
20) 0993-4 grs.
t2)m^l2 dwt.
291bs.loz.isdwt.4grs.
12)8756765087 -^^
8) 0081W3-6 inches.
igiil 20370300-3 ft
\i ^ •-. ^ '
11)40540^ "' "
.8) 93187-37 poles. • •
^^^^^-^s.Uur.37p.3,cIs.0ailin.91.
(0)
•16) 7678678950 d-^^ ^
25)39994839-1002.
2!^ 39994$^-! qr.
149971 ts. 8 cwf i.« ... ..
.' " "^"' ^^^o»- 10 oz. 13drs.
Ex. XXI.]
(10) -
12)121605 /?t^Ov
KEY.
(11)
24)98006 ''^
»9
8)10183 ft. -9 in. 20)4088-14grs.
5i) 8877- 2 ft.
2 2
11)6764
'40)614
8) 15-14 po.
1 ml. 7 fur. 14 p. Oytls. 2 ft. 9 in
13) 304-8 dwt
171bs. Ooz. 3(lwt. 14gr8.
(12)
10)2023752
16)126423
^A^
(13)
20)702917 ^'^-^
#85143 -17 fp§.
25) 7901 -6 oz. 8)U7l5-0sc.
4) 816-1 lb.
20)79-0qr9.
12) 1404-3 dr. .
132 lb; oz. 3 di-. sc. 17 gr.
3 Ions. 19 cwt. p qrs. 1 lb. oz.
(14)
e^
6^)173789?^ ^
6)31)3879^-13 sec.
(ir>) / ..
COi) 173425 y^
24)479-58min.
7)19-23111-8.
121)689700
4^) 570)31 s(i. poles.
~ , ^ , 4)143r.-20sq. poles.
2\vk.5dy.23lu\58'13" . ^ i *^'=*-
35 a. ^2 r. SO sq.po.
"^ ■"•fliw»i*>ir<.iiiiin,iiitiittinim> I
■' wTS'^w^c^TiRw^^fe^H^i^t*'' ■
40
If
KEY
y [Elbm. Arith.
(16) /fe*^^*. /|^v
1728) 18856888 144)1244160000 ^^
27) 8019 cut), ft. l)86400Usq.a
297cub.yds. -^1^) 960000
4 4
)Jo^ tlL 121)8840000
4)
4)126
31 yds. l:^,
(19)
6^)18107^ 4^0
40)81735~16isq.yds.
4)793 r.-15sq. per.
198a.lr.l5s.p.lGis.yd9.
(20)
60)8165760^ <^<^
6^)218^mm.~|»see.-^.. :e^5259g^^.^^
36 Ill's. 24 min. m see. 24) 8766 hrs.
365(ly8. Ohrs.
/
(21)
2)219612
4)109806 qts.
(22) ...
2)800738 /^^
4) 150369 qts.
54)27451 galls. 2 qts. 6§) 87592 galls. 1 qt.
5081ilids. t9gals. 2 qts. ""^ h^s. 44 gals. 1 qt
(^) // (25) y/
1^11 b„. 55 lbs. 20411bu.20n>..li7bu.81b..'
(28) ,
«0) 912715 '^
c. Arith.
Ex. XXI, XX v.]
(36)
1807.47
KEY.
(27)
4)978647
^
41
t.4-^
^
12)348411 d.-8q.
20)30384 8. -81 d.
£1014 . 4 s. 3f d
Is.
er.
I«is.yd9.
rs.
33373
Ex. XXV. (p. 59.)
lbs.
6 .
oz.
3
dwt.
. 3
grs.
. 17x3
61 .
9
. 17
. 2x8 •
10 <
618 .
3
. 10
. 30x8
10
6183 .
1
. 8
. 8
5
30910 .
1854 .
o 494 .
13 .
7
7
6
4
. 1
. 13
. 16
.' 7
. 16
. 13
. 16
. 10
1 . 18
18 . 7
'M.
. 1
* • ." *J^ !
■p . 1 |i. i i r i _» < r , V) p u inii i .
ras 6
3876 , M
6
. /
4f
11
4i
5
5
m
3. Iqt
.3 lbs."
ac.
20
164
1319
f
r.
3
(17)
per.
17
20
yds.
ft.
In.
15 .
3
. 3
8
13
B
2^t
3
la
f:
42
KEY.
(18>
[Elem. Ahitil. '
f' ^' ^^' y^«- ft- in.
1034 . a . 4 . . , a
£
d.
2 .
6
. Si
10
28
233
6
8
lOi
10
9
9
3100 . 18 . 1^
H
I
1337.15
100
$23715.00
5
$118575.00
bu.
.10
106
1062
8dOU
(21)
Pk- galls*
2 . 1
10
10
8
Ex. XXVI.]
KEY.
• Ex. XXVI. (p. 61.)
(1)
cwt. qrs. lbs.
8 . 3 . 31
852
oz.
5
10
39 .
3 .
13
. 2
8
817 .
.
5
.
85 .
2 .
16
. 13
21 . 13
(2)
83772 .10 .18
43
lbs. oz. dwt. grs.
6 . » . 8 . 17
10
61
. 9
. 17 .
2
10
618
. 2
. 10 .
20
10
6182
. 1
. 8 .
8
5
80910 . 7 . 1 . 16
2472 . 10 . 8 . 8
870 . 11 . 2 . 12
18 . 6 . 11 . 3
15
(3)
23
. 7
. 11
10
233
. 19
. 2
9
2105
. 12
. 6
70
. 3
. 9
18
. 14
. 4
2194 . 10
(4)
£
s.
d.
cwt qrs.
lbs.
oz. drs.
2 .
6 ,
10
d . 8 .
28
.6.7
10
29 .
8 .
9
.
. 3
10
298 .
1 .
15
. 3
. 12
6
1790 .
1 .
16
. 6
. 8
59 .
2 .
18
.
, 13
20 .
3 .
13
.13
. 1
1870
23
5
u
£
4
49
498
(5)
s.
18
19
2469 , 15
296 . 7
4 . 18
2771 ~~
d.
10
11
10
2
5
10
6
9*
KEY.
lbs.
15
152
1520
10644
152
30
2
3
4
[Elem. Aiuth.
(6)
oz. drs.
3
5
5
7
U 10826 .8.5
sc.
2
2
1
2
gTb.
7
10
10
10
7
1 .
2 .
10
1 .
14
»
(7)
$2.25
209
2025
450
$470.25
(8)
11.27
62
254
635
166.04
1625 cts.
6
197.50
',
(10)
. qrs.
lbs.
oz.
1
. 17 .
8
10
17
. .
2
34
. .
15
. 7 .
8
cwt.l2 . 1
,(11)
100000
40
$40000.00
8
Ex. xxvri.J
(1)
£ s.
5)278 . 15
55
10
KEY.
Ex. XXVII. (p. 63.)
45
d.
8
1^
(3)
lbs. oz. dwt. rrri.
8)237 .5.6.0
29
8
6
(3)
mis. fur.
0)217 . 5
per
. 10 .
yds. ft. in.
2.0.0
24 .
1
. 19 .
3 .10 .10
yds.
5)115 .
(4)
qrs. Ills.
.2.2
. 2
lbs.
C)865 .
oz. drs. fic. grs.
9.0.2. 10
23 .
144 .
3.4.0. 81=1
(6)
(7)
11)2078
s. d.
. 17 . Hi
•
. 19 . 9J
tons. cwt. qrs. lbs. oz. drs.
9)67 . 13 . 1 . 17 . .
188
3)7
. 10 . 1 . 13 . .
2 . 10 . . 12 . 10 . lOf
ac.
7)976
8)139
17
(8)
rds.
per. yds.
ft,
2 .
. 19 . 25 .
2
2
25
80
>y
10
7 X 7 + 3 = 52, true rem.
l\
\l
m.
87-3 rem.
55 -7 rem.
qra.
40
cwt.
705)613
4
2448
2115
333
25
1683
066
8343(1111,3.
705 ,
1393
705
587
16
8523
587
9393(13 oz.
705
2343
2115
237
16
1364
237
3634(5flU« di-s.
iib'40
KEY.
[Elbm. Akith.
(9)
lbs.
17
(7 fur.
109
Ans.— 3qi-s. lllbs. 13oz.
oz. drs
3 (3 qw.
(10)
mis. fur. yds,
•1.347)8637 6 ^3
7483
1145
8
9166
8730
437
40
17480(14 per.
1347
5010
4988
113
11
,133(0 yds.
3
369 (0 it
13
4428 (3iV7y iu.
3741
687
5|H Hi's.
4'
'#.-
Ex. xxvu.] KEY.
(11) •
bu. pks. gall. qts. pts.
13)612 2 12
47
(12)
£ 8. d.
fi)2851 16 4i
8)51 1 lrem,~8 6)316 17 4i
6 110 Orem.-8
8 X 12 + 8 = 44, true rem.
52 16 H
lbs.
57)247
228
19
12
(13)
oz, drs. sc. grs.
10 7 1 0(4 lbs.
288 (4 oz.
228
lo
8
87 (1 dr.
57
30
3
91(lsc.
57
84
20
680(11^? grs.
62/
53
Ans. — 4 lbs, 4oz. 1 dr. Isc. ll^fg^a.
KEY.
211)200
8
1603
1477
126
40
5046 (23 per.
422
826
633
193
___6i
965
106H(5yds.
[ElJ2ii. AllITH.
(14)
i»ls. fur. per
6 (7 fur.
^^?
61
3
194^
234 a in.
811
23
12
65
Ans.— 7fur. 23 per. 5 yds. Hq. j
s^AK
Ex. XXVII.]
KEY.
49
ac.
318)416
318
r.
3
(15)
per.
19
yds.
7 (1 ac.
98
4
895(1 ro.
318
77
40
3099 (9 per.
•
2862
237
30i
7117
\
59i
7176i(32ycls.
636
•
816i
636
4608
180J
30
9
4644(14Jrrim.
1622i(5ft.
318
1590
1464
32i
1272
144
192
138
'
128
318
82
An8.~1 ac. 1 ro. 9 per. 22 yds. 5 ft. U^flin.
if]
I
00
KEY.
(16)
tons. cwt ar<^
564)014 2 ^
[Elem. Arith.
564
60
20
1^02(1 cwt.
564
438
4
1755(3 qra.
63
25
315
126
1575(2 Iba.
1128
447
16
2682
447
7152 (12 oz.
564
1512
1128
384
16
2304
3(1 ton.
2304
384
iii A A /A J\K n A
Vi-i'i ii
5640
504
v^'^'zftf Urs,
Ex. XXVII.]
(17)
c. yds. c. ft.
169)917
845
73
27
513
144
9
1953(11 eft.
169
263
169
94
1728
852
188
658
94
KEY.
c. m.
100(5 c. yds.
51
162582(9611^1 c. in.
1521
1043
1014
292
169
123
(18) .
lbs. oz. drs. sc.
212)926 5 8 2^4 lbs.
848
12
941 (4 oz. .
848
98
8
747 (3 drs.
636
111
8
335(1 sc.
212
123
20
2460(1^^1 grs.
212
340
212
I
128
KEY.
I !
(19)
lbs. dwt.
634)3068 8(4 lbs.
2530
12
6384(10 oz.
6340
44
20
888(1 dwt.
C34
264.
24
1016
608
W6(9M5grs.
5706
390
Ans.— 41bs. 10 oz. Idwt
[ElEM. ARITlt.
(30)
8. d.
10 6 (£2
£
758)1914
1516
398
20
T970(10s.
7580
"890
12
4685 (6H?d.
4548
-** 137
Ans.— £2 10s. 6JHd.
£
317)215
20
4312
317
im
951
191
13
2298 (7d.
2219
79
4
317 (iq.
317
Ans.— 13s. 7id.
(21)
s. d.
13 6i(13s.7id.
^ ^Tr^^M ^MSS^e^
^;a«5?iwa|.,^»R^^.^_
ARITlt.
d.
5 (£2
:]x. xxvtl]
yrs. clys.
no?) 125 127
365
KEY.
(22)
Ills. mill.
16 47(115 days.
53
753
750
375
45752
397
605
397
2082
1985
97
24
404
194
2344(5 hrs.
1985
359
60
21587 (54 min.
1985
1737
1588
(23)
267) 12267.84 ($8.49iSf.
2136
1318
1068
2504
2403
101
(24)
425) 15693.75 (I13.39IM.
425
149
60
1000
8940 (22m sc. 794
1443
1275
1687
1275
4125
3825
300
7tf4
206
Ans.— llSdys. 5hrs.54'. 323gf
(l
[
KEY.
54
(35)
865) $000.00 (11.64 JH.
865
2350
2190
1600
1460
140 365 - 53 = 313.
313) $600.00 ($1.91H5.
313
2870
2817
' 530
313
217
(37)
57) $65.55 ($1.15
67
85
57
285
285
[E:_zM. Arith,
(36) -
57) $265.05 ($1.65
238
370
343
285
285
(28)
52)$133.00($2.53^<
104
"iso
260
200
156
H
Ex XXVIII. (p. 64.)
*/ou3. lua. = 182u0d. ^57 Os 7^fi — 97Q7f;i.i
164530 ^ 18350 = 9 times. sTlkl SKTO = S^
p lbs. 9 oz. 3 dwt.^ 13 grs. = 56244 giu
56344 -^ 139 = 43G""times.
Ex. XXIX.]
KEY.
(4)
55
4 mis. 1 fur. 2 yds. = 21780 tt
1 ml. 3 fur. 2 ft. = 9262 ft
21786 -i- 9262 = 3 times.
(5) (6)
6 cwt. 2 qrs. = 10400 oz. 12 lbs. 6 oz. 2 sc. = 72040 gr.
1 qr. 3 oz. = 403 oz. 1 lb. 6 oz. 2 sc. 10 grs. =
loloO ■+- 403 = 35iM times. 8690 grs.
72040 + 8690 = 8|H times.
(7) (8)
8 yds. 1 qr. 2 nls. = 54 nls. 1 dy. 1 hr. 12 miii.=1512 mm.
1 qr. 2 nls. = 6 nls. 1 hr. 8 min. = 63 min.
54 -4- = 9 times. 1512 -i- 63 = 24 times.
(9)
5s. per. 7 yds. 108 in. =205200 in.
2 yds. 1 ft. =2736 in.
205200 H- 2736 = 75 times.
(10) (11)
$-141.05 = 14105 cts. $221.00 = 22100 cts.
$ 2.17= 217 cts. $ J:.21= 221 cts.
14105 -f- 217 = 65 times. 22100 -i- 221 = 100 times.
Ex. XXIX. (p. 65.)
(1)
£25 X 4 = $100.00
6s. X 20= 1.20
3d. = 12q. x5-Hl2= .05
$101.25
(3)
£57 X 4 = $228.00
19s. X 20= 3.80
3d. = 12q,x5-^13= .05
(3)
$231.85
£207 X 4 = $828.00
17s. X 20= 3.40
8d.=32q.x5-i-12=: .18^
|83i,oBt
(4)
[Elem. AltlTU.
£153 X 4 = 1012.00
_ 188.x 20= 8.60
6cl. = 20 q. X 5 -f- 13 = .OSJ-
£217 X 4 = 1868.00
17s. X 20 = 3.40
1871.40
$015.68^
(6)
£310 X 4 = 11276.00
^ , 158. X 20 = SiK)
7icl.= 30q.x5H-12= .12 J
(7)
$1279.12i
£612 X 4 = 12448.00
1111 I- l»8.x20= 3.80
Hid. =4oq.x5-*-12= i8|
(8)
$245i.98f
£63 X 4 = $252.00
9ax20= 1.80
0K = 39q.x5-4-13= 16^
(9)
$253.96^
£912 X 4 = 13648.00
12s. X 20 = 2.40
6cl.=24q.x5 + 12= .10
$3650.50
(10)
£711 X 4 = $2844.00
Rii n« 5s.x20= 1.00
6id. = 22 q. X 5 -^ 12 = *
$2845.09i
(11)
rM3 o/^l^'^ ^ 4 = $4468.00
7id. = 30 q. X 5 -i- 12 = .12^
$4468,13i
IB»M i illMHil.Hi§iiLl!
Ex. XXX. j
KlilY.
57
(13)
£47 X 4 = $188.00
7 8. X 20 = 1.40
.15
J) d. = 86 q. X 5 -I- 12 ^
(i:5)
$180.55
£2017 X 4 = 11^)8.00
Oh. x20= 1.20
.18i
8a. = 83q.x5+12 =
(14)
$8060.83i
£75 X 4 = $300.00
98. X 20 = 1.80
8id. = 34q.x5 4-12= .14i
(15)
$301.94i
'2h
£37 X 4 = 1148.00
18s. X 20 = 3.60
>a q. X 5 -h 12
(16)
.121
$151.73i
£87 X 4 = 1348.00
13s. X 20
0d. = 36 q. X 5 -4- 12 =
2.60
.15
$350.75
(1)
Ex. XXX. (p. 66.)
(^w)
fe217-4-4 = £54 +
$327 -4- 4 = £81 -I- $3
125 cts. -f- 20 = 6 S.+ 5 eta. 355 cts. -?- 20 = 17s. + 15a
5 cts. X 3
= 3d.
£54 6s. 3d.
(3)
$17h-4 = £1 + $1
135 cts. -^ 20 = 6s. + 15c. 50 cts. -^ 20 = 2s. + 10 cts.|
15 cts. X 3 -s- 5 = 9d.
£81 17s. 9d.
(4)
4 = £21.
io cts. X 3
£1 Gs.
UO.
9d.
lU CIS. X o -T- :^ OCl.
£21 2s. 6d.
li ii ■
58
KEY.
I
ni"
[Elem. Arith.
(''5) (6)
395c. 4- 20 = 19s. + loc. 137^0. h- 20 = 68. + 17ic,
'•""li^'io^ol- mc.x3-^5 = 10id.
£18 19s. 9d. £31 (3s. iq^o.
$867 -^ 4 = £216 + $3
387ic. -f. 20 = 19s. + 7ic.
7^c. X 8 -*- 5 = 4id.
£216 19s. -Hcl
(9)
$1393 -^ 4 = £348 + ,.
162ic. -^ 20 = 8s. + 2Ac.
2^c. X 3-^.^=1^.
£348 8s. lid.
(11)
$2220 -4- 4 = £555
29c. ^ 20 = Is. + 9c.
tic. X 3 -T- 5 = 5^1.
£555 Is. 5fd.
(8)
$1162 -4- 4 = £290+ $2
240c. -^ 20 = 12s.
£290 12s.
(10)
$1937 -4- 4 = £484 4- $t
120c. -f- 20 = 6s.
£484 6s.
(12)
$3785 -^ 4 = £946 + $1
148c. -^ 20 = 7s. + 8c.
8c. X 3 ^ 5 = 6^d.
£946 7s. 5|d.
I
I
(1)
35700
24191
18777
18129
21187
117984
Ex. XXXI. (p. 60.)
PAPER I.
(2>
55146
23603 .
9889
6275
8369
4584
iUVVt)(j
(3)
looooa
229713
58705
612517
999999
833719
708809
60050
365301,'3
Ex. XXXI.]
KEY.
r»(i
(4)
5005
7018
17915
28719
9013
807513
717017
93503
212607
1898307
(5)
12) 178006
3) 14833- 10 in.
J
4944-1 ft.
2
[11)9888
4P) 89^-10 lif. yds. = 5 yds.
8) 22-18 per.
2-6 fur.
Ans.— 3 mis., 6 fur., 18 per., 5 yds., 1 ft., 10 in.
(6)
$ 8375180.20 -J- 1493332 = $ 5.60 and a fraction.
143054836.00 -f- 2506755 = $17.17
$17.17 - $5.60 - $11.57
PAPER II.
(1 (3)
8s. lOid. X 818 07 X $1.63 = $108.54
10 83c. X 13i = $ 11.07
$11.07 + $18 + $16 = $ 45.07 :
Total amount expended,
J.54 - $45.07 = $63.47
£4
8s. 9d.
10
£44
7s. 6d.
8
£355 Os. Od.
4 8s. 9d.
3 lis. Od.
£362 10s. 9d.
id
! ;|i
60
ac.
ao
KEY.
(8)
r. per. yds. ft.
[KliEM. AUITII.
807)7l>813(183 i' 'u ^ 7
897
«811
8170
1352
111) I
IGl
644 (Iro.
897
847 \
m
(4)
1()() X $1.00 = $050 00
$350-4-37 = 1 0.48
tf
(n)
40
0880(24
43iyds. ^-8i = 5
81^x6s. O^d. = £2 15s. 7id.
= £1042 178. Cd. = $4171.50
84xl7c. = $ J4.28
.75
,00
80
9.25
n PofM^5'^?.= ^3 108.= 14
:!^-. io!l^M^-^ 8=^20 14s. = 82,
794 £12 198. 9d. X 16 =£m* 88. Z Z
77
tm ... Depoavrnifsr .ii.ffi?d«
852
80i
10648 (36 yds.
794, ^
3708
2882
826
9
155
13227.42
14171.50 - $944.0' '=
Kx. XXXI. J IvEV. 61
IvEV.
PAPER iir.
£ s. d.
203701)9520732 14 (£40
815044 (2)
Suppose 1 to represent the 1st
1370292 man's share,
1222566 .•.1 + 3 + 5 = 9 = No. of snares.
$03000 ■+■ 9 = $7000 = value of
147726 a share.
20 $7000x1 = $ 7000
$7000 X 3 = $21000
2954534 (14s. $7000 x 5 = $35000
203761
916924
815044
101880
12
1222566 (6d.
1222566
(3)
£ 8. d.
20)354 11 6 (£13
26
94
78
16
20
«
831 (12s.
812
19
12
234 (9d.
234
I
^if-
m
ac.
20)10
4
42
29
13
40
KEY.
[Klem. Anrnr.
(4)
ro. per. yds.
3 7 3 (1 ro. 18 per. 5 yds. 3 ft.
(5)
tons. cwt. qrs.
347)300 15 3 (17 cwt.
20
637 (18 per.
29
\
237
233
5
80J
153
153H5yds.
145
9
74i (3 ft.
58
16i
30 mis. =367300 in.
2ft. 6in. = 30in.
.*. No. of steps taken ~
267200 -^ 30 = 43240
No. of minutes occupied in
walking =
43340 ^ 110 = 384
i hr. = 30 minutes' rest.
.-. 384 + 30 = 414 mill. =
467 (Iqr. Clirs. 54min.
347
6015
347
3545
2439
116
4
1^0
35
600
340
3000 (8 lbs.
3776
334
16
1344
334
3584 (10 oz.
347
084
114
114
16
■i act ,« /■- .1-,
1735
89
Kx. xxxi.J
KEY.
an
TAPETl IV.
(1) (2) (I)
£8 17s. 6cl. =: $37.50 8+3=11 4 x 38 = 153 doz.
£3 138. 9cl. rr $14.55 84-11-1=18 Owner net, 1 sh.
,-. sum = $37.50 + Owner boat, 3 slis,
$30.27 + $14.55+ $75.83 (3) Each man, 4 slis.
= $148.15.
(6)
84889 - 889 = 84000
84000 -f- 3 = 43000
43000 + 889 = 42889
54 -T- 6.= 9 Four men, 16 shs.
9x1 = 9 ,'. total no. of sha.
9x3 = 18 =14-3+16 = 19
9x3 = 37 153-f-19=8doz.=
value of 1 share.
8x1= 8 dozs.
8x3 = 16 "
8x4 = 83 "
rAPER V.
(1)
(3)
73678397
73697
X 11689 =
861444233
80073
861444233
+ 3687 =
861447930
318035191
508748779
37(
313 - 15908 = 11904
436070383
581437176
(5)
(6)
22983
10240
6355647664981
96801
704
64183
8084
(4)
91308
4313
89364-^7 = 13753
190000
73347
465335
95587
TAPEii v;.
(1)
(2)
160303 + 168795 =
329097
$6000000
71973 + 34537 =
90500
4866666
160303
1467750
339097
800000
71973
1909640
tr V '-' \r \F
590Sft2
863033
RK'yQ'TO
$16496471
G4
(3)
$7328140.08
1888576.7«
C21936.43
417474.00
60554.00
122142.77
$10444830.63
(5)
ac.
035) 80895 (130 ac.
035
2339
1905
4345 ^
3810
535
4
2140 (3 ro.
1905
235
40
KEY
9400 (14 per.
035
3050 15427J
2540 1270
[PJlem. Aritii,
(4)
$375, team,
$ 82, wagon,
$ 10, plough,
$ 10, stove,
$153, reaping machine,
$ 96, slieep,
$ 50, cows,
$ 18, pigs,
$ 60, wages.
1 otal expenditure = $866,
$975 - $866 = $109
$109 -i- $1.75 = 62.28f
no. of liundred lbs.
02.28^ X 100 = 6228f lbs.
mis. per. j-ds.
10 3 4
8
80
40 .
5i
16019
lOOH
17020^
3"
(-*4-.VA- yds. 5280H
12
510 2727^
30Jr 2540
634338
15.S00
lan-jL
127i
635 1270
Ex. xxxrr.] KEY.
Ex. XXXII. (p. 71.)
(1) ■ (2) (3)
G5
8)18(2
16
2)8(4
8
C) 15 (3
12
3)6(2
4) 22 (5
20
2)4i;2
4
(4)
16)28(1
16
12)16(1
12
..G.C.M.is2 .'.aC.M.isS .•.aC.M.is2 4)12(3
12
(5)
20)32(1
20
12)20(1
12
(6)
24)39(1
24
.-. G. C. M. is 4
(7)
8) 12 (1
8
1) 8 (2
8
.♦. G. C. M. is 4
15)24(1 26)44(1
15 26
9)24(2 18)26(1
18 18
6)9(1
6
8)18(2
16
3)6(2
6
2)8(4
8
(8)
30)42(1
30
12)30(3
24
6) 12 (2
12
.'.G. CM. is 6
58)174(3 -.
174
.-. G. C M. is 3
•. G. C. M. is 3 .-. G. 0. M. is 2
(0)
36) 56 (1
36
(10)
46)116(2
92
20)36(1
20
24)46(1
24
16)20(1
16
4)16(4
16
•. G. C. M. is 4
22)24(1
22
2)22(11
G. C. £ is 2
I
I
(13) .
315) 378 (1
315
63) 315 (5
315
.-. G. C. M. is 83
(15)
310) 630 (2
630
10) 310 (31
310
••• G. C. M. is 10
(17)
137) 445 (4
381
64) 127 (1
64
63)64(1
63
1) 63 (63
63
••• No G. c. n
(iS).
6408)7204(1
0108
850) 6408 (7
5992 ~
KEY.
(13)
138)360(3
256
110) 128 (1
110
LElem. AiuTir.
(14)
180)210(1
480
30)180(6
180
18)110(6 .-. G. C. M. islo
108
2) 18 (0
18
•G. CM. is 3
(16)
424) 1216 (2
848
368) 424 (1
368
(19)
-'^042)3094(1
3042
56)368(6
336
32) 56 (1
32
24) 32 (1
24
8)24(3
24
.-. G. C. M. is~8
416) S
v^6(2
32^
'ontlnued
832
52)3042(58
260
on next page.)
Kx. xxxii.]
KEY.
(18 and 19 continued.)
24)410(17
24
6"
176
168
443
416
26)52(2
52
G. C. M. u 8
8)24(3 ' .-.
24
- (21)
G. C. M. is 26
1441)1572(1
1441
(20)
040)7392(1
7040
^52)7040(20
7040
131)1441(11
131
131
131
, G. C. M. is 352
(23)
G. C. M. is 131
23025)46430(2
46050
1108)204024(0
190512
330)23025(59.
1030
3725
14112)21108(1
14112
ij474
r>
7056)14112(2
14112
251)380(1
251
G. C. M. is 7050
8
2)13(")
18
135)2"il(l
135
2
No G. C. M.
110)135(1
1 m
I
19)110(0
114
m
KEY.
(24)
29579)97482(3
88737
[Elem. Arttif.
8745)29579(3
26235
8344) 8745 (2
6688
2057)8344(1
2057
1287)2057(1
1287
(25) r
r38140) 828597(1
738140
r"*,
770) 1287 (1
770
90457)738140(3
723656
517)770(1
617
14484)90457(6
86904
253)517(3
506
11)253(23
253
8553)14484(4
14212 ,. 'J. a MAS 11
-
272)3553(13
272
/)272(10
17
102
O. C. M. is 17 ~
Ex. XXXIII.]
KE\.
60
(26)
836337)737800(3
053674
85126)320337(3
255378
70959)85120(1
70959
14167) 70959 (5
70835
134)14167(114
124
176
134
537
490
31)134(4
134
/. G. C. M. is 31 —
(1)
2 1 ;z, 4,
Ex. XXXIII. (p. 72.)
10
2,
5
4
3
.•.L.C.M. = 2x3x5 = 30
(3)
8, 9,
2, 9,
13
3
2
(3)
12, 16,
18
2
6, 8,-
9
3
3, 4,
9
2 8 1
.L. CM. = 4x3x2x3 = 73
(4)
20, 28, 36
2
2
10, 14, 18
n
1, 4, 3 .•.L.C.M.=:2x2x5x7x9 = 1260
.•.L.C.M.=3x3x 3x4x3=144
iT-
-l!fc
i'l
I
70
KEY.
[Ellm. Auitu.
o
10, 24, 30
8,
12,
15
4,
0,
15
3,
8,
15
2
2
2
3
24, 50, 84
12, 28, 43
0, 14, 21
2 1 5 " ^' '^' 21
.'. L. C. M. = 2x3x2x3x2x5-040 1, / 7
L. C. M. = 2 X 2 X 2 X 3 X 7 4 168
(7)
5i;^, 25, 105
5, 21
.-.L. C. M. = 5x5x21=525
2
8
(9) »
K 21, 6, 14, 25
2
2
2
3
(8)
^, 33, 24, 32
33, 12, IG
33, G, 8
11, 1,
8, 4
4
21, 3, 7, 25
' y^ -— :-'-T^-C.M.=2x2x2x3xlix4
.'. L. C. ]Vi. =2x3x7 X 25 = 1050. " ^^^^
(10)
2 17, -8, 9, 10, 12
2
3
2
7, 4, p, 5, G
(11)
24, 28, 3G, 22, 16
7, 2, 9, 5, ^
2
12,
14, 18,
11,
8
2
6,
7, 9,
11,
4
1
^,
7, 9,
11,
2
7, 2, 3, 5,
.-. L. C. M. =
2x2x7x2x3x5x3 = 2520. ^ 7 3 11 o
/.L. CM. =2x2x2x3x7x3x11x2 = 11088"
5 I 2, ^: 45, ;^, 25 3|jr, ^,8,^11, 27,
2.
.-. L. M.
9,
K Ky n ^; r\ . . r
'j .-> ,»
'J
ou.
L. C. M. ^
8, 5, 9
'} ^ 8 X 5 X - 1080.
Ex. XXXIII.]
(14)
15' 20, 24, 21, 35 2
2
8
15, 10, v., 21, 85 3
KEY. "'i
(15)
^, ^, ;, 8, ;^, 21, 30
4, 21, 15
7, 5
15 5. 0, 21, 35 4,
^ ' ' ' .-. L. C. M.=
^, ^, 2, 7, 35 2x3x4x7x5=^840
.•.L.C.M. =2x2x3x2x85 = 840
(16)
3
;Z, T, }?, ,13, 15, 62, 63 8
(17)
3, 7, 21, ;;, 77, 198
2
2
5
5
5, 52, 21 11 K 77, 60
,.C.M.=3x5x 52x21=16380 ^ ^^
/.L. CM. =3x11x7x6 = 1386.
(18^ ( ^^
100, 56, 3^, 125, 150 5 22, 55, J9, 1 5, _95,^3^>
22, ;;, 3," ;?, loti
.-. L. C. M.=
5x22x3x133=43890.
50, 28,
125,
75
^^. 14,
125,
75
14,
25,
15
•.L.a]?L = 2x2x5x5xl4x5x3 = 21000.
2
2
2
2
3
(20)
48, 64, 27, 33, 110, 165
34,
32,
27,
p;^, 165
12,
16,
27,
* 165
6,
8,
27,
165
3,
4,
27,
165
55
L. C. M. = 2 >'. 2 X 2 x 2 X 3 X 4 X 9 X 55
=r*y
AL
72
KEY.
[Elem. Arith.
Ex. XXXVII. (p. 76.)
(l)f = 3. (2)| = 3-i (3)i/ = 4i (4)i/ = 4.
(0) H = 7 (10) W = 8 (11) W = 8i| (L W^isH
(13) W= 9* (14) HU^ =103 -^j^- (15) 4/ = 12m
Ex. XXXVIII. (p. 76.)
1x3+1 4
(1)H =
(3) 1-^=
8 -3
1 x15 + 1 16
15 -15
(2) 2,^=?iil^-?5
^.'^ 12 -12
(4) 17f =
17x5+3 88
... . . 12x7+5 89 ,^
(0) 12f = =_ (6) 203H=
(7) 2^i=
7 -7
2x65 + 11 141
65
65"
(8) 29i=
5 -5
?03>^19+17__3874
19 -~19~
29x8+7 239
8
(9) 704iA=^5i^il?itl?-_§8716
126 136"
(10) 900 A\= ^^ ^ 401+ jl__360931
401 - 401 «
ni\ K 1 5x680+7 3407
8
680 - 680
53x63+37 3376
63 ~-~W
21^x1250+3 26253
1250
(12) 53f J=
^'^''^^^= 1350
(14) X4Bm=J^^^^±^~.^l
•^''^ 465 , - 465
(15) 13l<?8fl_15jl2160+1080_29160
2160 2160
ae^ 2T 3 R n „25 X 2400+389 60389
(17) l97;i^'V^ =
2400 -2400
197x3084+00
:08i
608543
308T
— •* A AJk«
Ex. xxxix.] KEY,
73
4.
Ex. XXXIX.
(p. 77.)
^2
(2)^ofif=J-J=|
m
a)»<'^t=|^H
^2ie
3
25
(3) * of H~
(4)AofA^i|
""12
_88
(O)|ofn = |>c|=|
5
3874
19
239
■ 8
• ^7) 18tof5i\'Of 10:
(8) 111 of 8? =
164 87 10 5945
" 9 ''16'' 1 - «
57 59 3363
5 "" 7 ~ 35
(9)tof2iof9 = |x|x? = ^
(10)fof3fof8i = |x:^x| = :^
: (11) t of -A- of fl of il =
36
113) ,\ of ^ of ^ of 6A- of -/^ = n^T^^^ii^8l
= :i (13)Aof3ioffofl0i = ^x|x5x^=^
11
m
(14)5ofl2ioffoffof|of9 = ^x^x^x|x|x?
= ~ (15) A of 5 of ft of f of A of 2 of A =
^ 7 36 9 £ 3 8_14
.18''8''l0''4''lo''l^27~"15
u
r
KEY, [Elem. Aritbl
(16) f of I of f of 70J of -A- of 1^\ of U7 =
5 3 6 632 3 18 147
7 8 7
6309
Ex XL. (p. 78.)
In each of the followmg examples we divide numer-
ator and denominator by their G. C. M., or as we shall
write It :
a)f =
(3) if
(5) tf =
(7) i¥i- =
2-4-2^
4-*-2~
14-4-7
'21-4-7
28-*-7
1
2*
77-t-ll
121-1-11
2
3*
4
9*
1
11*
= ?T. (8)
(3) is- =
(4) f § =
(6) n =
10-+-5
15.f-5'
80-*-6
/9)m|^-l^^±??-^-l
2
3'
5
48-S-6 "8'
64-f-4 16
21*
17*
84-4-4
48-4-16
(11) iWd =
(12) it§§ =
(13) mi =
272-*-16
(10) |4£B. - 14081-128 11
^ ^ ^^' 1664-^128~i3*
875-4-125 7
1000-4-125 "" 8*
1690-S-130 13
2600-T-130 "" 20'
837^-27 _81
2268-*-27~84*
ni^ WWft - ^^^"»-2002 3
^^"^^^ "8008:;:2002 = 4-
(15) ,^W^ =
(i6).m=l^iyE
805-«-23 35
2622-^23~■ll4•
jLVu»(©-t-iioO
8
VI <; 55rn? - 38769-i-121 "" 279'
Ex. XLI.]
KEY.
75
Mfi^ JUXi'^o 805994-37 _ 8^
(18) m 4Ttf - 2714694-37 ~ '7337*
(19) «H5- 8734-5-23 ^397' •
, 12364-12 103
(30) t6 32-ig32-i-13~136*
(31) tlMi^
(32) nm =
(33) \m =
2857144-142857 _
9999994-143857 ~
103954-11 945
3
r
168194-11
70404-35 3
73934-353
1529*
20
21' -
m\ iia&4 - ^^3854-495 _ 33
(^4) \tn% - 18335^495 - 33-
Ex. XLI. (p. 79.) '
(1) f, f. 13 is L. C. M. of denominators;
8x3 5x^ 9^ 10
4x3' 6x3^^13' 13*
.*. fractions become
(3) f, 1^. 13 is L. C. M. of denominators;
.'. fractions become
3x3 2x4
4x3'
3x4^^13' 13*
(3) -2, ^. 8 is L. C. M. of denominators;
3x3 7x1 6 7
.*. fractions become ttto^ jttt or ^, ^.
(4) ^, f. 63 is L. C. M. of denominators ;
8x9 5x7 37 35
.*. fractions become
7x9' 9 X 7 ^^ 03'
{^) ti> ft* *o is jj. u. iji. 01 aenommators ;
fractions become
1 1x3 3 1x3 83 43
16 xb' 21x2 ^^18' 4'(3'
T*».
i!
11
ii
f
70
KEY.
[Elem. Arith.
(6) {h th 120 is L. C. M. of denominators;
1 1x10 27x3 110 81
12x10' 40x3 *^^T20' 120*
.*. fractions become
(7) h; hU' 200 is L. C. M. of denominators;
.'. fractions become
7x20 183x1 140 183
or
10 X 20' 200 X 1 "* 200' 200'
(8) Ul Uh 6720 is L. C. M. of denominators ;
113x24 527x7 2712 3689
'. fractions become «;
or
280 X 24' 960 x 7 "" 6720' 072a'
(9) h H' 00 is L. C. M. of denominators ;
4x12 11x 5 48 55
5 X 12' 12 X 5 ^^ 60' 60*
.*. fractions become ■=-
(10) A, -Al I 1008 is L. C. M. of den". ; .-. fractions
3x63 8x48 5x112 189 384 560
or
become -
16 X 63' 21 X 48' 9 x 112 "' 1008' 1008' lOOS*
(11) -hy il, !i " 210 is L. C. M. of den"; /. fractions
7x14 11x10 23x7 98 110 161
or
become
15x14' 21x10' 30x7 210' 210' 210*
(12) h A, U, -iV 8415 is L. C. M. of den". ; .-. fract«.
become lii^ 8 ^'^^5 13 x 561 9 x 495
9x985' 11x765' 15x561' 17x495
or
6545
8415
6120
7293 4455
8415' 8415' 8415*
(13) \l ft, If, H. 1260 is L. C .M. of den". ; .-. fract".
become i5-^ ^^^^^ 14x84 40x20
14 X 90' 36 X 35' 15 x 84' 63 x 20 ^^
1225 1176 800
1170
1260'
1260' 1260' 1260*
(
1il\ .1. 11 iJ IB 7 -ir»/\.- T /"« -».r ^r >.i^~-^*^j~,™4.^~~ ,
, ,. , 7x15 17x6 13x10 15x9
.-.fractions become ^^^, __, j^-^-, ^^
Ex. XLI.]
KEY.
1 1
7x12
105 102 ICO 105 .84
15 X 13 °^ 1«U'
1«0' 180' 160' IdO*
(15) U, Ih ff , ii 7200 is L. C. M. of den". ; .-. fract"».
13 X 288 27 X 225 7x600 15x400
become 2- ^2^, ^2x225' 1^^x600' 18x400
3744 6075 4200 6000
^^ 7200' 7200' 7200' 7200*
(16) 1^-, if, -.^, il, ft, II 621180 is L. C. M. of den". ;
9x44370 13x34510 7x21420
.*. fractions become
14x44370' 18x34510* 29x21420
18x17748 23x14790 53x9135 399330 448630
fv-
35x17748' 42x14790' 68 x 9135 621180' 021180'
. 149940 319464 340170 4 84155
621180' 621180' 621180' 621180*
(!'?') h 6, f , if. 120 is L. C. M. of den". ; .-. fractions
2x40 4x24 3x15 14x8 80 96
become 7rT7i7{^ rrrTn^ — rn?. ttitz o^t?;a» thtt*
3x40' 5x24' 8x15' 15x8
45 112
120' 120*
120' 120*
(18) I, h h -uj- 120 is L. C. M. of den". ; .-. fractions
3x30 5x20 7x15 9x12 90 100
become
4x30' 6x20' 8x15' 10x13
105 108
120' 120*
120' 120'
(19) h f, h h -iV '^2 is L. C. M. of den". ; .-. fractions
become :
2x24 5x12 7x9 5x8 8x6
3x24' 6x12' 8x9' 9x8' 12x6'
48 GO 63 40 48
or
72' 72' 72' 73' 72
78
KEY.
[Elem. Arith.
(20) h I, i, A. 830 is L. C. M. of den".; .-. fractions
2x110 4x66 1x165 3x30
8x100' 5x66' 3x165' 11x80 °^
become
220 364
330' 330»
165 00^
330' 330'
Ex. XLII. (p. 80.)
(1) f, f ; 15 is L. C. M. of den".; .-. fractions become
3x5 4x3 10 13
3x5* 5x3 ^^15' 15
.-. in order of magnitude the fractions stand thus, ^, f.
(2) h A; 86 is L. C. M. of den". ; .-. fractions become
\ 7x4 9x3 38 37
36
9x4' 13 X 3 ^^ 36'
.-. in order of magnitude the fractions stand thus, I, ^\.
(8) ih H\ 813 is L. C. M. of den".; .•. fract"'. become
17x13 19x13 331 338
34x13' 36x13 313' 3i3
.-. in order of magnitude the fractions stand thus, i|, l^.
(4) h h H ; 504 is L. C. M. of den". ; .-. fract"«. become
7x56 5x63 11x36 893 315 396
9x56' 8x63' 14x36 ^^504' 504' 504
.-. in order of magnitude the fractions stand thus, ii, ^, f.
(5) iifl,M; 883 is L. CM. of den".; .-.fract"'. become
15x31 33x18 48x14 315 396
or
073
43x31' 49x18' 63x14 "'883' 883' 883
/. in order of magnitude the fract"'. stand thus, ^f , f f , ^f.
(6) tJ,fiH; 5040 IS L. C. M. of den".; .-. fract"». become
53x63 63x56 57x60 ^^ 8339 3328 3420
80x63' 90x56' 84x60 "'^5040' 5040' 5040
.*. in order of magnitude the frart"\ stand thus, ^jl, 1} ^5.
Ex. slil]
KEY
(7) f of §=A; i of ?=-,3^; 7f=V;.168 is L. C. M. of
denominators; .*. ^actions become
sTxS' 14x12' 8x21 "^ 168' 108' 168
of magnitude the fractions stand tlius, 7f , f of f , i of }.
(8) ii, U, H, U\ SOO is L. C. M. of den"; .'. fract".
11x20 17x15 21x12 29x10 m
^®^°°^'* I5T2O* 20105' 25x12' 30xl0 2i800'
255 252 290 j^ oj.(ier ^f magnitude tlie fractions
aOO' 300' 300' - ^
stand thus, f tl, Hi f i> ii-
(9) -,S- of H of 7i = H; 4i of -3% = ff; -9^- of
7i of 11 =M;* of 4^ of 14ff = -^fF; 6836 is
L 0, M. of denominatoi-s; .*. fractions become
29x5V8 3 X 576 55 x 99 1610 x 64 16704 1728 5445
11x576' Uxr 6' 64x99' 99 x 74 6336 ' 6336' 6335'
}^^^^^ . .^ in order of magnitude the fract", stand thus,
^836 ^ ^ „
? of 4i of ^ of 14f f, -h of i§ 7i, i,\^ of 7i of 11, 4i of -^.
(10) m of -.¥r=^, H of 61 of iir of 1A=¥; If of U
of 5is of i of 1 ,^=¥ ; 63 is L. a M. of denominators ;
4x7 11x9 20x21 28 99
... fractions become q^^Y'^Y^^—J^^^ ^^ 63' 63'
420
63
5^ of i of l/f, H of 6i of H of 1 A, f §^ of -i»A.
(11) i f ; 35 Is L. C. M. of den".; .\ fractions become
5x5 3x7 ...25 21 25 21 _ ^
7x5' 5x7
r^ .'. in order of magnitude the fractionslf of li of
Ui
•^5
35' 35' 35 35 oi
.\ f of a yard is greater by -k of a yard.
3S3Sm
I ff
^ KEY. [Elem. Arith.
(13) i, I; 6 is L. C. M of den".; .'. fractions become
1x3 2x2 3 4 4 8 1
. or — — _ — _
2x3' 8x26' 6" 6 6 ~6
.-. f of a yard is the greater by ^^ of a yard.
(13) n of -A- of If of U=-^ ; t of Tio of 5^=-A- ; 24 is
L CM. of denominators; .-. fractions become
5x2 7x1 10 7 10 7 3
fjt* — —
12x2' 24x1 "'^ 24' 24' 24~24~24
-• H of -a- of If of ft is the greater by #4- of a loaf.
21
Ex. XLIII. (p. 82.)
13
21
a)m*^=|f. (8)«+»=?±?=lI=i''
12 12
12'
(3)3^f=3i. (4)m=^^' = ||=l'
(o) -h-+-h =
12 ~12
25+28 53
12'
60
60'
(6)f-l-,._ j^ -j^- 1-= .^
(7)f-fA = ??±?-^ = |=l4
00 55 55
18) f+A=
214-20
4x
56 ~56' (^) ^^+-4%=-y-Q;
4 7 8+7 15 _3
33+4 _37
"90*
(10)H.U=3H-- = -T_i^^^,£.^,^.
(11) 71+8 = 74-8+!^
6
2'
Ex. XLIII.]
KEY.
81
(13) Uof 3i = |of| = y = 3|. 8|+6i = 8+6+
(13)1 + ^4-, f- 60"~-'60 -^60-^15•
/..^ n« « oi « n 3 5 1 ^ 27+20 + 6
(14) 2|+x\+3A=2+3+q4-^-+^ = 5 + j^ =
^ 53
53
72'
/iKsi«Pi3 1 i,10 10 ^ 3 10 ^7 ^ . 3
(15)iofl?=-of- = ^. 6j^+^+2^--6H-2+^
10 7 _ 27+60+98 - 185 _ 59_
■^2l'^9~°"^ 126 ~^"^126 ~ 126*
,.n. r.. .^ 19 7 133 ^^1 ^^1 13 1 „^
(16) 9i of 2^ = y X - = — r=22g. 22g+^+^ = 22
1 13 J__^
"^6'^18"^27 " ^'''
9+39+2 _ 50 25
54 r-'*^'^54"''^''3r
(17) ^ of (1+li) =^- of 2||= I of ^ = I ?+5+^=
12+15+14 _ 41 _ _5^
18 ~18~ 18*
(18) i+f +f +t =
30+40+45+48 163
60
60
2^
60*
(19) 2i+3K4i+5i =2+3+4+5+2+3+^+5 = 14+
30+20+15+12 ,.77 ,.,.17 .Jl
60 = ^^+60 = ^^ + ^60 = ^%
B2
KEY.
[ElKM. AttlTH.
(30)5^,+18A4.||+2tJ=5+134-2+~+| + g+^
- on^ 1«^'0-! i>on H 3920+2208 „^ 8708
2948 _ oA ^ 1 737 737
<21) 4Hf^+16ifir+25H =44-164-25+^+~+^+l|
.^ . 500 + 4204-405 + 468 _
900
1793 _. 893
900 ~ ^ ^ ^900
.= 46
893
900
(22) f of3i = |of-yi=f = li; 81+161+ 7-i'V + U = 8
72
72
= 29
49
72
(23) (2f+-3|) of 2A+3i of (16|+3i)+-lf of 11 of 3«V--^
(2+3+|+|)of ?-J+:^ of (l6+8+5+^)+| of (n
-S)-(^-
8
)
+ 3 =
45X /_ .?±«)of?Z^:L«of(i9V''+^^ 75
n ^ nf ^''4-^" nf iq'''u.'''5 " * 27 16 , 159 75
" ia °* 11+5- "'^ "8+¥ = 18 °* u+y °^ -8-+¥
63 318 75 3 3 1 fi
= T+-5-+¥ = ^^4+*^S+^^2 = 15+63+37+ j+
?.1_ 11, ^15+12+10 ^^^ 37 ,„ 17
<> ii;
m
20
;(^
116
17
20'
Ex. XLIV.J
KEY.
sa
13 19 1 13 *'0
13 ^10 1 ^13 .20 _
1044-114-f 13 i J IT h^O 119 119
£ ^-rr- = £^m+£0 = £llm
144
8 5 7 9
(35) — of 4 1L3.+^ of 4 lbs.+ j^ of 4 Ibs.H-;^^ of 4 lbs.+
14 «, 11 ,1,, ,2„ ,13„ ,4,,
o^ of 4 lbs.+4rK - 1« lbs. 1 - lbs.+l7^ Ibs.-i-l;, lbs.
27 15 o o lo 5
1 2 13 . 4
5
2 11 / 1 2 13 ^
-+-22;^lbs.-f ^Y5 lbs. = (^1+1+1-1+2 4-4+5+3 t-jg+;
2 11
_i 1 —
^27 15
\ ^ 2" ^90+117+108-4-10+99
) lbs.=lulbs.+ T^ lbs.
135
451 , 46 46 „
= 10 lbs. + jT^ lbs. = 10 lbs. + 3 j^g lbs. = 13 j^g lbs.
Ex. XLIV. (p. 83.)
5-^4 t 4-1 3
(1) i-i =-T,r = ^STv i2) +-i =
JO 20*
8 8
^3)f
5
ii
' 12 ~ 12~3" ^^^ ii-»t- -3
(5) 3J~2^ = 3-
4-1 , 3' ^
---- = 1+- = 1^
10-9 , . . .
(C) 7-2^ = 7 -3H-— o" = 4+- = 4~.
i = 4i
10 10'
f I
8^4 KEY. [Elem. Ahith.
c:),oA-8i=tog-»;-=i^(g-!).i,?«-^
86
1??
(8)17f-13^ = 17j-l4=8-f(J-?) =
21-10 11
13 ~ ^13*
8+
(9) 1A--I = l
29 __ 3 _ 116-75 _ 41^
25 4 ~ 100 ~ 100
(tO)4,-3H = 4°-3l| = lH-M2 = l.
1
140 ~ 140*
(ll)15,.7,= 15V^-s| = 7.?5_^^ = 7.g = 7L^^
(12) 20A-8.% = 20| - 9^ = 114-^^^ = ^
-^^1'^ n .-ills ,.113
^^+504 = 11 + 15-04 = 1^504-
^^''^ ^ 5~ 5 ~5'5 5~5'
VA*; W ij^ 36 at) ~ 36 ~ 9'
15-8 _ ^ 7
~1~ - ^10
(15) 5 d- -Q d. = — =;r- Cl. = :=x±
8 9
72
72
ttlTH.
6 ~
Ex. XLV.J
KEY.
Ex. XLV. (p. 84.)
83
(1)H2|' .' 3^=2+13-3+^+^+—^
= 13
'>5 + -'> 4.63-9
.119 _.^119
^^210 ~ -^^210'
(3)i-|+f-fJ =
6-9+20-13 6+20-9-13
24
■4 _1
24 ~ &
24
rl5
21-
(3) 12H-H+ W-t of if +f of 3f = 12^4-^ -^ 4f
16 3
11 21 16 16 1
-51+2 = ^^+'^+l + 17~34+51-51+i = ^^^
66-63+32-32+51 54 _ ^^ 9
103 " "^102 ~ ^"rf*
(4) (16|-3i) of 3K16|+(3i of 3i) = (^16-3+^)
16 . ,5 /13 . 16^
1 — 1!,
8 5 "8
8
!
'5~ 8
16 ^„5 ^^2 ,4 ^5 ^ 2
xy-16g+10g = 42^-16g+10g =42-16+10+
-16 ..5/13 .16\ .3 16 ,5 ^2 107
of y"!^^ \T 5 / ~ ^35X-^ — 16-+10- = -^
32-25+16 „^ 23
40 = 36+^^
36
28
40*
(5) 6i+f, of -A- of 3^-^^§-5f = 6^-+ (~ X ;^, X ^) -
45 r3 , ■ ^ 15+15-45-45 , 60-60 ,
^-55=:6+l-5+— ^ = 1 + __.= !.
:jLj£i4' :.t<i£;'
mm
11
• ,
8(|
KEY.
[Elem. Arith.
(6) 6i+ff of -h of (3i-H)-5| = 6^+j3 of ^ of
/ 4 ^"^ 3 ,1 7 , 9 ^/ 80-45\ 3
,1 7 , 9 ^ 31 a ^1 31 .3 - ^ ,
^4'^ 12 '' 14 ^^ 12 - ^4 = ^4-^32 " ^4 = ^"^"^
8+31-24 _ 15
«2 ~ 32*
89_/4 7 11\ ,89 / 96+105+110 \
^89 71 89-71 _ ^ ii _ 3^
^120 "" "^120 - ^""^+ 120 - ^"^120 ~ "^20*
120
JL8
120
1 S ' 1 3 12 1
(8) 3 of I = I =• B's pur ; 4-4 = 4 = 3 rem'r.
1 ^1 1 ^, 11 3-1 2 1
of o = A = C's pur.; 5-ft = -^ = ^ = 3 remr
2 6
5 of ^ = 5 = D'g pur. ; 3-9=-9-=9 = ^ « rem'r
3^* 2 6
3^^3-9
Ex. XLVI. (p. 86.)
(1) i- X i = i3- (2) 5 X f = 72* ^^^ ■'^^" "" »'^=26-
(4)lxA = i (5)7ix3^ = f x^:=25.
12
2
3 1 35 21 „5
(6) *of ^xl7i = 4XgX~ = — = 2g.
7 8 63 13 13
(7)TVof Ux3-Ax-irf = ^-2X^x-x^ = — .
. ,, ET 35 96 11 _
(8)5^x3-ft-xmxH = 6Xn''y5G = ^^-
5_
26*
Ex. XLVI.]
KEY.
87
7 11 27 5 16
(9) ^of l-/(jof lHx2ixS^ = ^x — X^X^Xy =
33 _ 5
7~ - V ,
11 15 24 45 13
(10)Hof3fx4^of2-^xl3 = jgX^xyx-xy =
5265 _ 1
16 ""^^V
57
(11) 2H of (4H3A) X H of 2 A- X 1/9 = 23
X (4+3-t-
14-f25\ 11 39 70_57 m 11 39 70_33
70 / ^91^19^69~23^ 70 ^91^19^69" 7
-4?
(12) (3§-lf2+n-2H)x38i of A = (3-1+1-24-
60-42+3}5-ll\ 153 ^_ 37 153 ^_111 _ ^15
72' Z"" 4 ''17~24'' 4 "" 17" 16 ~V
(13) f of (i+i-A+i) X i of (2A+I) = 4 of
/15+9-124-5\ 2 . / 3+10\
( 45 ;"3^H^+T6-) =
3 17 2 45
4 "" 45 ''3'' 16
17
82'
(14) i(i+i) of (li -I- 21)} X {{2h - H) of (3 A- - ?)i =
""6^12^7^ 70 "" 36 36*
jjgga^ajwwgrr
!P!SiiiniiS<
s '
88 KEY. [Elem. Aurni
(15) {1^ of 2H of (l-*)j X \2} of (4^-3|) of -j^cAj!
10 . 53 ^ 1 /„5 „ 8 . 45 \ 10 53 1
21
15^106" 2 ~ 2'
Ex. XL VII. (p. 86.)
(l)M-^^ =
15x7 21
(2)
a. j_
(3)-,
1 1
(4)4|-f.6| =
(5) 56-5-5^ = 56-5-
(6) 7^ -5- 4#r =
54
20 X 5 "' :
20 J
2x5
3
1 =
5x8"
^'6'
6x5
10
M
11x3
-11*
59
t
6 ■
55
' 8
29x8
6x55
40
■ 7
56
■~lx
x7 4
40"
80
54)
<21
20*
116
165*
49
8
:.-9;
21
__ 38
7^6 ~ 43 ~ 43'
1 83 83 83 8 2
(7) i of 201-J-lOf = gX-^ -5- -Q- = jgX^ _ g.
3 11 ^ 5 9 33 45
(8)^0f5i-fA0f9 = gXy4-^X:^=^-»-g^:
33x22 .46
10x45
^75*
(9)(|of7i-,«f)-f-l|={(
rd 15\ 8 ) 11
J"" 2^ 17J • 9 -
/9 8\ 11 137
V3~17; ^ 9 - 34 '
It 137x9 _ ^111
34x11 aV4
Ex. XLVIII.]
KEY.
89
(10) a+f-i) -i- c^+i) =
S2
4+15-10 12+10 9
(11) o:
20 15
9xlo'_g7
15 ■" 20 X 22 ~ 8b*
27x1
218=^-^-210
4x210
20
83*
8x1 3
(12)1^3 = 4-^^ = 3.
44.1, 4i 17^15 __llxi_l! =il.
(13) 4i:i=3i"-T 4 "^4xl5~15 15'
9. 13
2 is tlie next whole number; 2— 1|^ — ^5-
6V
Ex. XLVIII. (p. 87.)
(1) ^ =¥.-*- v-=¥x^=-m=im-
(2)^ = 6^1 = 0x^=1 = 21.
(3)| = |-»-6 = |xi = t.
(5)J = 5-^"»^ = ^^-^'^ = ^^ = ^^^^
.1, 7 145 -f ^_28
<^> fe " 45"*' 36 == 45; 145 - 7^'
(8)^-^^?-|^ = |f-^ = -.^^-'
I\
.00
KEY.
[Elem. Aiuth.
(10) 2i^8t+4^ = ^-±p^ = ^? = m X II = 1-m
t+f
It
(11) {y+4-Aof ♦} ^ li = (i?+-A-i«)x}=il
V 5C — S
X 4 — 5.
(12) (^ of -h) - (I of 15) = ^ X tIt X A ^ V- X A
xl5 = i^|§-*-V = imx4\=T(^^f¥-
lA
(13)
^tt3 of ^^ ^^^ _ 1. of ^ - -^A-
(14) gJ~+|-iA = 4M+A-ivV = 3mi
Ex, XLIX. (p. 88.)
2 2 X 100
(l)gOf$l =
cts. = 40 ctsk
3 , 3x8^ ^.
(2) g ml. = -g- fur. = 3 fur.
3 3x4 ,5 5 5x25
(3) }i cwt. = -^ qrs. ~lij qrs ; j^ qr, = —,j— lbs. =
.0
6
r. X 10
5x16
17^1bs; i^lb. =— — oz. = 13^ oz.; ij;OZ. =— ^
(Irs.:
Ik drs. ; .-. value is 1 qr., 17 lbs., 18 oz., 11^ clrs.
Ex. XLIX.]
KEY.
9x43
m
(4) 5ft of 2 tons, 3 cwt. = -^^ cwt. = 19^ cwt.; gTjcwt.
20
7x4 8 8
'20
20'
8x25
^20 "!*"•' 20'^''' ■" 20
.-. value is 19 cwt. Iqr. 10 lbs
lbs. = 10 lbs. ;
,^, 8" „ , ^^ 3x20 7 7
(5) jg of 3 mis., 2 fur.,= — g— fur. = 4^ fur. ; g fur. =
7x40
3 per. = 35 per. ; .-. value is 4 fur. 35 per.
4 ^ , « « , %(3 ac., 2 per., 3 3^ds.)x4
g of 3 ac., 2 per., 3 yds. =5^^ n — -
(6)5
12 ac, 8 per., 12 yds.
= 2 ac, 1 ro., 25 per., 20 yds., 4 ft.,
136^ in.
5
/i^v " ^^.„ ^« , (5 lbs., 13 dwts.) X 5
(7) g of 5 lbs., 13 dwts.- ^^ -—^ — =
25 lbs., 3 oz., 5 dwts.
6
(8) g of 68 yds., 2 nls. =
476 yds., 3 qrs., 2 nls
= 4 lbs., 2 oz., 10 dwts., 20 grs.
(68 yds., 2 nls.) x 7
8
8
(9) jj of £26 8s
£79 6s. 9d.
= 59 yds., 2 qrs.. If nls.
,_ (£26 8s. lid.) X 3
lid. = rr- =
11
6
(10) ^ of 128 lbs., 2 sc =
768 lbs., 4 drs.
= £7 4s. 3d.
(1281bs., 2sc.)x6
= 109 lbs., 8 oz., 5 drs. 8^ grs.
93
KEY
[Elem. AltlTII.
7,3^ ,,3 38 3, 3,
(11) o ^i r of lOnhrs. = — Ill's. — C^^hi-s. ; ?: lirs. =
,OU O t> o o
36 inin.; .*. value is 5 lirs., 86 miu.
(13) gibs. =9^oz.; goz. = 9Qclrs.; 7 lbs., 9 oz., Oidrs.
3 4
. (13) i^ of ~ of $43 = ij of $43 = $.34.
3 1 1
(14) Tq dy. = 7g lirs. ; ^ hr.= 13 min. ; 7 hrs. 13 min.
(15) yq of' 34 cds. = 18^ cds. ; ^ cd. = 04 c. ft. ;
, . .*. value is 13 cds., 64 c. ft.
Ex L. (p. 88.)
40 1
(1) 3s. 4d. = 40d., £l-340d.; .*. fract". = gio ~ 0*
(3) 3 r., 13 per. = 93 per., 3 ac. =480 per.; .*. fract".=
93
31
480 "~ 100*
(3) 3 wks., 10 min. = 30356 min., ibr. = 30 mm. ;
30356 15138
.-. fract". = -^0^ f -jg-. •
(4) 1 lb., 1 oz., 3 dwts. = 363 dwts., 3 lbs. = 480 dwts.;
. . n -^
.*. tract". — 4^0'
Jo) 1 lb., 5 oz. = 408 sc, 3 lbs., 1 sc. = 577 sc;
,*-. iract . — 'ii?^*
Ex. L.]
KEY.
93
(6) 8 ac, 3 r. = 1400 per., 2 ac., 32 per. = 352 per. ;
1400 175
.-. fract^ - ggg - ^^ .
(7) 4 yds., 2 ft, 120 in. = 8000 in., 3 per., 13i yds., 1 ft.,
72in.^l35000in.;.-.fractn.=:So = ^-
(8) £1 18s. = 88s., £7 =• 140s. ; .-. fract".
140~70-
(9) 2 bu., 1 pk. = 18 galst, 4 bu., 1 gal. = 33 gals. ;
. ^ _!?-£
(10) $209, $5043-; .-. fract". = ^"=^-
(11) 2 yds., 2 ft. =- 90 in., 13 per., 3 yds,, 6 in. = 2688 in..
.-. fraxst". _ g^gg - gg.
(12) 1 lb. Troy, - 5760 grs., 1 lb. avoir. = 7000 grs. ;
5760 144
••^^^^ --7000" 175'
(13) 3 qts., 7 bu. ~ 224 qts. ; .-. fract". = ^1^.
(14) H ycls. = 54 in., 4 mis., 2 fur. = 269280 in. ;
54 3
• • '''^^^ • - 2G9280 ~ 14960*
(15) 1 yd. 4 in. = 1300 in., 5 ac, 11 per. = 8140240*in.;
1300 825
• tropf — ————— — — —
■S8BBM
94
/
KEY.
Ex. LI. (p. 89.)
[Elem. Akitii.
^ of $14 2 14 2 ^__1
3 400
5^^ 1
9 _1_
^ 1 ^ 482
f of 2 ac, 2 ro. f of 400 per.
^^^ i of 3 ac., 2 per. ~ i of 482 per.
1080
" 241'
2i of 8 lbs., 6 dwt. __ f of 17424 gr8. _ 5 ^ 17424
^^^ li of 6 lbs., 12 grs. ~ ^ of 34572 grs. 2 1
3 1
^4^34572
5445
5762*
(4)
m of 3s. 6d. _ V of 4 2d. _ 51 42 1
£1
240d.
1 240
357
'160*
3i of 10 cwt, 2 grs. ¥ of 42 qr8. _10 42 J__7
<^) TT^, ■"" 80 qrs. "31 80-4*
3i of 2 ac, 3 ro. _ I of 880 h f per. _ 7^880^
(^^ 2ro.,2iper. ~ 165 hf, per. 2 1
1 56
165
n
O
(7)
l^ofnb. troy |of 5760 grs. _5 5760
1 lb. Avoir. ~ 7000 grs. "8^^ 1
7000
18
'8o
3 , £2 4s. 7^d. ^ of 1071 half-pence
(8) % of -
2s.
1071
120 half-pence
1 21
20
17 ""
.9)
(10)
1 "120" 2*
-j^f of 2f mis. __ - ,\- of V mis. _ ^
■J of I mis. ~~ i of I mis.
6i of 3 cords V^ of 24 cd. ll 13 24 1 156
11 2 9_27
11 "" 4 ''l''7~14-
vr VM. It.
Ex. L1I.J
KEY
(11)
8i of lbs., 3 sc. *i^ofl730sc. 25 1730
lib.
288
288 sc.
21625
432 •
(13)
,,o^ ^ o f f of 121 _ 4 2 21 1
^^^^ ""$7 ~7''3'^T''7
-t% of 8 yds., 2 nls. A^ of 130 ills.
2^ ells Eng.
/..x SloflOhrs.
H^ nls.
351
324*
"r
9^ 130
IG"" 1 ""
_3^
140
^oflOhrs .
24 hrs.
^^3 10
8"T
^24 =
115
00*
Ex. LII. (p. 92.)
(1) f of 7^ = f = what A sells to 0.
1^ of i = jV = what A sells to B.
i—{}+h) = -h = ^'s remainmg portion
-h+^ = -h = ^'s portion.
i = (7'8 portion.
(2)0 9-f-|=:24.
O 4i+3A=:8f; 4i-3,a, = f; 8|-f = 7|.
(3) Lesser fraction = (f — 1)-5-2 = -g^y.
Greater fraction = f-io or -gV-l-f = f^.
(4) C) U of 2^ = f I ; ^^th = 1-A.
e)iof2| = ^; 3f-^ = lM.
(5) A gives 5 i of his money; .-. he has ^ rem'g.
He then gives G^of^-l and has rem'g ^--| = f.
He next gives i) i of i= i% and has rem'g f - A=-,=»g-.
.-. ^ has /i ar d D has 1% ; or -4 has twice as much
as D.
(6) She spends \ leaving | ; next spends f of f =|; hence
she has spent i+| - ^^ and has left J, which by
question = $4.20; .-. her her whole sum was 84.20
X 6 = $25.20.
06
KEY.
[Elem. Aritii.
i
(7) T*f =r $90 ; .-. 1^- = $30; .'. value of vcssi 1 = $30 x
11 = $330. .-. i = $110.
(8) 100 cts.— 5 cts.= 95 cts. ; .-. whole income = \^^ of
$855 = $900.
(9) ^ rr I = amount of reduction ; hence | of $54= $36
= amount of reduction.
(10) f of a rabbit is worth |s. ; .". f is worth |s. = 2d.
and a rabbit is worth 2d. x 7 = Is. 2d.; .*. f of a
rabbit is worth 8fd.= the worth of ^ of a pig; .*.
a pig is worth 20 x 8|d.= 14s. and 100 pigs are
worth 100 X 14s. = £70.
(11) 1 rifleman shoots ^-P- rounds in 91 minutes.or in 1
28 2
minute ?«-^gT = t^ of a round ; .*. 37 riflemen in
4i hrs. (or 255 min.) will shoot (iV x 37 x 255)
rounds = 385^^ rounds.
(12) I = $12.60 ; .-. ^ = $4.20, and whole = 8 x
$33.60.
.20 =
(13) 28 sheep eat as much as 15 cows ;
.*. 1 sheep eats as much as H cow;
.•. 20 sheep eat as much as |f x 20 = 10^ com'S;
33 cows and 20 sheep = 33 cows-l-lOf cows = 43^
cows;
15 cows graze in 11 days 5 ac. ;
5
.'. 1 cow grazes in 1 day ..-■.. or -is ac. ;
.'. 43f cows graze in 1 day ^h x ^?^» or W ac.
18 X 77
.'. 43? cows graze 18 ac. in 18-*- W days, or-
= 131^ days.
102
(14) Q) A is to have half as much again as B, .*. $94.50
must be divided into 5 equal shares of which
A is to have 3 and i? 2 ; $94.50-i-5 = $18.90 ;
$18.90 X 3 = $56.70 = ^'s share ; $18.90 ;< 2 =
$37.80 r^ B'8 share.
(Continued on next page.)
(1
(1
(1
i^
•Ex. T.U.]
KEY.
0?
(14 continued.)
O 71 is to have half -4's share or . I is to have
twice i?'s; .-. $94.50 must he clivi ccl i o *:
eqiv\l shp^^, of which A is to have 2 and jj 1
$V =$31.50; $31.00x2 = $63.00 -^'s
shu , - oi.50 X 1 = $31.50 = J3'8 share. .
(t/^^ Amount of debt = $500 + ($250 x 2)+($75 x 3) =
$1225; amount of property = $625 ; .'. he will
pay $
ft26. —
\ i'Zli
$^^ in the $ and the first creditor will
receive $500 x t^ = $255.10i§.
(10) $750 would purchase dHv = f t7 of the mine ; .*.
■\\- of tl"^ man's share = -4^^ of the whole mine;
and hiF tire shaie = (^(j+i^^) of the miiie = f .
(17) The first and second dl/"*. contain i^+i = H of
the entire school, 1 erefore the remaining, or -^g
must belong to the tnird div"., which by the ques-
tion contains 80. If 80 = ^% -h = i of 80 = 10,
and the whole, or f f = 25 x 10 = 250.
(18) A can do in 1 day -1^,7 ; B can do in 1 day -^ ; there-
fore A and J? together do in 1 day -,^ + ^^ = ^^ ;
.'. no of days in w hich A and B will together do the
whole work 1
'^°'^ = part done iu one ^ = ii = ^^^ '^'"'^
(19) Eldest son rec'd ^ leaving i|.
Second son rec'd \^ of i| = ^f ^.
Widow rec'd l-(B^+if i?) = m-
Also by the question ii— ^f^ (the eldest son's
share minus the second son's) = $1690, or {f ^ =
$1690 ; .-. whole property = -^^^ — $6250.
Eldest son rec'd H of $6250 = $3250.
Second son rec'd iff of 6250 = $1560.
Widow rec'd ^ of $6250 = $1440.
(20) Since G receives 9 ac. more than A and B ;
.*. 85 ac, 2 ro.— 9 ac. must be equally divided be-
^Continued on next page.)
%->.*lna
IMAGE EVALUATION
TEST TARGET (MT-3)
fe
Va
1.0
I.I
1.25
■ttlM
1^ 1^
2.5
2.2
2.0
iA IIIIII.6
^1
#1
r^
Photographic
Sciences
Corporation
23 WEST MAIN STREET
WEBSTER, N.Y. 14580
(716) 872-4503
m
-^•v
:\
,v
\
^9>
%
'^^
6^
n;
)
^-.^
^^
,V#3"
.^
^
i/j
»8
KEY.
I Hi. KM. Ajtirri.
4^ A ^ (20 continued.)
tn-een A, B, and C7; hence .I's and B's sli^ire =
lO ac, a TO.
3 = 38 ac., 1 ro.
If ^receives l,i? receives A, .-. A'a andi?'8 = 1 A-.
A ^'9 = ^38 ac, 1 ro.) x H = 24 ac, 3 ro., '^
B'a = 13 ac, 2 ro., C's = 47 ac 1 ro.
<^^) £^^ys (one out of each third) paid (t8+304-42) cts
r ^?n' :'• the average payment made by each
boy = ^^ cts. == 80 cts. ; .-. no. of boys = Hi^=^^
(22) First pipe fills ^ of the cistern per minute ; second
and third pipes empty j^+^ = if of the cistern per
minute; .-. part of cistern filled per minnje = J-
cistern
H = .|V
5 = ^^-
No. of minutes =
part filled a min"!'
(33) (>) A and 5 do in 1 day -3^ of the work.
B does in 1 day ^ of the work.
•'• ^ does in 1 day -^—.^^ = ^g^ of the work.
.-. A can do the whole in ^ days = 63^ days.
^') ^ ^P!? T*<f 7^ = r^T? more than J9 in 1 day
.'. A does rt^ X 30 = I more than B in 30 days.
(34) A and i? do ^ of the work in 1 day.
S^A ^^^ ^' ^^ t^® work in 1 day.
/. « ^, 5, and G do ^^-f VV = i% of the work in 1
But ^, B, and C7do A of the work in 1 day
.-. A does iik—,^s =z /^% of the work in 1 day;
.-. no. of days required by ^ = — ;^«-Z?ik_
(26) f remaino in l-t. .J is put into 2^' , 3^. holds f -
(i of f ) = 5^ ; and fills A of 4*. cask, which con-
(Continued on next page.)
Ex. uii.J
KEY.
m
(25 continaed.)
scqnently liolds A -5- A' = h .*. 8<». and 4♦^ togetlici-
hold A+f = H leaving when taken from first
cask /a, which by the question is equivalent to 15
gallons;
.-. !•*. cask holds -^ = 140 gallons,
2"*. cask holds f of 140 = 60 gallons,
8'*. cask holds i^ of 140 = 45 gallons,
4^. cask holds f of 140 = 80 gallons.
(36) While A does i the work B does ^ ;
. •. while A does the whole work B does I ;
.-. while A does the whole work A and B do |.
But A and B do the work in 12 days ; .'.A requires
f of 13 days = 20 days to complete the work alone.
Ex. LIII. (p. 95.)
(l)-3 = -x%; -13 = -^-; •19 = 1^^0-; '301 = iWo ; -270
= -im ; -5653 = imv
(3) -504 = -, Wo- ; -73201 rr-iUWr; -791003 = ^«oWJ\,- ;
•03 = jh ; -0045 = -n^oW
(3) -300 = tm ; 18.741 = ISiVcf^ = WcjV- ; 2-1 = 2^
= H ; -000001 = T-o-shi5ms ; 5-0007 = StgIih! = m%h
(4) 347-02007 = mjmh = ^tmn^- ; 500-005 =
500i^^ J = ^«^S^ ; 5-60746805 = m J^tg§^- ; '0000500
Tff'(nn)oUo'
(5) 29-0050 = 29 hMj;j = WJl¥ ; 20-607 = 20,Wo =
WoV ; 5-00038 = 5to^So o = H^l
Ex. LIV. (p. 96.)
(1)tS = -4; f| = 2-3; W = 23-5; iio = -04; iWif =
•147; i^k = -047..
(2) ^^ = 500-1 ; TiMfeo = -00951 ; ^^ = 5-02 ; y^AftlW
= 00503.
100
KEY
[Elem.
Arith.
V^J iTnrfc^ = -0000002,- ^AWu¥ =. 2076854 :
TOTiWMiniT) = -0000053052.
(4) Seven tenths = -7; thirty thousandths = 030.
(5) Three hundred and three thousandths = 300003 •
one ten thousandth = -0001. '
A ^ZT^' ^""^ ^'^^ ^nn^vedi and four miUionths =
4-000504 ; seventy ten miUionths = '0000070.
(7) -6 = six tenths; •17=seventeen huudredtlis- -07=
seven hundredths. '
41 ^^^ *^Ir ^^^^"^ tliousandths ; -700 = seven hundred
thousandths or seven tenths; 63004 = six and three
thousand and four ten thousandths.
(9) 35-00205 = thh^y.fiveo.nd two hundred and five
hundred iiiousandths ; 400-34000 = four hundred, and
thu-ty.four thousand one hundred thousandths, or four
hundred and thirty-four hundredths.
* (10) -3x10 = 3; -3x100=30 ; -3x10000=3000 • -3 X
10000000 = 3000000; -ISxlol-l'S; -ISxlOollS-
•13x10000 = 1300; '13x10000000=1300000; -WSx
10 = -13; •013x100 = 1-3; -018x10000 = 130' -013 x
10000000 = 130000; 54-0003 x 10= 540008 ; 5'40003x
100 = 540003; 540003x10000 = 540003; 540003 x
10030000 = 540003000; 7430-1 x 10 = 74201 • 7420-1 x
103 = 742010,; 74201 x 10000 = 74201000 ; ' 74201 x
10000000 = 74201000000."
(11)
5-362 5-362 n-^a^
= -5362 ; ~ = -05332 ; -^— ~
"""' 1000000-
10 """-^ ' 100
•000005302 ; ^ = -03 • .-— = -OOT -
MO "'^'lOJ "03,j^^ =
(Continued on next page.)
Ex. LV.]
•0000008 ;
rooio7
KEY,
Cll contianed.)
= 7-00107
ICl
700107
= -700107 ;
10 • — • 100
70.0107 5000 nnno
i0000(n = -0000700107 ; ^ = 5OO ; ^ == tO :
_5000
1000000 "~ '^^'
2'03
^^^^ ioooooo = '^^^^^^os.
(1)
1035
•00643
27-
2-2146
53009
660-34603
Ex.LV. (p. 97.)
24-
185-3000
•98795
3098
•70006
. (3)
186-8
35-2779
1)000-
9-201
830-05764
214086^1
10061-33654
04-25
-008
187-96009
67-3916
5-998347
345-608037
(5)
12-5
20043
7-63201
♦0561
40-23111
Again 12-5 == 12-,^ = igx
20043 = 20tM-o
7-63201 = 7-,^„^oWo
•0561 = -iMio
ic>^-+9o-JL , 763201
^ 1000^ 100000 "^lOOOd
^61
iH?i = 394-
50000+4300 + 632014-5610
100000
ov + Z- . . - = 40
sa
= 40-23111.
!lli ^
100000 - *"iooo63
1
103
•0573
15-
304
507-98076
58507805
673
KEY.
(6)
i £Xi£M. AniTfl.
204=3Ti^o
5G7-98075=567-,WuVb.
™0±40q0i98075^ Z^^^ l^Z^
100000 ~~^®^iooooo=''^^-ooooo= ^^^•^'^^<^5
5060003
18-98
5853097
960-'
(7)
o0o-0003=505to^o
13-98=13-,V,j ^"
5353-097--=5853r!Jir
73330773
"^loooo+^^ioo^^^^^iooo
733l4-?±???^-±^-733il0773 ^_
10000 -^^^^ioooo=^3^2iooo()
=73330773,
-9G0=
773
600734
64-
15-70087013
800003
9-987789
(8)
6-00734=6n^„Vo-u
15-70087013==15ima^„Va.
9-9^7789=9MW4
93-69603913
« 734
^"00000-^^^+^^
92-1-
70087012
::4-8:
3 ^ - 987789
TT "7" v~;
'iOOO60OOO=*=*'«'*«03912.
AniTfl.
iOO*
35-07805
TouTVo
Ex. L\ I.]
KEY.
(9)
103
7-0003=7TTy|fiyij
408-5=408t%
•0808=Tma
•13
7-0003
408-5
978-
•0808
13&3-7111
^3 _3_
100 10000 — 10 ' 10000
1800-»- 3+5000-t-808 ,^„7111
Toooo =^^^ioooo=i^^^"^i"-
+ 40877:+
808
■978=13934-
(D
5-345
8087
2-258
EX.LVL (p. 98.)
(S)
26002
18-9564
70466
(3)
15-67
9-7003
5-9697
(4)
21-
19-90C9
10991
Pifo^
!2.-
302912
mm
(') 1-3 1-3=1A-
-13 -13=,^^^,
(5)
207-
2-07=2Tk
117 204-93
liV~i¥o =}H=1-17 ; 207- 2t5o =204-,ao%=204-93.
^"^ "^21 76-3=76,% 67-5803 67-5803 =67,Wu^
7C3 7-63=7iVo 67-3 67-3=67,%
CS-67 -2803
761%— 7,U-=68-iVu =68-67 ;
67A'y\,%-67A=-,Wo%=-2803 ;
(3) 601-
428-90456
428-90456=428iVoWa
72-09544
501-438 ,V«Vo%=72t35.VJj5 =72-09544 ;
(Contintiea on next page.)
104
5324-
53 21
5270-76
<^) 4-42
-00043
4-41958
•007
•0000007
•0069993
KEY. .
(5 Continued.)
53-24=53-AV
[Elkm. Arith.
5324-53AAy=5270i^%:=5270-76;
4-42=4-,^
•00042=T^ife
4i^ftT-Tiri?Tro=4iVbWo-=4-41958
•007=-n(W
•0000007=TwJWiF7 '
To'o ~ TiJ¥cfo(7tn) = TiA)WftjTf= -0069993.
(') 2-3
•23
2-07
< (6)
O 23-
3-07
20-93
•005
(7)
O 20-009
•029
•095
19980
i''
•7
•087
•613
(8)
79-8065
1-2
•12
•012
210^
211-332
(10)
(9)
•332=A%, l~-.Wo=
.Jifia ifii
10 00 — 76 0«
) 31-25
3059
(2) 215-263
69504
7-0004
•05
4508 ''
80-3007
28191
235-6758
208-3126
125-3807
a-9504
•
125-3807
263-8668
1840003
82-9319
'
Ex. lvil]
(1)
3-25
•35
1625
975
11375
20607
•20607
144249
123642
41214
4246-48449
67068
2-004
(r>)
228272
114136
114-364272,
.. 536
»• 700
375200,
■^ 701609
50-805
8507645
6612072
3507545
KEY.
Ex, LVII. (p, 98.)
C'osa
2-7
42245
12070
16-2945
,(8)
40004
2-03
120012
80008
81-20812
105
(4)
680-35
•0049
61^315
272140
3-333715
60-70
11
(6)
00-71 =60 iVtf-
667-81,
60-71 66781 ^,,^,
Too-^i^=-ioo-=^^^'^^'
57-068 X 2-004=H5§^a x m»!=
VWoWo^=114-86&72; '
5-36 X 700=H$ X iftii:=e^.
=*ft^M&^^^^=356-40164745.j.
356-40164745
too
48067
•00087
886469
144201
•01778479,
54-3047
900005
KEY
(7)
[Elbm. Arith.
48;0«7x -00037 = ^^f x t^§J,^ =
jmmh = -01778479;
2715235
4887423
488-745015235,
2-568
•00025?
HUnmW- = 488-745015235 ;
12840
6136
0)
5-5
•055
275
275
•8025
550
151250
15125
ie«-8750
•0055
831875
881875
2-568 X -00025 = m^ x tttMo a =
tjfI JJ^ft^rs- = -000642*.
•00064200 = -000642
(8>
6-5 X -055 X 650 x -0065 = ^|^ x tMtt x^^x^
1*17 = iWft)^- =-0150625; " ■ -
•9150625, (Continued on next psge.)
i^y.
Ex. Lviii.]
6-2
860
1050
KEY.
(8 contlnaed.)
107
=v^A^:i^r*=^**'<^^'^"^'<-«-
10860
85
6425
8680
922-25
•0004
(9)
37-85
7-35
18925
11355
26495
278-1975 yds.
(10)
885
•95
1825
8286
346-75 =:
346f loaves.
•368900 = -3689.
27) 88-372 02-36
27
%
Ex. LVIII. Q). 100.)
(1)
68
54
97
81
162
162
33^372+2-7 = ^Wcf x i^ = ^J^ = 12-36.
(2)
;27) •83372 (1-236 •33372-5--27 = -mm x W =
IMS =1-236.
Z(3)
•333724-27 = -,^m>^- - h =
(4)
•27) 83372-00 (123600 33372^-27 = ^^'-^ x W =
^H¥^^= 123600.
w -i
103
KEY.
(5)
[ElBM. AiUTH.
•00027) 8337200000 (123C00O0O 33372-*- 00027 ==
Aa^a X xii^^iik = 128000000.
•323) 561 0833 (17371
828
(6)
2380
2261
— 5G1-0833 ♦-•323 = mm^ x ^m = -^^^
1198 =17371.
969
2293
2261
323
823
(7)
•323) 5610833-000 (17371000 5610833-!- '323 = ^U^^
= Wi^ = 17371000.
(8)
3-23) 56108-33 (17371 56108-33-4-3-23 = '^^%^^ x
^ ■iSi==^VA^^= 17371.
(9)
•0000328) 5610-8330000 (173710000 5610-838-*-
•0000323 = ^Vj^ X ^^^i^^ = 178710000.
3-25) 552-5325 (17001
825
(10)
2275 552-5325+3-25 = mm^x m = ^W 1
2275 17001 ; ^
325
325
- *. *~ ^ ..»».,
\ *..«*V^-4 I'h Ji
Ex. rviii.J
KEY.
109
•0032o) 552'5m0 (HOO^Vr^lss' 5325 ^. 00325==
^nm^ X Ajyyyiii = nooio.
104-3) 2-419003 (00521
23215
(11)
9750 2-410003+464-3 = mUU x Mn =
9286
4043
4043
bUW = -00521;
•004043) 2-419003 (521
2-7) -000081 (-00003
81
2-4I9008-H -004643 = mUU
.i.n ^-'^A^'^'^ = 5Jil
'00008i-i-2-7 = i^.^,^xi^
= TT) <j\j = -00003 ;
•0027) -000081 (-03 •00081-f.-0027 = -nnfoW x ^W^
27000) -000081 (-000000003, -000081 -^27000 = \^hmo
j-rh-rro = iT^uxr-JVo (Jou = -OOOOOOCOa
(13)
2-00099) 218051 -081884 (108971-0
200099
1795208
1000792
1944101
1800191
1432708
1400693
320158
200099
218051-081884-^200099 =
1200594
1300594
200099) 218051081884 (1-08971«
218051-081884-^200099= ^
1 » (I (1 (, X i nlitfo g =
lounuoo — 1 Uoy/lO.
no
KEY.
[Elem. Arith.
(14)
11) 121 (-011 131-^-11 = iWo X A = -Oil ;
121
1100) -12100 (00011
•0011) -1210000 (110
mj_-l 1 AA iii. ^ _.I
. iiuu — 1 (, X 1 nrij — '
•00011 ;
LL
100000
•131 H- -0011 = -iWo X -Lfli^f A =
.110.
(15)
•000193) 393-720C - (2040000
386
-^ 393-72-^ ^000193 = ^^BF x ^H^^^
773 =2040000:
<■ 773
1^93) 393^73 (204 393-72-i-l-93 = ^U^ x f S3 =
893-72 204;
193000) 393-72000 (-00204 393-72 -^ 193000 = ^U^ x
39372000 TLifo -o-TS = to%%u = 00204.
li
(16)
•03275) 590-48250 (18030
3275
26298 590-4825-^-03275 = ^f,U^^ x Hm^
26200 z= 18030 ;
9825
9825
337500) 590-4825000 (0018030 590-4835-1-327500 =
Aaaisq. y. __..i — _ 1 «Q3 •nniQA'j
X
Ex. LVIII.]
KEY.
(17)
111
100103) 213-419596 (313-3
200206
133185
100103
S30329
800809
213-4195964-1-00103 :
X LQ.Q.Q.Q.Q.Q. — 2JL3l2.
To(.'ouuij
; 213-2 ;
200206
200206
100103) 213-419596 (002133 213^419596-^100103 =
ii.ail9.J19£ y !,-__ _ _-2JLai^
Tuuoouo '^luuloT — lorooJo —
•002132.
<18)
•0034
'24
■24) -2424 (-0101
24
(19)
-35) -000200 (-0008
200
24
24
(20)
1-75) 21-875 (12-5 clays,
175 orlS^da^^
437
850
875
'875
(31)
-75) 64-135 (85-5 limes,
600 or 85i times.
413
,J75
(33)
'033) 00070343 (03054
^9
124 •
115
OiO
575
8^
92
112
KEY. [Elem. Arith.
Ex. LIX. (p. 101.)
*3) 1-9000 (6-333 1-9
18
10
9
10
(1)
-iuVo=f^-3t = 6-333;
•03X1 •90000(63-333 1-9 --03 = ^ x ^ = ^^ x J-i^a ^
^^¥^^ X To^.ro = ¥oWL 63-333]
S00)l-900([-00633 l-9^300 = Hx,k = -3-o%^ ^- =
\^^h?- X TifoD- = tUIo = -00033, or
•006.
(3)
159)4^37 (-031 4-936 h- 159 = H^ x rf.
167
159
9 = .^iW X Ttfo-f?
1-59) 4-93700(3-ia5 4-937 -|- 1-59 = HU x jf B -^.W x
o'lOo ;
167
159
800
795
1590)4-937 (-003 4937 -^ 1590 = nU x t«Vo - HU x
LOtll)
— * I (I I i J I
lOUO
•001
Ex. LX.]
KEY.
113
(3)
53) 329744000 (0221*584 3'29744 -i- 53 = a.2.a.i^LQjiQ. ^
318 7^00= ^¥oW^ = 6221 -584 ;
117
106
I
114
106
84
53
310
265
450
424
310
260
212
•0053) 329744-0000000 (62215849'056,
329744 H-*0053 = 3297440000000 x ^^.J^io = ^^^Wu^u^^^^
= 62215849-056;
5300) 329744 (62*215, 329744 -i- 5300 = aaaxiin ^ i
=:W,-\,^ = 62-215. •
Ex. LX. (p. 102.)
(1)
4|l-00. 513-0. 4|60. 5|l-0 . .^ __. 5139-0
815000. 1013-0 . .^
~^025' ~3 •• '•
7-8
rt.o
16j4
20 -^' 4
3-00
-7500;
-1875
10
16 j 4
(
(3)
15-00
3-7500;
-9375
4 3100
£80; 33] 8
-05 (
Alls. = 8-9S75 ;
8 37-000
7-75000; 40
ftaft7.\
Ans. - 7.925.
I'
4'62i>
mri
114
5 470
50-^10
KEY.
IElem. Akith,
(3)
9;40;
•94
135
5
5
TO
1-40
•280
/. Ans. = 4056 ;
•056
fio
50oJ ''
3;0
•30
•030
635
•006;
lOLl
rs
8
8
2
300Q
" -375000
5
5
5
aw
O
9900
19-80
3-960
7930
^046875000
•1584;
Ans. =840029396875.
•0058593750
•0029296875
(4)
f of 1^ = ,%
138
8
65^00
" 16-8500
~ 40635000
41300
3i of 3 J = 8h
-70
8 15000
3^ of 4i of 5i = 70if , 04 -! 8
-5078135;
'. Ans. = 8-75;
1-875000
1-0 --8125 --7875
(5) '
5j3;0
•6
-234375
.•.11 = 1-6;
.*. Ans. =
76-334375,
7875 + 3-<35 = 3-9135, ^^ j ^
130
3-25
11} =-8125;
.01 rtr
(Oontiuuocl on nextpa;:):tv)
ITU,
056;
75.
s. =
375.
125;
Ex. LXI.]
5 5-
40-^8
KEY.
(5 continued.)
1000 .-. 3-A = 3-125;
•125
116
1HH--75 of U of 6| = 11-5 + -75 of W = ll'5 + -75 x
6^1 = 115 + -75 X 6-48 = 11-5 -\- 4-86 = 16-30.
Ex. LXI. (p. 104.)
(1) '
3|20. OjlO. 7|G0 . 12IZ:?__. (^
•583' 1'^- 3
5 110
•C
•1
9 3
8M9
4
44 -J 11
•857142
(3)
r3.
'^^^33 .-. Ans. :^G037; 37)5'0(-135
37
•037
700
1-75 .•. Ans. = 1001590;
-159'J
130
111
190
185
Ans. =
7-135 ;
50
17) 15-0 (-8823529411764705
136
140
136
40
34
50
34
160
153
GO
51
90
85
70
68
20
30
17
130
119
110
102
80
GS
.-. Ans. =
2-8823529411764705.
120
119
100
85
150
136
1 110
)
!
495^
'5
9
11
670
18-4
KEY. [
(3)
'5
5
1375 S 5
11
.•. Ans.
Elem. Aritit
170
3-40
1-488
•680
•185
•186
; .-. Ans. = 11-18^;
•01286
= 2301236.
(4)
•2 = t; -05 = A; 'lS = U = -h; -156 = ^10^^=1^4 =
-,V« ; -027027 = -UUo^,^ = ^mk = iff ;
•285714 = UUU = h
(5)
•560 = nW^ = U^ = ^ ; -743 = Hto^ = ^|§ = a|| .
•20235 = HmT^ = tUU ; 19-305 = lO^Wo^ii- = 19|^f
= 19U; 20-02916 = 20^%\%-,%^ = 20#,V,4, = 20j5o.
(6)
6-18153153 = 6^18153 = OHW.Kf^ = C^r^M = 6^i%;
15-692307692307 = 15092807= lofg Iff | = 15,%.
(8)
- (7)
. 4-3333383
164545454
757352852
96-5281139
••• Ans. = 96-528114.
(9)
3-8564646
2-0887777
8-2883333
26-7967967
7-4134184
87-4435484
Ans. = 37-443543.
(10)
52-8666666
8-3723572
1-8176869
.•. Ans. = 1-817686.
7-6+5-3 = 7fx 5^=40^
44-4943094
.•. Ans. = 44-494309.
(11)
40-8; 85i X -736 = m X f M
= i?- X iVo = im = -2587223 ; -13 x -2 x -4 = ^§ x i
X t ^ A X -^ + ^ = ^h =-0li85.
Ex. Lxn.]
KEY.
117
(12)
6-7 -4- 2-6 = CJ -^ 2f = ^ X I = f i = 2^ =2'5416 ; '2627
^ 1-926 = nvu-ci^ -^ i^w^ = uu -*- nu =i¥o^- -*-
m% = iWA- =-136 ; -371 -i- 5 = ^^o^ - 5 = f |8- -h 5
= i^^ = -0743 ; 42-0463 -*- 136 = 42t Uh -*- IM =
42T-Jg!u X U = \5»W,l^ = 80-833953.
Ex. LXII (p. 105.),
(1)
(2)
(3)
•75 , ■
100
•875
5
-625
loa
75 00 cts.
Ans. 75 cts.
$4-375
100
62-500 cts.
Ans. 62i cts.
Ans. $4.37i cts.
37-500 cts.
(4)
(5)
(6)
•625 cwt.
4
•375
8
•179
20
2-500 qrs.
25
3000 fur.
Ans. 3 fur.
3^500 cwt
4
2500
1000
2000 qrs.
Ans. 3 cwt. 2 qrs.
12-500 lbs.
16
^ 3000
500
1
8000 oz. Ans. 2 qts. 12 lbs. 8 oz.
118
(7)
•46876
50
23-437503.
12
6-25000d.
4
KEY.
(8)
•0625
90
[Elem. Arith.
(9)
•175
12
\\
5-6250d.
4
2100 oz,
20
2-5000q.
2000 dwt.
I'OOOOOq.
(10)
4-65 X 4 a. 2 ro.
4-65
18
Ans. 5id. 5q. Ans. 2 lbs. 2 oz. 2 dwt.
Ans. 23s. 5id.
(11)
1004
100
372
465
100400 per.
Ans. 1004 per., or 6 a. 1 ro. 4 per.
83-70 ro.
40
28-00 per.
Ana 83 ro. 28 per., or 20 a. 3 ro. 28 per.
(13)
2-56
625
1280
612
1280
134400 qrs.
Ans. 1344 qrs., or £1 8s.
(13)
5-00875
25
2504375
1001750
125-21875 dys.
24
87500
43750
5-25000 hrs.
Ans. 125 dys. 5 hrs. 15 min., —
or 17 wks. 6 dys. 5 hrs. 15 min. 15 00000 min.
JITH.
BX. LXII.]
KEY.
119
z^
TVt.
dwt.
per.
(14)
(16)
•604
6 lbs. 2 sc.= 1442 sc.
24
305
2016
1008
12096 hrs.
60
5-760 mm.
60
45-600 sec.
Ans. 12 dys. 12 hrs. 5 min. 456 sec.
(16)
£4 Is. = 81s.
3-0085
81
7210
4326
4398-10
20
200 grs.
Ans. 4398 sc, 2 grs., or 15 lbs.
8 oz. 2 drs. 2 grs.
(17)
1 ac. 3 ro. 5 po.= 285 po,
7034 -
585 "^
30085 j
^40680
243-6885S.
12
8-2620^.
4
35170
56272 "
14068 4^
2004-690 per.
m
l-0480(i.
Ans. 2438. 8d. 1048q. or
£12 3s. 8id. -048q.
20700
1725
20-8725 yds.
9
7-8525 ft.
144
Ml i»* U^^\^ MfA •
at A/VA J _- _ ^^ ^^ ._ _.
or 12 a. 2 ro. 4 po. 20 yds.
7 ft. 122-76 in.
34100
34100
122-7600 in.
120
KEY.
[Elem. Aiuth.
(18)
14 lbs. 1 oz. 6 grs.= 92646 grs.
92646
5005
463230
463230
463693-230 grs.,
or 80 lbs. 6 oz. 1323 grs.
(19) -3 of $2 r: ^ or i of $2 = 66f cts.
(20) -54 of 16s. 6cl.=: f ^ of 198cl.= 108d.= 9s.
^V-) *^iL^^ * *^^ = ""^sW^ of 20 cwt.= m of 20 cwt
= -Ilk of 20 cwt.= 4 cwt. 8 qrs. 11 lbs. 10 oz. lOf drs.
(22) 6-83 of £5 = 6^^^^ of £5 = 6^^ of £5 = 6f of £5
= £34^ =^£34 8h. 4d.
,,.^^^^ J'?^^ °^ 2* l^«-= ^^^"^'^^ of 2i lbe.= 2m of 2i
lbs.= 2H of 2 lbs. 6 oz.= 2tJof 30oz.= 71i oz.= 51bs.
11 oz. 10 dwt.
(24) 6-2 of a c. yd.= 6^ of 27 c. ft.= 168 c. ft.= 6 c.
yds. 6 c. ft. ,
(25) 18-72 of an ac.= 18|| ac.=: 18A ac.= 18 ac. 2 ro.
86 po. 11 yds.
Ml^'^^^ ^^ 1^^ ^^^®^s '^ 2f a-|L of lOOa ga. = 2^§ixr
of l^Mr" 3d?lir of 1000 gs.= 2006i g^.= 3006 gs. 7s,
= £2166 10s.
•025
,25
(27) £-634375
30
12-687500S.
12
a250000d.
1-OOOOOOq.
125
50 .
625s,
12
7-500d.
4"
2000
8-16 of 808.= Sif o-L
of 80s. =r 3i of 30s.
= 95s.= £415s.
.-. value reqd = 13s. 8id.+ 7id + £4-15 = £5 8s. 3fd.
Ex. Lxin.]
KEY.
121
(28) -6 of an ac.=.f ac.= f ac.= 2 ro. 20 po. 20 yds.
I ft. 73 in. ; 035 of a ro.= e25 of 40 po.= 2'6 po. A- po.
= A of 30i yds.= 11 yds. . f 1 1 i'
2 ro. 20 po. 20 yds. 1 ft. 72 in.+ 25 po. 11 yds.= 8 ro.
II po. 9 yds. 1 ft. 72 in.
(29) 0-714385 of Is. 9d.= ^lUW of 21d.= Of of 21d,
= 141d.=: lis. 9d. ; -0833 of £7 4s.= HM^ of 144s.=
^oSr of 144s.= -,\ of 144s. = ISs.; -251190470 of Os. 8d.
= f HiJ^Jf^o^^ of 80d.= MiHSB^ of 80d.= Hir of
80d.= Is. 8 Ad.
/. value req"» = lis. 9d.-12s.-h Is. 8-Acl.= Is. 5-Ad. *
Ex. LXIII. (p. 100.)
, (1) ' (2)
1 qr. 5 lbs. = 30 lbs. / $2*50 = 250 cts.
1 cwt. = 4 X 25 = 100 lbs. $10 = 1000 cts.
.-. fr. req<i is -,%^o or i% ='3. . .*. fr. req^ = -j^^JV =
or thus: (3) i=-25.
30-
40
4
25
4
(4;^
11-
A"
•3
CO
24
3-5
•14583
8-275
4
12
(5)
•8175
0-5
-5410
(C) 2 fur.= (2 X 40 ¥ 5^ x 3 x 12) in.= 15840 In.
.-. fr. rcq* is ^M\% = ttW ='00022095.
<7) 2 oz. 18 dwt=53 dwt. ; 1 lb. =240 dwt
.-. fr. reqd = -/^^ = -22083. ._,.
<8) 41bs. 2 sc.= 1154 sc; 1 oz. =24 sc >
.-. fr. reqd = J-i-f 4 _ 4S'Qsk -
(9) .^
73' ^ - (10
T lib. Troy = 5700 grs.
1 lb. Avoir. = 7000 ffrs,
V fjf&= •82285714 /
0083333
0-X{\af\A A A
'3785493827100
m
KEY.
[Elkm. AiiiTir.
v-
(11)
12 9-
20
10-75
(12)
12
30
17-5883
•5875 I .3791(5
(13) 2 wks 6i dys.= 48G iirs. ; 4 dys. 3 brs.= 99 lira.
.-. fr. req" = Vs^ = 4-90.
(14) 2 lbs. 14 oz.= 46 oz. ; 18 Ibs.^ 288 oz.
/. fr. req<» = A%- = lA =15973.
i:x. LXIV. (p. 107.)
PAPEIl I.
(3)
(0 1018269
I 20979
100001050
54000003000
400000006
999990
54302043294
('-) 400001
300725
9927G
(4)
268936785
5689
2420431065
2151494280
1613620710
1344683925
268936785) 1529981369865 (5680
1344683925
1852074448
3613620710
2393537386.
2151494280
2420431065
2420431003
L'ir.
Ex. LXIV.I
KEY.
1*>^
ira.
JIultipUcatlon may bo proved by division and ^isa Vfmi.
(5)
C974)27027027".27 (3875308HU
20933
01050
55793
9
57167
65793
8875398
0974
«
53583
48818
15501593
2712778C
34878583
23253388
37647
84870
27037035653
1375
27770
20923
68482
G27G6-
27037037027
1375
(C)
13
8
it ^
40
8
t ^
mi. fur. per.
13 3 6
8
98
40
777348 in.
3936
64779 ft.
5i
21593 yds.
3
19630
11 43186
1963
3926 per.
21593
3
98-6 per,
12-2 fur.
L3 mi. 3 fur. 6 i
04779
13
77734y
134
2
2
3
(1)
27 36 43 48 '
KEY.
PAPER II.
[Elem. Arith.
27 18 21 24
27 9 21 13
3 5
6 9
9^74
L. C. M.= 2x2x3x9x7
X 4 ==3034.
5 2 S
L. C.M.=: 3x5x3x3 =90.
2
(4)
8 14
239i miles.
4 7
L. C. M.=: 2 X 4 X 7 = 56 ; 1000 -^56 .= 17f .
' ^ .'. Ans. 17 times.
J (5)
0) l26K40^+10i-+lU + 50i
(^•4380000
8550000
1300000
550000
7000000
560000
$22540000
957)87920000(91870-43
8613
(3) $22540000- $500000 =
$21980000 ; $21980000 -^■
239i = 87920000 -^ 957 =
$91870.43 and $8.06 over. J
1790 . -
957
8330
' 7656
6740
6699
..
4100
3838
9790
1914
2730
C03
Ex. LXIV.]
KEY.
125
PAPER III.
(1)
0) 2i (i + f) + ^ (1-4) = (2i X f) + (t x|^i) = -L^ +
2i (t -h -hK) = 2i X ^n = I X ^^1 .= 3,%-.
(2) I of 4.= $15000, or I = $15000 ; .'. i = $5000, and
the whole steamer is worth $5000 x 8 = $40000. If he
sells f he has remaining ^ — | = i • i of $40000 =
$5000.
(3)
'XA — .1.
l\)=^-i^-x5|^.:xff:=JAl.
e)-.\(8i-2^)-i(i.
(4) -55 X £5 = £2-75, or £2 15s. ; 5-5 x £5 =:^ £27'5, or
£27 10s., and £27 10s. -£2 15s. =zz £24 15s.
(5) 1-25 yds.= f of '75 yds. .-. No. yds. req* = f of
87 = 145 yds. ; and 145 yds. -87 yds.= 58 yds.
(6) •5=i = part given to u4; l—i = i = part remain-
ing ; -3 of i = f of i - i of i = ^ = part given to C:
i + ^ = ^ = i = whole part give away ; 1-| = i =
part remaining to A.
PAPER lY.
(1) i = part sold to ^ ; f = part remaining; i of f
= -h- = part sold to i?; l-(i^ + -1^^)= A = part sold to
(7, which by tlu question = 32. If -^^g = 32 then /o =
32 H- 8 = 4, and jf or the whole = 4 x 15 = 60.
(2) 13i + 5G| + 14f = 13 + 5G -h 14 + i + ^ + f = 83
8
81-875.
13i = 13-5 ; 561 = 5375 ; 14f = 14-025.
.*. Sum is (3)
13'5_ 2-7) 033372 (01230
66^.) 27
14-625 —
03
84-875 54
97
81
16
o.
162
ill
1 120
■t _
1
KEY.
[Elem. A]
1'; • ■ ""^^
(4)
ii
27 X
4 =
$108.00
^
19 X
4 = $70.00
•if'
' 6x
20 =
1.20
5x
20 = 1.00
: 9ix
4x5-7-
12 =
.15f
$109.35f
8x4
x5-i-
■12 = .13i
$77.13i
$109.35^
. 3x
4 =
: $12.00
$ 17.22
t
' ISx
c20 =
= 2.40
$ 77.18i
7x
i
4x5-5
-12 =
= .llf
$14,511-
$198.05
$ i4.51i
$4l6.27i
(5) -875 = -,Vo^ = 1 ; 21 = I of the larger side, or \
— 3 an(J f or the whole = 24; 21 -1-24 = 45 = whole
number of players, which is equal to '625 or iWo, or f
of the onlookers ; if | = 45, i = 45 -J- 5 = 9, and f or
the whole = 9 x 8 = 72.
. <6) -014 of n of ^ of f of 4-5 of tti of 71^=-rir^T5
' 5| I— -i
of \ of ^of f of 4iof -|- of ^^^ = :j^o of ^ of t of
^ of I of \ of ^F = 7.
.-. one side scores 7 times as many runs as the other.
PAPER V.
(1) Let 1 represent what B owes to A; then '6,
or -j% or I = what G owes to-B; 1— f = |^ = how much
J5's debt to A exceeds that of 6"s to B. If f = 5s. then
\ — 2s. 6d., and ^, or the whole = 2s. 6d. x 5 = 12s. 6d.
(2) -J -(-50s. = what was first taken out; .*. i— 50s. =
what then remained. -2 ot -^j, or i of (i— 50s.) -i- 30s.
=-,^0 + 20s. = what was next taken ; (^-f 50s.) -f (-i^j +20s.)
= (-i% + 'J'Os.) = what had then been taken out; .*. -,^o —
70s.= what was left. -25 or i^^^, or i of (At -70s.) 4-
20s. = -,^0 -17is. -l-20s. = -fo+2is. = what was taken out
the third time. (A + 70s.) -\- (h -I- 2is.) = A+ 72^s. =
total amount taken out ; .'. -,% —72-^8.= amount remain-
ing in the bag, which by the question = 10s. .'. i^r—
72^s. = 10s., or -,% = 82is., or i\- = 27its., .'. fJl or the
whole = 27.VS. x 10 = 275s.
Ex. LXIV.]
ICEY.
137
(3) A supplies 26 cub. yds. in 3i hrs., or 8 cub. yds.
per hr. ; B supplies 12^ cub. yds. in 2i hrs., or 5 cub.
yds. per hr. Together A and n supply 8 + 5 = 13 cub.
yds. per hr. G discharges 11*375, or 11| cub. yds. in
If hrs., or 6i cub. yds. per hr.
In 12 hrs. A will supply 8 x 12 = 96 cub. yds. ; and
G will discharge 6^ x 12 = 78 cub. yds. ; .'. the number
of cub. yds. actually filled will be 96- 78 = 18. Num-
ber cub. yds. requiring to be filled ='75, or f of 286 =
214i cub. yds., and number already filled = 18 ; .'. Na
remaining to be filled = 214|— 18 = 196^ cub, yds.
Now if A and B together fill 13 cub. yds. per hr. while
G discharges 64- cub. yds. per hr., the number of cub.
yds. actually filled per hr. is 13~6| = 6i ; and number
of hrs. required to fill 196i cub. yds.= 196^-5- 6^ =
80i% hrs., which added to the previous 12 hrs. will
amount to 42-i% brs,
(4)
500 envelopes at 44 cts. per 100 . . =$2.20
3 boxes elastic bands at 33 cts. . =$0.99
\ gross penholders at 19 cts. per doz. =$ 1.14
2^ rdams foolscap at 21 cts. a quire . =$10.50
4 doz. quill pens at 9 cts. . . =$ 0.36
13 note books at 27 cts. . . . =$3.51
250 official envelopes at 48 cts. per 100 =$ 1.20
(5)
7i lbs. lamb at 10 cts.
19i lbs. mutton at 8 cts. .
18 lbs. ham at 15 cts. .
o^ lbs. suet at 10 cts.
9 chops at 4 cts.
(6)
17 yds calico at 19 cts. .
25^ yds. at 55 cts.
34| yds. flannel at 60 cts.
-j 4 • -^ !_• _i on _i_
1 t ptlii"S blliv/Kilitpj III OO CIS.
$19.90
=$0.75
=$1.56
=$2.70
=$0.55
=$0.36
5
pairs gloves at $12 per doz.
$5.92
:$ 3.23
:$14.02i
: $20.70
:$ 5.00
S?1S.2T-.V
128 '
KEY.
4
z— = •12-64
Ex. LXV. (p. 11^.)
(2) 00
[Eleai. Aiutii. '
(4)
&2
10 X 4-5
•05
(8>
1-2 X -39
•3
= 15.
1-a
•86.
(9)
(10)
4-22x17-6 ^
■~23i -^'^'
Ex. LXVI. (p. 115.)
(1) 8 bus. : 24 bus. :: $16 is to the price required.
.*. Pr^ce required = $ — ^— ^ = $48.
(2) 2 bus. : 33 bus. :: $1.10 : required price.
. -p . , . ^33x1.10 ^,^,
.-. Required price = $ = $18.15.
(3) 9 bus. : 4 bus. 20 lbs. :: $36 : required cost.
.-. Required cost = $^^^^ = $17.38^.
540
(4) 55 cts. : $21.25 :: 1 bus. : no. of bus. required.
2125 X 1
.-. Ko. required = - ^^ bus. = 38 bus. 21 fr lbs.
(5) 84 cts. : $17.20 :: 1 bus. : number required.
17^0 X 1
.-. No. required = — ~ — bus. =: 20 bus. 28f lbs.
(6) 1 oz. : 21 lbs. 4 oz. :: 6s. 5d. : required price.
256 X 77
.-. Required price =— ^---^d.= 19712d.= £82 2s. 8d.
(7) 16 cts. : $46-2.'16 ;: 1 lb. : number required.
46'^36 X 1
.-. No. required =-—^l~ lbs. =28891 lbs. =28 cwt.
16
3qrs. 14 lbs. 12 oz.
(8) 133856 : $10498.64 :; $1 : dividend in $1.
. n- • 1 1 -1 ^1049664 x 1 ^ , , , ,
. . Dividend required = $-^^^-^^=$-44 = 44 cts.
Ex. LXVI.]
KEY.
^*i.
120
V
(0) No. of days in 18G4 = 36G.
mo dys. : 1 dy. :: $100.14 : amount required.
. . , . - 10614x1
.-. Amount required = — — - — cts. = 29 cts.
(10) 1 ml. : 20 mis. 5 fur. 23 yds. :: |393'75 : req^
cost.
.-. Required cost = $^^?:^5??? = $8126.01^.
(11) $133.12 : $449.28 :: 6 cwt. 2 qrs. : weight req-*.
26 X 44928
.-. Required weights ^^^^^ - qrs. = 87^ qrs. =
21 cwt. 3 qrs. 18 lbs. 12 oz.
(12) $32.15 : $286.66i :: $183*75 : value required.
.-. Value required = $ ^^^ ^3a''J^^^^ =$1638.40-MV
(13) $10000 : $3875 :: $1 : dividend on $1.
3875 X 1
.'. Dividend = $ ^^^^ = -3875 = 38f cts.
.-. Each creditor will lose in $1, $1 -38| cts. = 61i cts.
(14) 60 men : 84 men :: 5 months : time requh-ed.
.-. Time required = ■ ^ mos. = 7 mos. 7 mos.
~5 mog.=r 2 months.
(15) 1134 yds. : 5313 yds. :: 3s. 4id. : value req*.
,, - , 5313 X 81 , ,,
.-. Value veq^. = -^^7- — half pence = 15s. 9f d.
(16) £1 : 17s. 6d. :
.'. Value of effects
1134
: £3057 12s. : value required.
210x61152
240
s. = £2675 8s.
(17) 10 ft. 8 in. : 1 mi. 1280 yds. :; 4 steps : required
number of steps.
109440 X 4
.-. No. required = - — -— steps = 3420 steps.
(18) 31 ac. 3 ro. 9 po. 21 yds. : 49 ac. 3 ro. 38 po.
22- yds. :: £3025 12s. 4Hi : required price.
• • Keq^ price = t^t^k^ half pence =£4754
lOs. 10id.
615853
XdO
KEY.
[Elem. AniTii.
(19) Loss on $1 = $1-59 cts. = 41 cts
$1 : $13675 :: 41 cts. : required loss! '
. , 13675x41
. . Loss = cts. = 15606-75.
(20) 6 mi. ; 10 mi. :; 1 lir. : time req'». by l^t boy,
.-. time required = ~- Urs.= 1 lir. 40 min. ; also 7^
mi. : 10 mi. :: 1 hr. : time required by 2"* boy, .-.
time required = -~- lirs.= 1 hr. 20 min.
Therefore since 1 hr. 40 min.-l hr. 20 min.= 20 min.
the first boy must start 20 minutes before second boj^
(21) 55 yds. : i mi. ;: 5 ft : required gain.
. T» • 1 . 880 X 5
. . Required gam = —^^ ft. = 80 ft. = 26 yds. 2 fc.
(32) 45 cts. : 55 cts. :: 36 do?, pairs : required no
of pairs. ^
. T» . , 36x55 ,
. . Required no.=-^^ doz.= 44doz.=: 528 pairs.
(23) 168 dys. : 266 dys. :: 108 men : required no
of men. ^ •
. T> • -! 266x108
. . Required no.= ^^^ ■ men = 171 men.
(24) $12571.871 : $1 :: $419.06J : rate per $.
.-. Rate per $ = $il?:??iiil_ oi ^ts
^ ^ * 12571.87i ^ ^^^•
Also, $1 : $1734.37i :: 3* cts. : required payment.
.'. Req^ payment = $?15^^-l?icts.= $57-812^
(25) ISTumber of days in 1863 = 365.
Yearly expenditure = $2500- $994. 37i = $1505.621.
v.ndlui^^* ' ^ ^^' '' ^^^^^'^^^ •■ average daily ex-
H^^q". expendituro ^ $^^p± ^ $4.12^.
)
i
I
Ex. LxVi.]
KEY.
131
i
I
(2G) 20 (lys. : 27 clys. :: 100 men : req^ no. of men.
^ , p 27x100 ,_
.•. Req*^. no. of men= — — — men = 135 men.
(27) 44 ft. : 109 miles :: 1 sec. : time req^. by train.
r«. . -,' 575520x1 .„«o^ o
.-. Tune requu-ecl = — sec. — 13080 sec. = 3
44
lirs. 38 min. ; 8 lirs. + 3 lirs. 3S mir,= 11 hrs. 88 min.
(28) 22 cts. : $1718.75 :: $1 : amount of debt.
„ ^ , ^ 171875x100 ^ ^^o-.«rA
.-. Required am*.= — cts. = $7812.50.
Also, his amount of indebtedness to first creditor will
be $7812.50-C$1250x2 + $81Cx3)= $7812.50-$4948
= $2864.50.
Then $1 : $2864.50 :: 22 cts. : what first creditor
will receive.
. 286450x22 ^ ^^oa-^a
.*. 1st cr. will receive —- cts. = $630*19, and
will therefore lose $2864.50- $630.19 = $2234.31.
(29) 42s. : 70s. :: 4^. : required cost.
.-. Req*^. cost=— -j^^ — half pence = 7id.
(30) 5 men 4- 5 boys = 5 men +3 men = 8 men.
10 men : 8 men :: 15 days : time required. ^
.•. Time required = — -~ days = 12 days.
(31) 1 lb. 10 oz. 10 dwtd. : 1 oz. :: £6 3s. 9d. : req«».
4th term.
, 20x1485- ^ ^,
.•. 4th proportional = — j— — a. = os. od.
(32) Expenditure for the year will be $2034.50 - $250
= $1784.50. Also, tlic year 1864 contains 366 days,
"and January 31 days.
366 days : 31 days :: $1784'50 : req*^. expenditure.
■r. . ,. 31x1784.50 *,^.,^,,,,
.". Req"*. expenditure — —- = $151.14Hi
jno
Ofi
KEY.
[Elem. Ahith.
(33) £1-Ga. = 19s. Gel.
19s. Gtl. ; £1 ;: £877 10s. : orii^inal income
/. Original income = ^^p^ ,^ ^ ^.^^
(34) (0 7a. : £39 8s.^4cl. ;: £1 : required income.
.-. -Req^ income =£^5?5ili = £iooo. '
(^) £l-7d. = 19s. 5cl.
19s. 5d. : £1 :: £933 : required income.
.•.ReqMncome=£?l™=£960.
on^fJL"^^^^^^ Of gold = (£150 -i- £3 17s. lO^d.) oz =
oors H% oz. '
. lib. : 38iViArOz. :: 54s. Gd. : required value.
.-. Reef, vai =j5^^J54 __73000 x 654 _1308000^
! 13 1869^^2" — ""fioo"^*
= 2099id. ,^4,-q.= £8 14s. Hid Wkq.
I (36) If. 25 men can finish the work in 16 days, 1 man
in 1 day will ^^0^(7^^=4 04 of the work. If all the men '
work for 4 days they will do i of the whole work. • 4
remam to be done. " *
> Then ^^^ : f :: 1 man : no. that would finish it in
1 day. .-. No. red- =i^.=liliifi20 =300 men, and
therefore 10 men can finish it in 30 days.
(37) 1 ct. + li cts. =3i cts. $1 -2i cts. = 97^ cts.
07i cts. : $1 :: $1855 : required income.
.-. Req^. income =^2^^=^t^Q2.om
(38) f qrs. : f bus. :: 54s. : required price.
.-.Req'i. prices «^^'^ ^^^'^x^
(39) {} cwt.
••. Req'i. price=
£90.
^x8
3s. Od.
6x9x8 '
IT L"u .-; £7 3s. : required price.
Ax 20x1^3 0x20x143x15
^- ton
if
3.=-
11x13
d.
^X. LXVI.] KEY. l^;j
(40) l5^jd. : £1 6s. Gil. :: li? of f of 2i of 4 lbs :
required uuuiber of lbs.
^- „„ T^i X I :< 2^x40x318
.-. Reqd. no. of lbs.=-I2I— i-_l_ lbs - 104,^
lbs.= 1041b3. 3f oz.
(41) From 6 A. M. on Sunday till Tuesday noon arc
54 hours, and till 1 P. M. on Saturday the clock will
indicate 151 hours.
.'. 54 hrs. 24 min, : 151 hrs. :: 24 min. : gain on
true time.
n ■ ... 151x60x24 . ,^ ■, .
.'. Gam on true time= --— mm.=66|i mm.,
.-. true time will be 1 P. M.-66|i min.=ll-53i| A. M.
(42) Wliile hour hand travels 5 minutes, minute hand
travels 60 minutes, .'. the minute hand gains 55 minutc';4
per hour.
.-. 55 min. : 1 hour :: 60 min. : time required.
.-. Time reqd=— — — =65 A min.=l hour 5/,- min.
(43) 5 lbs. : -0625 cwt. :: '0703125 of $4 ; req*. price.
■o A . ^-0703125 X 4 X -0625 x 20 ^ „^, ,^„^
.-. Req*. price =$ =$'3515625
=3515625 cts.
(44) 1 man=| boys; 1 woman =f boys; .*. 5 men=
\^ boys ; 4 women = ^7^ boys ; therefore 5 men, 4 women
and 3 boys=(\^ + ¥ -f 2) boys=18H boys.
.'. 18H boys : 9 boys :: 18 days ; no. required; .*.
required number of days=^Va- x 9 x 18=8111 .
(45) If f of the estate be sold, the rem'", will be f .
^ of f of f : f :: 1^ of f of £600* : required price.
.-. Bequircd prir, = sl^Ll^LmH = /^S x J^
14x3
t of I of I
] 46
134
KEY.
[Elem. Ari'i V
(46) 1 oz. : 2083 lbs.*:: £iOb : required price. '
.-. Required price = £409 x 2-683 x 12 = £4-A x 2* A x
41 X 161 X 12 10 bu
(47) 7 dys. : 1 dy. :: |22.12 : amoii it earned by 4
men and 5 boys per day; .. amount of earninirs =
22.12 X 1 "
-; = $3.16.
Also, 9 dys. : 1 dy. :: $28.98 : amount earned by 3
men and 5 boys per day; .-. amount = $??:?2iil=
And if 4 men and 5 boys earn $3.16 per day, 12 men
and 15 boys will earn $9.48 per day ; similarly, if 3 mer*
and 8 boys earn $3.22 per day, 12 men and 32 boys will
earn $12.88 per day; or, 12 men and 32 boys will earn
$3.40 more than 12 men and 15 boys ; .-. the $3.40 must
have been earned by the extra 17 boys.
Then 17 boys : 1 boy :: $3.40 : amount of a boy's
earnings per day; .-. amount = $~^^l= 20 cts.
Now if 4 men and 5 boys earn $3.16 per day, 4 men
working alone will earn $3.10 -$1 (the earnings of 5
boys), or 4 men will earn $2.16, or 1 man will earn 54
cts ; .-.a man and a boy will together earn (54+20) cts.
per day= 74 cts.; .-. 12 men and 12 boys will together
earn (74 x 12) cts. = $8.88 per day.
Then $8.88 : $186.48 :: 1 day : req'i. no. of days.
. -R^^ . , 186-48x1 , -^
. . Keqmred no.=: -— -— — days = 21 days.
(48) If A completes the work in 5 hrs., in 1 hr. he
will do i of it; .-. 1 hr. : 40 min :: i : .amount of
work that A performs; .*. amount that A performs =
40x*
60
Also, ^f B can finish the work in 9 hi-s., in 1 hr. he
will do ^; .-. 1 hr. : U hrj. :: | : amount that^per-
Ex. LXVIl.J
KEY.
lliS
fonns ; .-, .1ln^ that B perforras=^— - = ^.
1— (A + i) " amount remaining to be done :^ i^.,-.
Also, if G can perform the work in 15 hrs., in 1 hn
he will do -,^-r; .-. ,^- : ^- :: 1 hr. :' time required by
to finish the remainder.
.1. X 1
.-. Time required = -^^- hours = 10^ hours.
'15
(49) (1500 + 700) men : 1500 men :: 11 months. :
time required to consume the remaining provisions.
. rr- -A 1500x11
.-. Time required = ^^^^ mos. = 7i mos., whicl!,
' added to the 2 months during which the 1500 men had
been consuming the provisions, gives 9i months.
(50) The first travels 4i miles per lir., find the second
3 miles per hr., therefore they together travel 7| milci
per hour. .-. 7i miles : 30 mis. :: 1 hr. : no. of hra.
m which they will meet.
T^T- „, 30x1 , , , -^
.-. No. of hrs. = hrs. = 4 hrs.; and 8.30 A. M.
+ 4hrs.= 13.30P. M,
Also, 7i miles : 4^ miles :: 30 miles : distance first
travels. .
30x44
.-. Distance=— — -^=18 mis. ie. 13 mis. from Whitby,
or 10 miles from the given place.
(51) The 2 trains together go (24 + 27) miles = 51
miles per hour ; the length of the 2 trains is (310 + 180>
feet = 390 feet.
Therefore, 51 miles : 390 feet :: 1 hr. : req*. time.
. T5 . w 390x60x60
/. Required time =—^^^—- sec.= 5^^ sec.
Ex. LXVII. (p. 121.)
4 weeks ; no. of weeks reovnred.
M - - - . ■
4 X 15 X 13
No. of weeks req'' - — -— - — weeks ~ 8 wks.
10x9
(1) 10 : 15 / .
n
47
i-.-*
Itf.-'
130
KEY.
[ElBM. AllITU,
(2) 1 * 2 )
27 : 80 i •• ^'^ ^^^^ ' '''^^"^rcd number of men,
' . -D -1 1 42x30x2 ,,^
.'. Required number = — — -— — = 113 men,
27x1
(3) laS : GO} .. on A • i
1 : 4) 30 dys. : requu-ed number of dya.
30 X 4 X 00
.-. Req'*. no. of days :=
135x1
days = 04 days.
^^^ ^34 • 122 [ " ^^^'^^ ' required cost.
,-. Requn:ed cost = $'^^^'^'- = $307.44. •
34 X 104
(5) $100000 : 11500000 ).. ^o^AA • i •
jj . 7 f •* f^SoO : required gajn.
. L . , . ^2500x7x1500000 ^ ^
.% Required gam = $ = S87500
^ * 8x100000 ^o'»^w.
$2.80 : 4.00 [ '• ^^ ^^^^^ ' required no. of miles.
/. Req*. no. of mls.=i^:?^ = 174 miles. '
(7) 7 : 45
20
: 45 ) ..
: Of ••
2.80 X 7
required cost.
. -D • J ^ >J0 X 9 X 45 ^
-•. Requu-ed cost = $ ^q^'^ " = 1^02.50.
(3) 24 : 10 ) ^.^ , .
560 : 1200 f •" ^^^ liorses : req*. no. of horses.
„ . 140x1200x10,
. . Req'i. no. = — m~^^ — ^^'^^^ ~ ^^^ borses.
(0) $ 250 : $ 025 } \n .^
$2000 : $5000 f •• ^^ niontbs ; req^ no. of mos.
. T3„^a ^ 16x5000x625 , ,^
. . Keq^. no. of mos.= — ~— =100 months.
2000 x 250 "lyutns-
(10) 1878 : 22586 ) . ... , /
t^'m . 110 I- .: <03 ors. : rcd'^ no. of ors.
. T> rt t> 702x112x2^536
- . Keci". no. ot qrs.= --;^.-- - -^:^2808 qiu
oob X 1878
Ex. LXVII.]
KEY.
W7
(11) 6 : 24 I. . .^.
• 4 : ii) *^ ^^^'*^^ ' required no. of acres.
/. Req'i. no. of ac.= *^/*, ^ =39 ac. 1 ro. 20 po.
4x6 ^
<12) £240 . £234 )
49 >• :: 20 months : req*. no of mos.
91
56
48 j
. ■Rar.A „^ ^P 20x48x49x284 ,
.-. Req«. no. of mos. = — =9 months.
56 X 91 X 240
(18) 1008 lbs. : 618616 lbs. ) .. «^
61-45 d>3. : 3 dys. f •• ^^ ^^^ = requu-ed
number of men.
. -D „d « 20 X 8 X 518616 "",
.-. Req*. no. of men= = OO men.
51*45 X 100 8
(14) 1 • 4 )
I ! f j- .'•• 26 men : required number of men.
. T?.^d 26x1 xj 26x1x1x7 ^,
, . Req*. no. = = -.-91 men.
or thus :
85 ac. : 424^ ac. ) .. ofi i ,.
l^dys : 12 dys. i " 26 men : req'\ number of men.
.-. Reqd. no. of men= -5?^i^|i?t = 9I men.
(15) 16 men : 8 men )
1 : 2 [ :: 6 dys. : req*. no. of men.
9 : 10 )
.-. Req*. no. of men =-^1^ = 2i days.
(16) _
' men : req*. no. of men.
9xlx
24 : 16 )
18400d. : 24840d. ^ :: 25
i : 1 )
.-. Required no. of men =^^^^11^ = 45 men.
ix 18400x24 '
(17) 6664 : 798 )
57 : 119 j- :; 857 qrs. : requh-ed no. of qrs.
.-. Req*. no. of qr9.= EI^1^^= ns* qrs.=
178 qrs. 4 bus.
i x 57 x 6664
^m
1
(il^H
awBKMfi
'ffl^^^^BB
SI^I^Hh
I^^^B
•
^^^^^3
KEY. [Elem, AiUTH.
(18) 47'5 • 3*35 )
16 : 3.20 \ •• ^^'^^ • ^'e^'^ired price per bua
. T> • ^ • 1 14 X 3-20 X 3-35 ^, „^^
.-. Required pnce = = |1'608.
16 X 47d
^^^^ 25 ! T i - ^1*-^ • required price.
.-. Requirci price = l^i^ifiJi^L^^: ^7.20.
(20) 6 : 41
13 : 8
220 : 175
35 : 86j
.*. Req*. no. of dys.=
25x12
- :: 11 days ; required no. of days.
11x36x175x8x4
35x220x12x6
= 4 days.
(21) 20 : 18
135 in. : 60in. J .. n J • ^ ^ -,
878 in. : 168 in. f *' ^ ^y^' ' required no. of dys.
80 : 100
. r>^ 'A 9x100x168x60x18 « ,
/. Requn*ed no.=- q^^,c^o ..^^^ ^ ^ -= 2 days.
(22) 5
105
4
5
80x378x135x20
3
175
^^■ :: 10 days ; required no, of days.
6
. -D^^ • A 10x6x4^x175^3 , '
.-. Required no.=-^J^^-^ dys.= 13i dys.
8 * 12 )
$1.26 :* 11.80 f *• ^ ^^' ^^ ^^' ^^ ^' ' req'^.w'ght.
/. Required weight=i^4^i?^^ drs. = 6660 drs.
=31bs. Uoz.7f drs.
126 X 8
^^^^ 15 ! ^1 h: 74 horses (equivalent
22 : 825 \ ' required number
k.„
to 13 ponies),
of horses.
.-. Req^. no. of horses = ' ^%^^Iq^^^ = 36 horses.
Ex. LXVIII.]
(25) 11
KEY.
9)
iyi- 5o men : req''. number of men.
.-. Req^. no. of men^^^^^i^ = igO men.
(26) 15
10
12
1
5
15
5
4
f xjxll
:: 3 feet : required number of feet.
.-. Required no. of feet = g^4x5xl5x5 _^
1x12x10x15 --^^*^^^-
Ex. LXVIII. (p
(1) 25cts.= iof $1 $75.00 =
2
. 124.)
value at $1 each.
$150.00
18.75 =
(2)50cts.= iof $]
(3) 50 cts.= i of $1
25cts.= iof50cts.
(4)20cts.= iof $1
value at $2 each.
value at 25 cts. each.
$168.75 = value at $2.25 each.
value at $1 each.
value at 50 cts. each.
$157.50 = value at $1.50 each.
$910.00
455.00
227.50
$105.00 =
52.50 =
(5) 25cts.= iof
value at $1 each.
value at 50 cts. each.
value at 25 cts. each.
$1592.50 = value at $1.75 each.
$876.00 = value at $1 each. *
2
= value at $2 each.
= value at 20 cts. each.
= value at $2.20 each.
= value at $1 each.
$1752.00
175.20
$1927.20
$1075.00
$3225.00
268.75
value at $3 each.
value at 25 cts. each.
$3493.^5 = value at $3.25 each.
. (6) 50cts.= iof $1
25 cts.= i of 50 cts.
12icts.=iof35cts.
KEY.
[Elem. Aeith.
$1278.00 = value at $1 each.
639.00 = value at 50 cts. each.
819.50 = value at 25 cts. each.
159.75 — value at 12^ c. each.
$2396.25 = value at $1.87^ each.
(7) Is. = A of £1
£ s. d.
397 =value at £1.
19 17 =value at Is.
£416 17 =value at £1 Is.
(Sy 5s. = i of £1
2s. 6d = i of 5s.
6d. = iof2s.6d.
£ s. d.
250 = value at £1 each.
2
500 =value at £2 each.
62 10 = value at 5s. each.
31 5 =value at 2s. 6d. each.
6 5 = value at 6d. each.
£600 =value at £2 8s. each.
(9) 50cts.= ilf.$l
25cts.= |of 50cts.
$1324.00 =value at $1 each.
3
$3972.00 =value at $3 each.
662.00 =value at 50 cts. each.
331.00 =value at 25 ct.s. each.
$4965.00 =value at $3.75 each.
(10) 5s. = i of £1
2s. 6d. = i of 5s.
£ a. d.
2678 =valiie at £1 each.
2
669 10 =value at 5s. each.
334 15 =value at 2s. 6d. ea.
£6360 5 =va'. at £2 7«. Q\ ea.
Ex. LXVIII.]
KEY.
141
(11) 10s.=iof£l
5s. =i of 10s.
ls.=i of 5s.
6cl=iof Is.
2d.=i of 6d.
id.=J of 2d.
(12) 5s.= iof £1
10d.= ^ of 5s.
ld.= -,JoOf lOd.
id.= ^ of Id.
(13) 10s.=iof£l
3s.4d.= iofl0s.
4d.= i^o-of 3s. 4d.
i = iof 4d.
(14) 10s.=lof£l
Os. 8d.=^of £1
ls.=-i\ of 10s.
ld.=-iV of Is.
id.=^ of Id.
id.=i of id.
£
s. d.
973
486
10
243
5
48
13
24
6 6
8
2 2
2
6i
£812 17 2i
:value
rvalue
: value
rvalue
rvalue
rvalue
rvalue
rvalue
at £1 each.
at 1 Os. each,
at 5s. each,
at Is. each,
at 6d. each,
at 2d. each,
at id. each.
at 16s. SJd.
£ s. d.
236
7
rvalue at £1 each.
1652 =value at £7 each.
59 = value at 5s. each.
9 16 8 =value at lOd. each.
19 8 rvalue at Id. each.
9 10 = value at ^d. each.
£1722 6 2 r=va'. at £7 5s. Hid.
£
9978
s. d.
0:
8
rvalue at £1 each.
79824
4989
1663
166
20
£86663
£
15739
=value at £8 each.
= value at 10s. each.
r=va^ at 3s. 4d. each.
6 = value at 4d. each.
15 9 =value at ^d. each.
~r9 revalue at £8 13s. 8id.
s. d.
9
:va^ at £1 each.
141651
7869
10
5246
6
786
19
65 il
32 15
16
7
£155668 10 lU
=va^ at £9 each.
=va^ at 10s. each.
=va^ at 6s. 8d. ea.
=rva'. at Is. each.
r=:va^ at Id. each.
9^ n;:va*. at id. each.
10| =va^ at id. each.
vai.at£017».9f^
8
7
12^ct8.=iof50cts,
$2«791 1.87i = va'.at $0.G2^ each.
(16) 50 cts.=i of |1 $a7832 00 =vuluc at $1 each.
18
20 cts.=i of $1
20 cts.=^ of
(17) 20cts.=iof
5cts.=iof 20cts.
4cts.=iof 20cts.
(18) 50cts.=i of
25cts.=iof SOcts.
KEY
[Elem. AniTft.
$27835.00 =:: value at $1 each.
9
$250515 00 =value at |9 each.
1391750 =va'.at50cts.each.
8479 37i =va'. at 12^ c. each.
1080976.00 =vahic at $18 eacli.
18916 00 =va'. at 50 cts. each.
7566.40 =va'. at 20 cts. each.
7566.40 =va'. at 20 cts. each.
$715024.80 =vai. at $18.90 each.
$250215 00 =value at $1
5004^.00 =value at 20 cts.
12510 75 rrvalue at 5 cla.
10008.60 = value at 4 cts.
' $72562.35 =value at 29 cts.
$12815.00 =value at $1.
6407.50 =value at 50 cts.
3203.75 =value at 25 cts.
(19) 10s.=i of £1
ls.=iV of 10s.
ld.=iJy of Is.
id.=i of Id.
(20) id.=i of Id.
$9611.25 =value at 75 cts.
£ s, d.
4970 =value at £1.
2485 =value at 10s.
248 10 0=valueatls.
20 14 2 =value at Id.
7 1 = value at id.
iof 1U =
£2764.11 a=\alne at lis. lid.
d.
83 = value at Id. per yd.
11
£3 16 1 =value at lid. per yd.;
§ 5i =i= value at id. per yd
3 19 6i = value at Hid. per yd.
5|
£4 0} rvalue of 83i ytls.
Ejf. LXIX.]
* KEY.
143
(Id. = i of Is.
4d. = i of Is.
■f of Is. lOd. =
Id, = -,^ of 9d.
£ s. d.
2 17 —value at Ifl. per 3'd.
18 = value at 6d. per yd.
19 —value at 4d. per yd.
5 4 = value at Is. lOd. per yd.
1 4i
£o 5 lOi =valuc of 57^ yds.
8. d.
9 10 = value at Id. per yd.
4 8 = value at 9d. per yd.
7 4^ = value at id. per yd.
£4 15 10^ = value at 8|d. per yd.
£
s.
d.
4
6
5
4
15
m
£14
9i = total amount.
Ex. LXIX. (p. 120.)
(1) 201bs.=ioflbus.
5 lbs. = i of 20 lbs.]
(2) 2qrs.= iof Icwt.
101bs.= i^ of 2 Qi-s.
10 lbs.- i of 2qr3.
.20 = value of 1 bushel.
65
100.00 =value of 55 bushels,
40=valueof20lbs.
10 =value of 5 lbs.
$00.50 =value of 55 b. 25 lbs.
10 cts.= value of 1 lb.,
.-. $10.00 =value of 1 cwt
16
$100.00 =value of 16 cwt.
5.00 =value of 2 qrs.
. 1.00 =value of 10 Iba.
1.00 =value of 10 iba.
$107.00 =value of 16 cwt.
2 qrs. 20 lbs.
}
144
KEY.
(3) 2 ro.=^ of 1 ac.
5.50 =
8
[ElEM. AltlTK.
value of 1 ac.
$124.00 rvalue of 8 ac.
12
10 per." ^ of 2 ro.
11488.00 ='
7.75
•9687^
value of 96 ac.
^i»lue of 2 ra
ae of 10 per.
$1496-71875 :- va^. of 96 ac. 2 ra.
10 per.
(4) 10dwt.=iofloz.
2 dwt.=i of 10 dwt.
1 dVt.=iof 2dwt.
s. d.
7 1
32
£11
6 8
3 6i
8i
4J
£11
11 3i
= value of 1 oz.
=val of21bs. 8oz.
=value of 10 dwt.
= value of 2 dwt.
= value of 1 dwt
=va^ of 2 lbs. 8oz.
13 dwt.
(5) lft.6in.=iof 1yd,
1 foot = i of 1 yard.
1 inch = 1^2- of 1 foot.
s. d.
12 6
15
£9 7 6
6 3
4 2
^
-yalue of 1 yd.
rvalue of 15 yds.
■■y&K of 1 ft. 6 in.
rvalue of 1 ft.
rvalue of 1 in.
£9 18 3i =
jP o /I
(6) 72in.=iof ls.ft. ^1 7 o'
259
36inche9=iof72in.
a inches = -,^8- of 36 in.
£349 18
13 6
6 9
u
|£350 13 7^
=value of 15 yds.
2 ft. 7 in.
•
= value of 1 s. ft.
= value of 259 s. ft.
or 28 s. yds. 7 s. ft.
=value df 72 in.
=^ value of RB in.
=value of 2 in.
=ya}. of 28 s. yds.
7 s. ft. 110 in.
H
Ex. LXIX.J
(7) 3 fur. = i of 1 mi.
1 ftir. = I of 2 fur.
55 yards = uV of 1 mi.
KEY.
145
$11000.00 =value of 1 mile.
11
$121000.00 =valu6 of 11 mi.»
2750.00 =value of 2 fur.
1375.00 =value of 1 fur.
343.75 =value of 55 yds.
$125468.75 =value of 11 miles
3 fur. 55 yds.
- il
(8) 57ilbs.x2 = 115 lbs.
73f lbs. X 3 = 221i lbs.
336ill3S.= 3cwt. 36ilbs.
25 1bs. = ioflcwt.
101bs.=-,i,rof Icwt.
1
ilb
lb.=-^ of 10 lbs.
1
iof
lib.
$25.00 =value of 1 cwt.
3
$75.00 =value of 3 cwt.
6.25 rvalue of 25 Ibsi
2.50 =value of 10 lbs.
.25 = value of 1 lb.
Mj =value of i lb.
,06i - value of 3 cwt. 36 J lbs.
(9) 50 ft.= iof 100 ft.
10feet = i of50feet.
$5.00 = value per 100 feet.
34
$170.00 rvalue of 8400 feet.
2.50 rvalue of 50 feet.
.50 = value of 10 feet.
$173.00 rvalue of 3460 feet
(10) 500 = i of 1000
100 = i- of 500
50 = i of 100
$4.00 rvalue per 1000 bricks.
24
$96.00 =value of 24000.
2.00 rvalue of .500.
.40 = value of 100.
_^20 =vnlue of 50.
|98.{]0 rvalue of 24650.
14G
KEY.
[EliKM. Arith.
(11) 500 = i of 1000
50
25
10
5
-,hj of 500.
iof 50.
i of 50.
i of 10.
,25 = value per 1000 ft.
40
of 46000 a
of 500 feet,
of bO feet,
of 25 feet,
of 10 feet.
1471.50 = value
6125 =value
•5125 =value
•25625 =value
•1025 =value
•05125 =value of 5 feet.
$477-54750 =value of 46590 ft
(12)
f of,19icts.=
-,% of 551 =z
194- cts.= value of 1 yard.
17
,31i =value of 17 yards.
12A
$3.43H =value of 17f yards.
55 J cts.= value of 1 yard.
85
42^ =value of 35 yards.
.7311 =value of 35-i% yards.
70^ cts.= value of 1 yard.
96
-i«rof 70icts.=
$67.68 =val«e of 96 3^ards.
51A
.19 A = value of 96-iV yards.
33^ cts.= value 1 yard.
104
&of 32itcts.=
27
A
$34.0T-,A, =valuc of 104,1 yards.
Ex. LXiX.J
f of 17i cts,=
KEY.
17i cts.= value of 1 yard.
13
$2.07 = value of 12 yards.
.00^
$2d34f =value of 13| yards.
$ 3.43H
19.73*^1
G8.19-i\
84.07-,^
2.13;'rl
$127.57/iiV = total amount.
iif"
(13)
H of 12i
12^ cts.= value of 1 pound.
25
• .$3.12i rvalue of 25 lbs.
lOf
.23^ -value of 251* lbs.
ii of 11 ^
11 cts.= value of 1 pound.
19
$2.09 =value of 19 lbs.
io,v
$2.19iV =value of 19H lbs.
iof 8^
8^ ots. rvalue of 1 pound.
35
$2.97^ =value of 35 lbs.
.07?6
p.04-1^ rvalue of 35| lbs.
iof Gi =
(14)
of 12i
f of 17i
A of 75 r:^
7 Ul ^U =:
KEY.
[Elem. Aiuth.
Ci cts.= value of 1 pound.
17
[.10^ =value of 17 lbs.
.03i
$1.13| rvalue of 17Ubs.
2.19,^
3.04H
1.131
§9.C1A = total amount.
131 cts.= value of 1 pound.
17
$2,121 =valro of 17 lbs.
.Hi
$2.23H =value of 17^ lbs.
171 cts.— value of 1 pound.
18
$3.15 rvalue of 18 lbs.
.13i
$3.28i=valueof 18f lbs.
75 cts. rvalue of 1 pound.
5
75 = value of 5 pound.
.201
$3.95 1 = value of 5 A- lis.
40 cts. = value of ] pound.
10
$4.00 rvalue of 10 lbs.
$4.28t revalue of lOHbs.
-
r ^"^
Ex. Lxx.] KEY.
140
25 cts.= value 1 pound.
7
$1.75 =value of 7 lbs.
i of 25 = .IB*
$1.93f =value of 7f lbs.
$2.23ii
^
3.28i
i
3.95g-
4.28t
1.93* .
$15.69Uf = total amount.
Ex. LXX. (p. 128.)
(1) $217.25 (2) $21^.25
,8 8
$17-3800 = int.
$17.38+ $217.25 =$234.63
— amount.
(3) $527,371
7
$17-3800
3
$36-91625
3
$34.76 = int.
$217.25 + ^^"34.76 =
$25?!.01 = amt.
$110-74875 = int.
$527.871+ $110-74875 =
$638-12875 = amount.
(4) $93.50
$5.6100
2
i
$11.22 = int.
$93.50 + $11.22 = $104.72
= amount.
(5) $75.75
7
$5.3025
51
$10.6050
2.65125
$13-25625 = int.
$75.75 + il8-25625 =
$89-00625 = amt.
150
(6)
6d
8. (1.
18 dk
8
KEY.
(7)
[El EM. ArITBT.
11075.75
8
503 10 4
H
1510 11
251 15 3
£1762 7 2
20
1860600
4i
$344.24
21-515
$365-755 = int.
$1075.75 + $365-755 =
$1441-505 = amt
h 5
12-478.
12
5-66d.
4
2-64q.
(8)
$684.00
8
$54-720v>
5
$273.60
C9)
£17 12s. 5id.= interest. 12 : 8 :: $54.72 : int. for 8
£62 18s. O^d. + £17 12s. 5id. ^54.72 x 8
= £80 lis. 3d.= amt. ^^s- ; $ — j^ — "^ ^^^''^'
$273.60 + $36.48=$310.08
= interest.
$684.00 + $310.08=^
$994.08 = amc it.
No. of days from May 6th
■ to October 26th = 174.
365 : 174 :: £234375 :
interest req*. ,\ Int. req*.
_ 234-375x174
£234-375 "" 365 '
174
£7500
3i
22500
937.5
£234-375
937500
1640625
234375
£40781-250, or £40781 5s. ;
(Continued on next page.)
Ex. LXX.]
KEY.
151
£ s. £ 8. d.
865(40781 5(111 14 7A =
= interest
0\jO
428
365
£7600 +£111 14s. 7V^d.=
£7611 14s. 7Ad.= amt.
681
865
1675
1460
266
80
215
13
5325
365
2580
255r'
1675
£ s.
(10) 4865 11
d.
5
5f
iftfr = A
24327 17
1824 11
1
91
^ 26152 8 101 -J- 100 = £261 10s. 5-86375d. ;
Number of days from Jan. 1st to Aug. 28th, 1868 =
240. 366 : 240 :: £261 10s. 6-86375d. : interest req**.
.-. Interest req'.= £?«122!:5||75dx_240 ^ ^^^, ^^
9-94d. Amount = £4865 lis. 5d. + £171 9s. 9-94d. =
£5037 Is. 2-94d.
(11) Interest = ami— principal = $994.56 — $672.00
= $322.56. Interest on $672.00 at 8 per cent, for one
year =$53.76.
Hence, $53.76 : $322.56 :: 1 year : time required.
. ^, 32256x1
\ .*. Tmie reqmred=— ^^;^^ — years = 6 years.
(12) $816 : 100
.*. Rate required =
5376
i of $346.80 : rate required.
69-36 X 100
'J i
810
= 8i.
^^-3^'
K
133
KEY.
[Elem. Auith.
(m £100 will amount in 15 months at 5 per cent, to
£106 5s. Hence, £106 6s. : £1B8 2s. 6d. (given am*.)
:: £100 : sum required.
. ^ 100x33150_ ^
,-, Sum required = — t-^-z — — t-iou.
(14)
25500
£ fl. c. m.
578 3 1 2-5
1156 6 2 50
289 1 5 625
14-45 7 8 125
2i
28-91 5 6 250
3^61 4 4 53125
£.32-53 78125=£32 5fl. 3c. 0-078125m,
(15) $2293.75 : $100 :: ^ of $2293.75 : ratcreq^^,
^ ^ ^ , 91-75xl00_ .
,-, Rate required = 2293'75 ~~
Ex. LXXI. (p. 130.)
(2)
$742
8
(
$59.36=in*. for 1"* yr.
.', $801.36=2'^^ principal.
(1) $800 ^
L. ' $64.1088=in*.for2''«»yr.
$56.00=in^ for 1«^ yr. .'. $865. 4688 =3'^'^ principal.
,-. $856.00=2°*^ principal. 8
7
$69.237504- in', for 3'* yr.
$59.92=in*. for 2'^'^ yr. .'. Comp. i^^^ f^^-^,^+
. nnrr^r. int ^ Si.'^fi.OO -4- ^64.1088 + $69.237504 =
$59.92 = $115.92.^ Am*. = $192.70+. ^^\'-=«/^+
$800 + $115.92 = $915.92. $192.70+ = $o<.4.70+ .
Ex. LXXI.]
KEY.
153
(3) $560
10
$56.00=int.forl«tyr.
.'. |616.00=3°* principal
10
$61.60=in*.for2n<iyr.
7.60=3''^ principal.
10
$67.76=int. for 3rd y^.
.-. $745.36=4*^ prin^.
10
$81-9896
$74 -536
$67-76
$61-60
$56-00
$74.536=int.for4*^yr.
.\ $819,896=5*^ principal.
10
$341.8856 = comp. in*.,
or $341.88+. Am*. =$341.88
+ $560 = $901,884-.
$81.9896=in*. for5*^ year.
let pay't of int. =$308.
2nd pay't of int=$313'62
3rcl pay'tof int =$317 -3093
4th pay't of int.=$3a2'1689395
x;f^=$4.62
X ^= $4-6893
K {-^= $4'T596395
X J-^= $4-8335340925
1}^
St,h pay^t of int. =$327-0024735925 x ^= $4-9050871088875
tith payH of int. =$331-9075107013875 x ^= $4 ;* ?8619660520812i>
.-. Comp. intere8t=$28.7861233619083125
or, $28.'V8+.
,-. Amount = $308.00 + $28.78 + = $336.78+.
::M
154
KEY.
(5)
[Elem. AllITlt.
1st pay't of interest = $610. x Tk= $34*40
2d pay't of interest = $634-40 x jU^ $25-376
8d pay't of interest = $659776 x t^o= $26*39104
4tli pay't of interest = $68616704 x t^o= $27-4466816
.\ Comp. interest = $103-6137216
$61000
(6)
l8t pay't of int. =$1000.
2d pay't of int. =-$1035.
3d PY't of int. -$1071 -225
4th pay't of Int.-.$1108-nT875
Amount = $713-61+.
x|^= $36-225
x?^- $37-492875
x^= $38-805125625
3;5^
6th pay't of int.-.$1147*523000625 x^^ = $40*163305021875 ^
lUu
Cth pay't of int.-$1187-08630584375x J^ =- $41-56902070453125
100
— ^— ■■ ■ — ■ I !■■ ■ ■ Him ■! ■■■■■■IWll«^
.% Comp. interest'- $229-25532635140625
or. $229-25 +.
Amount = $1000+229.25 ... = $1229.25...
(') £880
2640
440
(7)
• simple int.
(Continued on i
icxt pa
£62-678
£61-60
£1.078
20
1-560S.
12
6-72d.
4
2-88q.
1s. 6M. '88^
£30-80
2
£61-60 =
Ex. LXXII.]
C) £880
3i
KEY.
(t continued.)
155
£30-8 = int. for 1st yr.
.-. £910-8 = 2a principal.
3^
£31-878=int. for2"'iyr.
£30-8+£31-878=comp. int.
= £62-678.
O £178-7116 /
171-75 \
£6-9610
\ 20
' 19-232S.
, 12
1 2-784cl.
3-130q.
£6 19s. 2|d. -ISOq.
O £1431-25
4
£57-2500
3
£171-75 =: simp. int.
£1431-25
4
£57-25= int. for 1st jt.
£1488-5 =2(1 principal.
4
£59-54= int. for2clyr.
£1548-04= 3d principal.
4
£61-9216=int. for 3d yr.
£59-54
£57-25
£178-7116=comp. interest.
^ Ex. LXXII. (p. 133.) ' •
(1) $108 : $216 :: $100 : present worth.
^100 X 216
.-. Present worth = $ — T^r^ — =
108
(2) $121 : $968 :: $100 : present worth.
^ , ^100x908 ^„^^
.-. Present worth = $ — -- — = $800.
(3) $103 : $1236 :: $100 : present worth.
• Piv>«eni Tvowii — jilt = &noo
" ' lOo
150
KEY.
[Elem. Arith. '
(4) $107.50 : $225.25 :: $100 : present worth.
xu ^100x22525 ^ ^
.-. Present worth = $ — — -~- — = $209.53+.
lv<OU
(5) $117.60 : $1057.50 : $100 • present wortli,
.u ^100x105750 ^^^^
.-. Present worth = $ — — r =$900.
11750
(6) £125 : £161 13s. 5id. :: £100 : present worth.
T^ X ^ « 100x155205 „,„^^ ^,
.;. Present worth =£ — :n^7^i: — = £129 6s. 9cl.
l/sOOOU
(7) £107 18s. 4d. : £193 17s. 4Jcl. t: £100 : present
worth.
_ 100x186113
.*. Present worth = £ — ^7:^7^^ ^=: £179 12s. lOM.
X5 9U*
103600
(8) £100 8s. 5Hd. : £458 8s. 9id. :: £100 : present
worth.
.*. Present w'th=£
100x4-i%iii-L
=r £456 9s. llfd. HHq.
-LIA^^li
£
440101x100x73
"4xl75'9440
(9) $124 : $217 :: $24 : discount.
T^. . ^217x24 ^,„
/. Discount =$ — T--J — =$42.
124
(10) $110.50 : $221 :: $10.50 : discount.
.^ ^ ^1050x221 ^^,^^
.-. Discount=$ — — — - — = $2100.
11050 t
(11) $105 : $2000 :: $5 : discount.
.-. Discount=$-^^^|^=$95.23H. ^
105
(12) $106 : $1750 ::
.'. Discount=$
J 5 \j\r
100
: discount.
:$99.05|i '
Ex LXXIII.l
KEY,
157
(13) £100 183, lOHcl : £345 16s, 3cl :: 18s, lOHd
: discount.
. T)- 'i=^Jfl^l^il?:^f±^^ _ 10512x 6058635x78 _
•'• ^ ii^v^^iA — 78 X 73 X 176851a
^¥/i¥M.=£3 4s. 6|d. flHq.
(14) £100H : iB549 :: m : discount
•n- , n^pxH ^40077x82x73 ^^ ^
••• Discount=£-^- = ^-332^731773- = ^^ ^^
Also,' £100 : £549 :: £^ : interest on £549.
T . . „ 549 X 32 «^ ^ . , , , ,
.-. Interest = £^^^^^^^£2 8s. Hd. iUq.
£2 8s. lid. iHq.-£2 7s. lid. iHq.=2id.iWu¥«q.
(15) £100H : £450 :J £^5 : discount.
r,. . oH¥^xH p32850x 73x45 „„,,
.-. Discount=£— |Tj~- = £i^^Tp~n=^-7;T=£215s.
^ta^ 7345 X 73 X 73
li^d.
Also, £100 : £450 :: £H : interest. >
450 X 45
.-. Interest = £ ^^^^^^ =£2 15s. 5m.
£2 15s. 5Md.-£2 15s. U%^d.= h^^hd.
(16) In 18 months the tradesman allows 5s, or 3s.
4d. per year on £3 6s. 8d., that is -gV of the whole.
Then 1 : -/j •: 100 : rate of discount. .-. Rate =
100x1 ^
-^^^=5 per cent.
Ex. LXXIII. (p. 137.)
(1) $126.50 : 1527.25 :: $100 : amount required.
' .-. Amount req'^.-$ ^^''^'^^^ -- — =$410.79+.
12650
/0\ a^iCiCt Kf\ . dbOAA .. dhiAA . -»»„^ «i. -^ J ,1
.-. Amount re(piircd==$——^—-=: $780.48^1.
158
KEY. v T [Elem. Arith.
(3) $100 : $1556 :: $98 : required value, 'f^
„, ^98x1556 ^,,^,^^
.-. Value = $ — — — = $1524.88.
(4) $99 : $535.50 :: $7 : required income.^
.*. Eequired income = $ — =$S7.15gf. (
(5) $7i : $900 :: $125^ : income required.)
^ .5023x900x2 ^,,^,^ ^
.-. Income = $ — tt-jk — = $15069.
15X40 ^ :^.
(6) $100 : $2140 :: $65 : amount required.]
.*. Amount required= $ — — - — = $1391.
^ 100
(7) C) £901 : £666 8s. 3d. :: £3 : gross incomeX i
Income = £
90|
£22.
Income tax = (22 x 4)d.= 88d.= 7s. 4d. Net income
= £22-7s. 4d. = £21 12s. 8d. H^lf-yearly gain = £21
12s. 8d.H-2 = £10 168. 4d. i
O Income tax on £100 =(100 x 4)d.=400d.=£l 13s. 4d.;
.-. £100 income would yield £100-£1 13s. 4d.= £98 6s.i
8d., or £98^. Hence, £901 : £98 J- :: £3 : req^. rate.!
_, . ^ ^3x98^ ^3x295x8 „, , .^«.J
.'. Reqd. rate = £-j^k7^= £ o..>^n>^ -^3 4«. II-7Y7*.
901
3x727
(8) £136 : £100 :: £8 : required rate. ^^
.*. Rate required = = 5*88 -H or nearly 6 per ct.
Ido ^^
(9) £136 : £100 :: £8 :' Int. received from i? of
Montreal. , ,^
*. Rate of Interest = ,^^ = 5*88 +J^
£104 : £100
ronto.
136 '-- ^
£7.5 : Int. received from B of Toy
7-5x100 ^^
.•. Kate of interest = — — — — = 7*21-1-
104
Therefore the Bank of Toronto is the better invest-
ment. ■
■
'Ex. LxxiiL
KEY.
159
^ (40) £93 r£4650j:: £100": quantity of 3 per cent
stociibQdglit.
,.•. Qtiantit;5f of stock bought = £^?55^15?_ £5000.
The stock stood at 93: now having fallen i'pfer
cent., it stands at 93^.
.-. 100 : 5000 :: £93^ : value of stock.1 '
--TTi xy . . „5000x93i «,^«^.
.-. Value of stock = £ — ^ = £4625^
.•rLoss of property = £4650 - £4625 = £25.
^ (H)'£§0f'7£99jT: 1E29000 j^uantity of 8 per cent,
stock -^ ' ""**"' — -
c^ *•* iTo- — , ^ y ^29000x99x5-
.'. Quantity of 8 per cent stock = £—
£31680.
' . „29000x8-r «^^.^^
1st income = £ — rr?:— ^ = £1015
100
-31680x3 ^„^^„
,2d income = £ — = £950 8s. .
'.-^Loss = £1015 - £950 8s. = £64 12s
(12) $115 : $200011 $8 : gain.
...aain=$?^^.= $m^,/
-725
. (13) £100 : £95 .:: £5000000 : value of in. £5000000
in 3 per cts.
15000000x95 ;,,^^^^^^.
, .-. Value = £ —: =£4750000.
Amount still due = £5010000- £4750000 = £266000.
. £3 : £3^- :: £95 : vahie of the 3^ per cents.
.-. Value = £!i*^ = £iio|. ,
o
£110^^ : £100 :: £266000 : amount of 3^ per cent,
stock. .
, .'. Amount of 3^ stock =£?^^55^— =£240000
'llOs "
160
KEY.
. [ElEM. AlUTU
(14) £QSi : £18700 :: £3i : income. :
. T «18700x3i „ .
/. Income =r £ — ^ = £700. •
i of £18700 = £3740 ; f of £18700 = £149B0 ;
.-. £98 : £3740 :: £4 : income from 1st investment.
, „3740 X 4
.-. Income = £— - — = £155 16s. Sd.
£90 : £14960 :: £3 : income from 2d investment.
. T «14960x3 ^
.-. Income = £ — — — = £498 13s. 4d ;
.-. total income = £155 ICs. 8d. + £498 13s. 4d.=
£654 10s.
Hence loss = £700 - £654 10s. = £45 10s.
This^ question may be solved by obtaining tlie am't
of stock in each case and then the incomes.
(15) £91 : £5460 :: £100 : am't of 3 per cent. st'k.
.•.Amount=£-15?|^ = £6000.
£100 : £93^ :: £2000 : produce from 1st sale.
. -D 1 ^2000x934 _
.-. Produce = £ — :^~^ = £1870.
£100 ? £85 :: £4000 .-'produce from 2d sale.
. -D 1 p4000x85 ^„,^^
.-. Produce=£ — — — =-£3400;
.-. total amount realized.= £3400 4- £1870= £5720
£102 : £5720 ::£100 : amount of 4^ percent, st'k!
. A . ^5720x100 „ ,^
/. Amount = £ — ~ — = £5166 13s. 4d.
Income from 3 per cent, stock = £— ^_ = £180
100
T_„__ ^.._... ., -. __. .. .,, ^5166 13s. 4d. X 4*
luuuuiu iiuui tfc^ per ct. si k :=^ a,
£233 10s.
/. Gain = £233 10s. - £180 = £53 10s.
100
Ex. LXXIV.]
KEY.
161
(16) £3 : £050 :: £100 : is to amount inrested in
3 per cents.
.*. Amount invested =£ ^ = £11666^
£100 : £116661 :: £87i : value of 3 per cent, stock.
„349x 35000 ^.^.^^,
.-. Value = £ .^, ^ . = £10179i
100 X 3 X 4
£104| : £10179^ :: £5 : income from 5 per cents.
_5x61075x8
.'. mcome from 5 per cents = £ — —- — - — =
bov X o
£485 5s. llfd. Miq.
£485 5s. llid.fHq-~£350 = £135 5s. llfd. fi^q.
Ex. LXXIV. (p. 141.)
(1) $100 : $4300 :: ^^ : commission required.
. . A4300xi -^„^,
.-. Commission = ^—t~- = $5,37^.
lUU
(2) $100 : $9636.55 :: $2.60 : premium required.
T, . . , ^2.60x9626.55 ^^^^^^ao
.-. Premium required = $ r^ = $250-3903.
(3) $1560 stock : $100 stock :: $4.60 : percent.
.-. Per cent. = i^?^^ = UkU = 29if cts.
1560
par cent.
(4) $2.40 : $100 :: $45.60 : sum required.
. , ^45.60x100 ^,^^^
.-. Sum required =$ — ^^ — =$1900.
(5) 25 yds. x 36=900 yds. : 900 yds. at lOJd per yd.=
£39 7s. 6d.
O £39 Vs. 6d.-(£32 16s. 3d. + 6s. 8d.) = £6 5s. =
"Nvliole gain.
/2\ ^aa 9a ftfl • £100 '.: £6 5s. • rp.nnirfifl o-ain nor
cent.
24000x125 ^,„ ,^ ^^, ,,
,-. gam per cent. = — —- — s. = £18 17s. 2^d.Hq.
UVi
KEY.
i Klwm. Aj!iTir.'«
H
(fi) Cost of 1380 bus. at $1.20 per bus. = {JloSO.CO
(') (1380 X 3f )ct9. = camu<^e etc. expenses = $48 00
Totaffexpenses = 11530.00+ $48.00 = $1584.00
1280 bus. at $1.40 per bushel = $17^2 = sellin""price.
.-. Gain = $1792 - $1584 = $208 ; « i •
$1584 : $100 :: $208 : gain per cent.
/. Gain per cent. .-= ^'^-^—^ = $13-i3
(3) Also to have gained $400 he should have sold the
wheat for $1584 +$400 = $1984.
And $1984-?- 1280 = $1.55 = required price per bus.
(7) Q) If he buys for 6s. 8d. and sells for 7s. 4d. he
gams Bd.
.'. 6b. 8d. : lOOd. :: 8d. : required gain per cent.
. n„- . 8x100 _
. . Gain per cent. = _ , - = 10 per cent.
Also if he buys for 7s. 4d. and sells for 6s. 8d. he
loses 8d.
('^) .-. 7s. 4d. : lOOd. :: 8d. : required loss per cent.
. T . 8x100 ^,
. . Loss per cent. = ^^ = 0-^- per cent. = £9 Is.
9fcl. -A-q.
88
(8) If it cost $96 per cwt. the price per lb. will be
96 cents.
.-. $100 : $135 :: 90 cents : price required.
. T> • ., 96 X 125
.'. Price required = cents=| •"'^
(9) $6 per cwt. = 6 cents per lb.
.-. Gain per lb. = (10-6)d. = 4 cents.
6 cents : $100 :: 4 cents : gain per cent.
.-. Gein per cent. = ^-^ = $66.66^ = GGl per ct.
(10) £100 : 112i :: 4s. 8d. : required price.
.'. Required price = 55^^cl. =. 6bd. = 5s. 3d.
Ex. LXXIV.]
KEY.
108
(11) £112^ : 4s. 8(1. :: £1000 : prime cost.
.-. Pnmr' cost=— g-^— d. = 4s. l^d. iq. ^
(12) 40 lbs. @ 84c. = $33.30
44 lbs. (^ 93c. = $40.92
55 lbs. @ $1.08 =: $59.40
Total cost = $183.92
.-. Gain = $188.10- $133.92 = $54.24.
$133.92 : $100 :: $54.24 : required gain per cent.
100x54-24 .-,,0
.-. Gam = -133-93- = 40Ht per cent.
(13) 26 lbs. @ 5s. 3(1. cost £6 16s. 6d.
32 lbs. @ 5s. 7d. cost £8 18s. 8d.
36 lbs. @, 6s. Id. cost £10 19s.
.-. 94 lbs. cost £26 14s. 2d.
u£100 : £40 ::£26 14s. 2d. : gain.
^ . 6410 X 40 , n^ A ^ o o 1
.-. Gain = — — r — d. = £10 13s. 8d.
.♦. Selling price will be £26 14s. 2d.+£10 13s. 8d. =
£37 7s lOd
.-. Price per lb. will be £37 7s. 10d.-^94=7s. Hid. tlq.
(14) £90 : £100 :: 15s. : buying price.
T, . . 15x100 ,- „,
.-. Buymg price = — ^^ — s. = los. bcl.
£100 : £110 :: 16s. 8d. : required selling price.
. .-. Required price =^^^^d. = 220d. = 18s. 4d.
(15) He gains on 11 eggs the price of 7 eggs.
.-. 11 : '/ :: £100 : required gain. v
100x7
.-. Gain = =^^j~- = £63 12s. 8id. i^q.
(16) $130 : $100 :: $1.56 : cost price
^ 1.56 X 100 ^. o^
.-. Co6t price =% — r^- — = S1.20.
164
(1)
104
96
02
90
82
81
6)643
90-83
1
KEY.
Ex. LXXV. (p. 142.)
(3)
$4.25
15.75
16.60
17.80
$3.50
$5.58
6) $33.48
$5.58
[Elem. AniTir.
(8)
87-8
877
87-6
86.8
850
84-5
83-8
78-0
779
77-6
10)836 7
83 67
(4)
United ages of 17 cliildren = 102
United ages of 26 children = 195
United ages of 35 children = 32375
United ages of 20 children = 200
United ages of 8 children = 98
years,
years,
years,
years,
years.
'. United ages of 106
Average age = 91875 years
of 106 -91875 years.
14-106=8-667... years.
(5)
United ages of 27 men = 1539 years.
United ages of 11 men =583 years.
United ages of 8 men = 474 years.
. TTnitP.f1 acroa r\f 10 yvton — Inft'T -.^^^-^r,
.'. The united ages of the remaining 8 men = (1539
-1057) years =482 years. /.The average age = 482
-8 = 60i years.
Ex. LXXVI
KEY.
165
(G) 100 : 113 :: 31S30 populatiop of 1st ia 1861.
.*. Population = ~ = 8508512.
100 : 110 :: 42324 : population of 2d in 186J.
_, , ^. 42324x110 ,^^^. ,
.-. Population = -— = 46656-4.
100 : 83 :: 0706 : population of 3cl in 1861.
.*. Population = — — — — = 5496 ■92.
.-. United population in 1861 = 3508513 +46556'4+
5498-93 = 87140-44.
.'. Average population = o7140'44 -*- 3 = 29046*813.
(7) Whole gain from 1853 to 1863 = £184 lis. 6d, x
11 = £2030 6s. 6d.
£2030 6s. 6d.+£15i 9s. lOd. - whole gain = £2181
16s. 4d.
£2181 16s. 4d.- £76 8s. 4d.= £2105 83.= whole gain
during 11 years. .*. Average gain == £2i05 8s.-:- 11 =
£191 83.
Ex. LXXVI. (p. 145.)
(1) C) 2+3+4=9.
9 : 12 :: 1008 : 1st part.
. ^ ^ 1008 >< 2 ,,_
.*. 1st part = —T — = ^24.
9:3 :: 1008 : 2d part.
_, ^ 1008x3 __^
.*. 2d part = — - — = 336.
9:4:: 1008 : 3d part.
„, ^ 1008x4 ...
.-. 3d part = : — - — = 448.
O 5+11+16=32.
32 : 5 :: $260 : 1st part.
.*. 1st part = $
OCA v^ K
33
= $40,631.
(Continued on next pagc.^
I
ia6
KEY.
[Elbm, Arith.
(1 Continued.)
33 : 11 ;: ^260 : 2d part.
.-. 2d part = $—3^ = $89.37i
32 : 16 :: $260 : 3d part. _
«.260xl6 ^,„^
.-. 3d part = $ — --^r — = $130.
O 11 : 5 :: 145 ac, 3 ro., 33 po. : share of 1st. ,
ou jn J. 145 ac, 3 TO., 33 po. x 5 „„
.-. Share of lst.= ■ ~ = 66 ac.,
1 ro., 15 po.
11 : 6 :: 145 ac, 3ro., 33 po. : share of 2d.
. Qi ^ rtj 145ac,oro,33po. x6 ^- ^ ,
.-. Sh^e of 2d = '■ — ^^ — = 79 ac, 2 ro.,
■*•■'• »
18 pb.
U ' ^ '•'• £110 : share of 1st.
.-. Share of Istr^ £^-^ = £42 17s. lid. fq.
U : i '.: £110 : share of 2d.
.-. Share of 2d = ^^ = £28 lis. 5|d.
77 X 3 '
U : i :: £110 : share of 3d.
.-. Share of 3d = £^~ = £21 8s. 6f d. f q.
77 X 4 • * 7 1
U : ^ :: £110 : share of 4th.
.-. Share of 4th = £^ ^ = £17 2s. lOid. \q.
77 X o * ' 1
(2) 0) |320+$560+$720=T.|1600.
$1600 ; $320 :: $680 : J.'s share of the ffain.
' Ay r. ^680x320 ^,- ,
.*. A'& share=$— — — = $136.
$1600 : $560 :: $380 ^ B's share of the gain.
* JU^ t^ ^/AJLlAlX \^
.680 X 569 ^„„„
<2^ (frOQQ
" 1600 ^
(Continued on next page.)
Ex. LXXVI.]
KEY.
107
(3 continued.)
$1600 : 1730 :: $680 : (7's share of ||ie ffain.
. n^ u hk680x720 ^
.-. (7's share =:$-^^_- = |306.
O £175+£310+£265 = £650.
£650 : £310 :: £423 10s. : (7's share.
. ^, , ^423^x210
.-. C's share = £ — 1_^ =: £130 iqs.
(3) 48'85G+43-265 = 92-131.
JSn~*'ll' o^A= '^■^^^ = P^r centage of hydrogen.
100 : 48-856 :: 3340 : No. ox ibs. of okygea.
. ruc r.f 3240x48*856
. . Lbs. of oxygen = —Jirir— jA^^.g^j.^^
100 : 43-265
130
2240 : No. of lbs. of carbo*.
. TT,c .p 1 2240x43-365
. . Lbs. of carbon ^ -^-^ Z = 939-136.
100 : 7-879 :: 2340 : No. of lbs. of hydrogen.
.-. Ko. of lbs. of hydrogen = ^^p^^m^^SdH
(4) 3 : 3 :: 100 : per centage of gold.
.-. Per centage of gold = ^51^1^ -.qq^.^
3 : 1
3
100 : per centage of silver.
.-. Per centage of silver = 3t5^ =: 33^.
(0) Equated time =i5^t^,^^i^= 5 ^os.
130+210 + 130
(6) Equated time J-^^^!^^^dm^ ^
1000-400
8 mos.
$8000+ C^ 10.10 + $000 r:^ 19950.
$9950 : jSt.3000 :: $7960 : yl's share of the ffain. '
.*. .Is «'inror:.-$lilI--^p: ^ 16400. \
\tftO\J
(C;>ntimiecl on next page.)
108
KEY.
[Elem. Arith.
(7 continued.)
$9950 : 11050 :: $7960 : J5's share of the gain.
^, , 1050x7960 ^^,^
.'. J5's share = — -— - — = $840.
$9950 : $900 : $7960 : (7's share of the gain.
^, , ^7960x900 ^^^^
.-. C's share - $ — =$720,
ovOKJ
(8) 10 per cent of £1600 =£160; £1600- £160 =
£1440.
£6400 : £2400 :: £1440 : .I's share of the ffam. .
2400 X 1440
.-. A' a share = £ — — -- — = £540, which added to
6400
£18b = £700.
£6400 : £4000 ;: £1440 : ^'s share of the gain.
.-. ^'s share =£li^Ji^ = f 900.
6400
(9) Since the keep of a horse : the keep of a sheep
C'l 8 : 1, therefore 20 horses are equivalent to 60 sheep.
,. In- the same manner 15 oxen are equivalent to 30
^heep.
* ,*. A puts in 60 sheep,
B puts in 30 sheep,
G puts in 10 sheep.
C0-i-304-10 = 100.
100 : 60 :: $60 : A'^ share of the rent
., ^ ^60x00
/. J.'s share=$-
100 e
100 : 80 :: $60 : J5's share of the rent
„, ■ ^60x80 ^,^
,% i?'s share=$-— -- = $18.
100
10) : 10 :: $00 : C's share of the rent
.„ , ,..()Oxl0
-ii:.
Ex. Lxxvn.]
KEY.
169
(10) 9 : 10 :;lipts. : widow's share.
■m-.j . , 1^x10
.-. Widow's Bhare=-~ — pta. = If pts.
5:6 :: If pts. : old man's share.
.-. Old man's share = -——pts. =2 pts.
If one widow receive If pts. 9 will receive (9 x If )=
15 pts.: similarly 6 single women will receive (6 x 1|)
pts. = 9 pts. .*. The total amount given to the women
= (15+9) pts. = 24 pts. But the men had twice as
much as the women, .-. the men received (24 x 2) pts.=
48 pts.; and as each man received 2 pts. the total num-
ber of men must have been 484-2 = 24.
Ex. LyXVII. (p. 149.)
(1)
196 (14
24
\ 96
96
^^ ' A
J
(2) 841 (29
4 /
49
441
441
.*
(3) 2401 (49
1A
89
801
V
801 .
V
(4) l242i (111
1
21
23
21
221
221
221
27
289 (17
189 '
189
45
625(25
4
225
225
900 (30
9
1764 (42
16
60
167
400
00
00 \
8
2 164 i
164
md (87
64
9604 (98
81
1169
1169
ISi
1 1504 ■:}
1504
40006(200
4
388129 (623
86
0000
0000
122
1243
281 ^
244
""
8720
3729
170
KEY.
[Elem. Arith.
(5) 494209 (708
49
1403
(0)
(7)
(8)
4209
4209
146
1523
582169 (763 259081 (509
49 25
1009
921
876
9081
9081
4569
4569
1234321 (1111
1
28547649(5343
25
21
221
23
21
243
221
^2221
2221
2221
108
354
309
106^
1061
i 4576
4256
33
32049 .
32049
62504836 (7906
49
• • . •
33016516 (5746
25
149
1360
1341
15806
94836
94836
107
1144
801
749
A y
5265
4576
11486
68916
68916
•■.•.•
49112064 (7008
49
14008
112064
112064
• • •
182493081 (13509
1
23
83
69
265
1349
lontt
270<
09
243081
243081
12-9
47-61 (6-9
36
11-61
11-61
Ex. WKVII.]
KEY.
171
(9) ^OmSQ (094
00
^ 09 88
V 81
•
4
4
41"
431
4230
145-886609 (
45 ^
41 ^
184
736
736 '
433
431
V /
3 136609
136609
X
(10) 000633679939 (035173
4
45
383
335
601
867
501
5037
86690
35189
50343
151039
151029
(11) 5
4
141
d
300
141
}00600 (7-1414
b
1424
590
569
14281
3C100
14281
tAOAO
4 Ai 1 onn
569696
> • • • »
-0000000009 (00003
9
"-.•-•
•51000000 (-7141
49
141
300
141
1424
5900
5696
14281
20400
14281
" fli
172
KEY.
[Elem. Arith.
(13) 510060606 (2-2583
4
42
445
110
84
•05160600 (-2258
4
42
110
84
2600
2225
445
2600
2225
4508
45163
37500
36004
143600
135489
45081 87500
I 36064
1436
(13) 806-52060606 (2803992 96304-99300000 (3103304
9
406
384
48
563
5669
56789
567982
63
61
2252
1689
56300
51021
527900
511101
61
6203
62063
6206604
30499
18609
189030
186189
28410000
24826416
1679900
1135964
• • •
(14) -333333 (577
25
(15) -027777 (-166
107
1147
833
749
8433
8029
26
326
177
156
2177
1956
(16) 4H= 4-734693...
4-734698 (2175
4
41
(17) 2304 (48
16
73
41
88
704
704
fail oato
2989
. ^ /^*r^
6'ibi {oH
25
4345
25793
21725
109
981
9ftl
'
.-. vm^^
I
'
Ex. LXXVIII.
KEY.
173
(18)
41
4-41 (2-1
4_
41
41
•64 (b 21-i--8 = 2-625
64
U9) 5832 sovereigns = 13906780 pnnce and 2s. 6d. =
30d.; .'. the sovej igns -vvere worth (1399680-*-30) times
the box = 46656. ^
The square root o^ 46656 is 216 ; .'. the sovereigns
were worth 216 times the shilliogs and the shillings
were worth 216 t' nes the box. But the value of the
box is 2s. 6d.; .-. the value t)f thu shillings will be 216
times 2s. 6d. or 540 shilhn.'js.
(1)
Ex, LXXVIII. (p. 152.)
1728(12 8000(20
1
8
3x12=3
3 X 102=300
3x10x2=60
22=4
728
000
000
364
2
728
728
3 X 12=3
3 X 102=800
3x10x8=240
82=64
604
8
4832
5832 (18
4832
4832
(!
74088 (42
64
3x42=48
3 X 402=4800
3x40x2=240
22=4
5044
10088
10088
421875 (75
343
10088
3 x 72=147
3x702=14700
3x70x5=1050
52=25
15775
78875
78875
78885
(Continued on next page.)
174
KEY.
[ElEM. AllITH.
3x92=243
8x90«=34300
3x90x2=540
2»=4
49688
24844
2
49688
49688
(3 continued.)
778688 (02 (8) 912673 (97
729 _^ 729
3x0«=243
3x90«=24300
8x90x7=1890
7«=49
2C239
7
183673
183673
188673
I
8 X 1«=8
8xl0«=300
8 X 100»=30000
3x100x8=900
8»=9
1092727(103 (4) 134217728(512
1 125
92727 3x5«=75
3x502=7500
30909
8
92727
3x50x1=150
.1«=1
7651
3x512=7803
3 X 510«=780300
92727 3x510x2=3060
2«=4
783364
2
15en2S
9217
7651
1566728
1566728
#'^
■
64-481201 (4'01
64
8x45=48
3 X 40«=4800
8x400^=480000
3x400x1=1200
1«=1
481201
481201
481201
Ex. Lxxvin.]
(5)
KEY.
A
444194-947 (76-3
843
8x7«=147
3x70«=14700
8 X 70 X 6=13BQ
6?=3d
15996
8x76«=17338
3x7602=1782800
3x760x3=: 6840
8«=9
1.739649
3
.5218947
101194
95976
5218947
5218947
175
•00(i202262003 (0587
126
3x53^=75
'3x502=7600
[3x50x8=l«00
88=64
77262
8764
70113
3x685^^=10092
3 x580«= 1009200
3x680x7=12180
72=49
7150003
1021429
7150003
170
KEY.
[Elem. AritQp
(6)
18i 019108039(^079
125
3 X 5«=75
3x50«=:7500
8x500'»=750000
3x500x7=10500
7^=49
760549
8x507«=771147
8x5070»=77114700
,3x5070x9=136890
9»=81
77351671
601910B
5323843
695365039
695265039
f 408518488000 (7430
348
3 X 72=147
3x702=14700
3x70x4=840
42=^6
65518
15556
62224
3x742=16428
3 X 740«=1642800
3x740x2-4440
2«=4
8294488
1647344
3294488
000
m V27=3 V64=4 .-. vlT=4
'q.
Ex. LXXVIII.]
{
(8) A ='96
KB^.
177
8x62=108
8x608=;=10800
8x60x4=73C
4«- 16
•2^ jdeoec^ (-6 ^
50f8a
11686
8x64^=12288
3x6408=1228800
\,8x64tx 8=5760
8»=9
N 1284669
461^ t
4522686J
8 i3707
(9) 3J=38
8 X 19=b
8x102-800
3x10x5=150
5*=25
476
8xl5»r 675
8xl50»=67600
3x160x6 :2700
6«=36
8-800000000 (1-560
1
2800
2875
70236
3x1562=73008
3 X 15602=7300800
___05
73001 )
426000
421416
8584000
I
I
■^ 'iSM
(10) vl=l
178
(H)
KEY.
[Elem. AniiH.
400000000 (-464
64
8 X 4»=48
]
-^
3x^=4800
3x40x6=720
6^=^36
3 X 46»=«848
3x4608==e84800
8x460x4=^6520
4»=16
640336
J8000
33336
2664000
2561344
E
(1
(12)
•016006006 (-215
8
3x22=12
2000 ^
3x20»=1200
3x20x1=60
12=1
1261
1261
8x31«^ie38
739000 /
3x210'»=lS2S00
3x210x5x3150
5«=25
677375 \
136475
id
Nf
'V i :'.. %•■*'■
Ex. LXXVllI.]
KEY.
170
(13)
OOOOOOOOOO (3-154
8
3x20x1=60
12=1
1261
3x21»=1328
3x210«=182300
8x210x5=3150
52=25
135475
8x2152=138675
3 x2150»x 18867500
.8x2150x4=25800
42=16
13893316
2000
1261
789000
67737 5
61625000
55573264
m)
037373737 (333
27
3x32=27
3x302=2700
3x30x8=270
L 32=9
2979
10373
8937
3 X 332=3267
3x8302=326700
3x330x8=2970
3«=9
1436737
180
KEY.
[Elem. Akith.
Ex. l:?
(p. 153.)
r4) 553553
16
r
28
4)138388—14x0 +
[Irrl oz.
' 4)64597—0
7)8649—14x44-
PAPBB I.
(2)
o
144 : 175 :: 12 oz. : popor-
tion of i* lb. Avoirdupoise.
175 X 12 , , ,
[1=17 lbs. Troy.
144
1 oz. Avoir. : 1 oz. Troy
: 14-1^ : 16 or as 175 : 192.
.-. loz. Avoir, is i^f of 1 oz.
4) 1235—4
20) 308—3 qrs.
15 tons, 8 cwt.
15 Tons, 8 cwt, 3 qrs.,
17 lbs., 1 oz.
(3)
2qrs.=iof Icwt.
lqr.=iof2qrs.
141bs.=ioflqr.
21bs.=|ofl4ibs.
£ fi.
2. 0.
c. m.
7. 0.= value of 1 cwt.
16
32 11
1
5
2
~2 = value of 16 cwt.
3 5 = value of 2 qrs.
1 75 = value of 1 qr.
5 8-75 = value of 14 lbs.
3 6-964C8571=val. of 21bs.
£34. 9. 6.
8-21428571 = value of
[16 cwt, 3 qrs., 14 lbs.
i
Ex. LXXIX.]
(4) (') 20803) 67273 (3
6240S
KEY.
181
4864) 20803 (4
19456
1347)4864(3 -
4041
823)1347(1
O 823
2) 8, 9y 10, X?, 15, 18, 35, 84
2) 4, ^,
— 524) 823 (1
15, 9, 35, 42 624
3)2,
15, 9, 35, 21
299) 524 (1
299
?, ^, 8, 35, T
/. L. C. M. = 2 X 2 X 3 X 2 X 3 X 36 = 2520. 225) 299 (1
74) 225 (3 225
22a —
74
3) 74 (24
72 '
1)3(1
2
* 1
.*. 1 is the G. C. M.
(5) (') I of -A- of 99H = f of A of HF = 17
^ of t of 69 A = f of f of W = 11
f of f of 806i = f of f of ^^^ = 35 .
17 + 11 + 35 = 63.
(2) 13s. Hd. = 315 half pence
f of li of d guinea =f off of 504 h'f p.=567 h'f p.
.'. Fraction required is |^f = f .
(Continued on next page.)
KEY.
[Elem. Arith.
(6 continued.)
107 y 20
(') m of a ton=-~^ cwt.=4A^ cwt.
87 X A
^\^ of a cwt. =-—--- qrs. = 3/? qrs.
• A of a qr. = ?^- lbs. = 3 lbs.
4 cwt, 3 qrs., 3 lbs.
(6) -37) 7792-20 (21060
74
39
' a7
222
222
370) •0077022 (00002106
74
89
87
222
222
7792-2 = 7792i '007792 = -n^rnhnf
•37 = T^- To So iTJ X alo = TbiMMnrir
7792i ■+.-.% = ^n ^^ X W = -00002100,
=:x31060.
PAPER II.
(I) (') $7300
$31900
5475
$373.75
865 : 130 :; $273.75 :
interest required.
, ^273-75 X 120
.-. Int. req* = $-
(2) Int. on £100 for 2f yra.
at 3i per cent.=£9 12s.' 6d.
£109 12s. 6d. : £3204 14s. id.
:: £9 12s. 6d. : disc't req*
^. ,, 769139x2310^
•'•^^^^= 26310 ^'
= 675'^.9d.= £2817s. 5d,
= $90
365
Ex. LXXIX.]
KEY.
188
(2) 13320 - $3656 = $664.
$2656 : $100 :: $664 : required gain ner cent.
„ . ^ . 664x100 ^^^
.'. Required gain=$ — =$25.
$3820 : $100 :: $664 : loss per cent.
- , .664x100 ^^^
.*. Loss per cent.=$ ^^^^ = $20.
(3) 0)
605
3320
936372604 (30502
9
8037
3025
61002
122004
122004
o
16777216 (256
8
3x2«=12
3x20»=1200
3x20x5=800
^6^=25
1525
8777
7625
3x255^=1875
3x250^=187500
3x250x.6=4500
68=36
192086
1152216
1152216
(3) Surface of square = 2533 sq. ft., 6 4 sq. in. o r 364816
sq. inches; .'.side of square = y364816 sq. in »= 604 in.
= 16 yds., 2 ft., 4 in.; .". perimeter of square =16 y^.,
2 ft., 4 in. x4= 07 yds., 4 in.
1(4) 365
1825
r
] 365 t
r 20
7300
365
• 300
109500
100500
7300
1825
l.iJ
w
184
(5)
KEY.
[ElEM. AllITH.
2) 22933
S) 11466
8) 5733
3) 1911
7)637
2x2x3x3x7x7x13.
7)637
7)91
13
(6) If he travels 22| miles per hour, he will travel
20
20 miles in— of an hour, or f ? hours.
He then travels the remaining 32 miles at the rate
of (i of 22i) miles per hour = 3|| miles per hour.
.-. To travel 32 miles he would require (32-f-3|f) hrs.
= 8{U hrs. which added to the above f f hr.=9-iV5 hrs.
or 9 hrs., 34' 27:,V'.
If he start at 9 A. M. and travel for 9 hrs. 34' 27-3^"
he will arrive at his tourney's end at 6 h. 34' 27A" P- M.
PAPER III.
(1) If A fire twice in 3 minutes, he requires 1^ min-
utes to fire once; .'. to fire 55 cartridges he requu-es
(55 X 1^) minutes = 82i minutes.
Similarly B will requh-e (55 x If- minutes — 91f min-
utes ; ,\B will be fii-ing (91f -82i) minutes after A has
ceased =9^ minutes : and as he requires 1^ minutes
to fire once, he will fire (9^-f-lf) times := 5i times.
17 17
^^'^^^20x8~160
160) 17-0 (-10625
160
1000
9.60
(2) 3s. OR = 73 half pence
£5 = 2400 half pence
.-. Fraction = jH (J and .dec. =
2400) 7300 (030416
7200
400
320
^
\
800
800
16000
14400
10000
9600
4
4000
2400
1600 10000
(Continued on next page.)
^■£y^
Ex. LXXDC.]
KEY.
18S^
(3 Continued.)
(») -36 of a guinea = :i3(^ = ^ of a guinea.
21
189 (7s. em.
175
14
13
•36 of a £
4
20
11) 80
= A-ofa£
7s. 8A-d.
168
150
IF
/. -36 of a guinea = 7s. 6Hd. •
and M of a £ = 7s. 3 Ad.
.*. "36 of a guinea is the greater.
{*) 7s. 6ifd. - 7s. 3Ad. = 3',m.
(3) Int. of $100 for 1.5 mo's at 5 pci cent.=$6.25n
$106.25 : $552.50 :: $100 : required sum. '
.a . , ^100x552.50 ^
.-. Sum required=$— j^^g^- =$520.
(4) Number of sq. ft. on the walls = 143 x 3 x 2 = 858
This is obtained from (2 length -f- 2 breadth) x 11. r
. \ (2 length x 2 breadth) x 1 1 = 858.
or 2 lengthH-2 breadth = 78 ; but length = 2 breadth> -
.-. 3 breadth = 39. .-. breadth = 13 ft. and length = 26 ft.
No. of sq. ft. in floor = 26 x 18 = 338, or 37 sq, yds.
5 sq. ft. -
(5) From 9 A. M. on Tuesday till 11 A. M.'^on'
Wednesday there are 26 hours, during which time the
slow clock loses "Xf rrjnutes.
Also from 11 A. M. till 9 P. M. on Wednesday there'
are 10 hours.
26 hours : 10 hours :: 10 minutes : NoT'of minutes
which the slow clock loses in 10 houre = ^r^min.='
26
3 mmutes, 501^ seconds.
50i§ seconds = 13 minutes, 50}?} seconds.
I
►;■ I
< iti
4 fl
186
KEY.
[ElKM. AlUTH.
(C) 43 shares at £1U =£494^.
/. 138 :. 494J :: 100 stock : stock required.
.-. Stock required =:^^i^=38CH.
Annual income therefrom at 6 per cent =£23 3s, 7id.
#
TAPER rv.
.„ ^^ 4 5 4 5 36 IS ^ , \
^^ ^^ 21=3 ^ il=3 ^ 25=™* •"• Fraction required is
^^ \^ i5''i)j"3(r
O -027} 3-330 (133^
37
63
54
90
81
— .-. -037 can be taken 123 times from
'A=l 3'33 and the fraction remaining is ^.
(2) Each person received £3 3s. 4id. .-. The 43 per-
sons received £3 3s. 4id. x 43=£136 5s. Ud. '^
Then (£l-6d.) ; £1 :: £136 5s. l^d. : original am't.
Or 19s. 6d. : £1 :: £136 5s. lid. : original am't f
. ^ . . , , 65403x40, ,,
•. Origmal amount = ~ half pence = 67080
half penc3 = £139 15s.
39
(3) 0) 13 cwt. 3 qrs. 19 lbs. : 41 cwt, 1 lb. ) ..- «. \^'
35 : 49 * i" •• ^*l^s-
6d. : required amount.
Or 1531 lbs. : 4593 lbs.
35 : 40
in pence.
. ,, 1170x4593x49, ,^,,,
j- :: 1170d. : required amount
1581
Oi>
:Ex. LXXIX.J KEY. 187
O The bankrupt ows I) $2085— (1^235 +$325 4- ^fi9^^
=$2085-$1085=$1000. y'P^oo+^64o + ^525)
$1000 : $1 :: $525 : required payment in the |.
; . -Do^, ^. .„ ., ^ ^525 X 1 ^_
.*. Payment in the $=$
1000
52^ cts.
(4) £112i : 45s. :: £100 ; original cost per dozen
/.*. Original cost per doz.=- — —
/^. . 2250
s.=40s.
Since there arc 52 dozen in a butt, the averao-e cost
for a butt will be (40 x 52)s.=£104 ; and for three butts
,th&^ cost will be £(104x3)=£312. But the first and
second butts together cost £(120+110)=£230 • The
third butt costs £310 - £230-- £82. • • • ^ ac
(5) 2 Turkeys and O' fowls cost £2 18s. 6d.
.'.;. 10 turkeys and 45 fowls cost £14 12s. Cd. : also 5
turkeys and 2 fowls cost £4 8s. 2d..
•*v. 10 turkeys and 4 fowls cost £8 16s. 4d.
^But 10 turkeys and 45 fowls cost £14 12s. Cd
f \- ^ .^P^^® ^^^* ^^ l^s- ^^^-y ^^^ oiie fowl costs 2s lOd
- And jf 2 turkeys and 9 fowls cost £2 18s. 6d.. 2 tur-
keys will cost £2 IBs. 6d.-(9 x 2s. 10d.)=£2 18s. 6d.~
£1 5s. 6d.=£l 13s. .-. 1 Turkey will cost £1 138.+2
= los. 6d.
^(6) Area of field = 13 a c, 81 y ds. -63001 sq. yds.
\\ One side of fields V63001 yds. = 251 yds • Pe-
rimeter of fleld=251 yds. x 4=1004 yds. "^ ' " *
3} nils. : 1004 yds. :: 60 min. : required time
60x1004 . 60x3012
A
[.'. Required time =
.10 min. 16f f sec. ,
5866f
-mm.=
17600
-mm.=