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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 
 
 i /^'/f/ 
 
 •■■W M »pg)»iiii> l ii tj i ^ i jw i< n wiB|iawW j lil^i , ' ■ 
 
 V 
 
 4 -» ^^ 
 
'■i 
 
 ad 
 
 Mi. 
 
 r 
 
 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 
 
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 . 8 
 5 
 
 30910 . 
 
 1854 . 
 
 o 494 . 
 
 13 . 
 
 7 
 7 
 6 
 4 
 
 . 1 
 . 13 
 . 16 
 .' 7 
 
 . 16 
 . 13 
 . 16 
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 1 . 18 
 
 18 . 7 
 
 'M. 
 
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 * • ." *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^ 
 
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 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 
 
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 . 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 
 
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 1790 . 
 
 1 . 
 
 16 
 
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 59 . 
 
 2 . 
 
 18 
 
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 , 13 
 
 20 . 
 
 3 . 
 
 13 
 
 .13 
 
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 1870 
 
 23 
 
 5 
 
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 £ 
 
 4 
 
 49 
 
 498 
 
 (5) 
 s. 
 18 
 
 19 
 
 2469 , 15 
 
 296 . 7 
 
 4 . 18 
 
 2771 ~~ 
 
 d. 
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 11 
 10 
 
 2 
 5 
 
 10 
 6 
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 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 
 
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 (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.=