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Edited with the trial version of, Foxit Advanced PDF Editor, , SOE COMPETITIVE CLASSES, e, , 11, , To remove this notice, visit:, www.foxitsoftware.com/shopping, , Work done by 1 man in 1 day =, , 4. INSURANCE EXAMS, , 1, 12  36, , Work done by 8 men in 20 days =, , Answer Key, , 8  20, 12  36, , 1, , e, , 2, , d, , 3, , b, , 4, , c, , 5, , c, , 6, , d, , 7, , c, , 8, , c, , 9, , b, , 10, , b, , 11, , d, , 12, , c, , 13, , c, , 14, , a, , 15, , b, , Work done by 20 women in 20 days =, , 16, , c, , 17, , b, , 18, , a, , 19, , c, , 20, , d, , Total work done in 20 days, , 21, , d, , 22, , a, , Again, work done by 1 women in 1 day =, , =, , 1, 18  60, , 20  20, 18  60, , 8  20 20  20 20, +, =, 12  36 18  60 27, , Remaining work, , SOLUTION, , =, , 1. NATIONALISED BANKS &IBPS PO/ MT/SO EXAMS, 1, , (a) 12 men can complete the work in 36 days., , 7 , 20 , = 1 − , 27  27 , , Now, work done by 1 women in 4 days =, , ∴ 12 × 36 men can complete the work in 1 days., Again,, , ∴ 7/27 works is done by, , 18 women can complete the work in 60 days., , 18  60  7, = 70 women, 4  27, , ∴ 18 × 60 women can complete the work in 1 day., 12 × 36 men = 18 × 60 women, , 2, , = 12 × 162 women, , Now, 8 men + 20 women, , ⇒ 45 children = 18 men = 27 women, , = (4 × 5 + 20) women = 40 women, , ⇒ 5 children = 2 men= 3 women, , ∴ 18 women complete the work in 60 days., , Now, 4 men + 12 women + 10 children, , ∴ 40 women’ 20 days’ work, , = 4 men + 8 men + 4 men = 16 men, , 40  20 20, =, 18  60 27, , ∵ 18 men can complete the work in 72 days., , ∴ Remaining work, =1-, , (b) Clearly,, 9 × 360 children = 18 × 72 men, , ⇒ 2 men = 5 women, , =, , 4, 18  60, , ∴ 16 men can complete the work in =, , 20 7, =, 27 27, , 3, , 18  72, = 81 days, 16, , (b) ∵ 56 men can complete 1 work in 24 days., , ∵ 18 × 60 women do 1 work in 1 day., , ∴ 1 men complete the work in 24 × 56 days., , ∴ 1 woman does, , ∴ 42 men will do the same work in, , =, , 1, work in 1 day, 18  60, , =, , Method 2 :, , ∴ 1 woman does in 4 days, , Quicker Method, , =, , 4, 1, work, =, 18  60 18  15, , ∴, , 1, work is done in 4 days by 1 woman, 18  15, , ∴, , 24  56, = 32 days, 42, , ∵ M1 D1 = M2 D2, , 7, 18  15  7, work is done in 4 days by =, = 70 women, 27, 27, , Or, , ∴ 56 × 24 = 42 × D2, ⇒ D2 =, 4, , 56  24, = 32 days, 42, , (a) Days, , Women, , 18 ↑, , 42 ↓, , 21, , x

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , ∴ 21 : 18, , : : 42 : x, , 9, , 42  18, ⇒x=, = 36, 21, , 5, , (d) M1 D1 = M2 D2, 30×16 = 20 × x, , (b) (B + C)’s 1 days’ work =, , 1, … (ii), 12, , (A + C)’s 1 days’ work =, , 1, 16, , … (iii), , (a) As per given information,, , On adding all these three equations,, , 8 × 4 men = 12 × 4 women, , 2 (A + B + C)’s 1 day’s work, , = 8 × 8 children, , =, , ⇒ 32 men = 48 women, = 64 children, , 1 1, 1 6 + 4 + 3 13, +, +, =, =, 8 12 16, 48, 48, , ⇒ (A + B + C)’s 1 day’s work =, , ⇒ 2 men = 3 women = 4 children, = (3 + 6 + 3) women = 12 women, , Aliter :, , 1, Remaining work =, 2, , Total work Efficiency, , A + B – 12, , ∴ Required number of women = 12, , B+C–8, , 48, , Children, , 12 ↑, , 18 ↓, , C + A – 16, , 8, , x, , Efficiency of 2 (A + B + C), , ∴ 8 : 12 = 18 : x, , ∴ efficiency of A + B + C =, , 12  18, = 27, 8, , 3, , 13, 2, , ∴ Time taken by A + B + C, , Note: you can use the formula :, , =, , M1 D1 = M2 D2 and solved it., (a) According to the question,, 1 man = 2 women, , =, , ∴ 8 men + 4 women, = (16 + 4) women = 20 women, 4 men + 8 women = 16 women, 20 women’s 2 days’ work, =, , 6, , = 4 + 6 + 3 = 13, , ⇒ 8x = 12 × 18, , 8, , 4, , (d) Days, , ∴x=, , 2 1, =, 6 3, , 10, , 48, 2, = 48 ×, 13, 13, 2, 5, 96, =7, days, 13, 13, , (e) 10 men complete the work in 8 days., ∴ 80 men will complete the work in 1 days., 20 women complete the work in 6 days., ∴ 120 women complete the work in 1 days., ⇒ 80 men = 120 women, , Remaining work = 1 -, , 1 2, =, 3 3, , ⇒ 2 men = 3 women, ∴ 16 men + 18 women = 16 men + 18 ×, , ∵ 20 women complete 1 work in 6 days., ∴ 16 women will do, =, , 20  6 2,  = 5 days, 16, 3, , 96, =7, 13, , 5, days, 13, , 1, 2, , 12 women’s 2 day’s work =, , 13, 96, , ∴ A, B and C together can complete the work in, , ∴ 2 men + 8 children + 3 women, , 7, , … (i), , (A + B)’s 1 day’s work =, , x = 24, 6, , 1, 8, , 2, work in, 3, , ∵10 men can do the work in 8 days, , 2, men = 28 men, 3

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , ∴ 28 men can do the work in, , 5 men + 8 women ≡ 16 women, , 10  8 20, 6, = 2 days. 11, =, 28, 7, 7, , M1D1 = M2D2, , (c) Ayesha’s and Amita’s 1, , ⇒ 8 × 32 = 16 × D2, , day’s work, =, , ⇒ D2 =, , 1 1 1+2 3, + =, =, 16 8, 16, 16, , 16, ∴ Ayesha and Amita together can complete the work in, =5, 3, , 15, , 8  32, = 16 days, 16, , (b) 2 × 6 men ≡ 2 × 9 women, ≡ 3 × 8 children, 2 men ≡, , 1, days., 3, , 3 women ≡ 4 children, , 3 women + 4 children ≡ 4 men part of work done in 1, , Aliter :, , days by 4 men =, , Total work Efficiency, , Ayesha - 16, , ∴ Remaining, , 1, 16, , Amita – 8, , 12, , 2, work will be finished by 8 men in 1 days., 3, , Hence, 8 men would be required., , 2, , Time taken by both of them together to complete the, work, =, , 1, 3, , 16, , (d) Number of days =, , 17, , (d) ∴ A completes, , 16, 16, 1, = 5 days, =, 1+2 3, 3, , 6, work in 12 days., 7, , ∴ Time taken by A in doing whole work =, , (a) 72 men ≡ 144 women ≡ 180 children, ⇒ 2 men ≡ 4 women ≡ 5 children, , ∴ Time taken by B =, , 14, days., 1.5, , ∴ B’s 1 day’s work =, , 1.5, 14, , ∴ 4 men + 12 women + 20 children, = 4 men + 6 men + 8 men = 18 men, When 6 men do 1 work in 12 days,, , ∴ Remaining work =, , =, , 1, 2, , 1, × 6 × 12 = 1 × M2, 2, , 6  1.5 9, =, 14, 14, , ∴ Remaining work, , MD MD, Now, 1 1 = 2 2, W1, W2, , ⇒, , =118, , (d), , 9, 5, =, 14 14, , 20m 8, =, 30w 5, , ⇒ M2 = 36 = Number of men, ⇒ 1w =, , (a) Tricky approach, ⇒ 18 men = 5 × 18 ≡ 90 women, , = 10m + 18 ×, , ∴ 4 men 10 women = 30 women, M1D1 = M2D2, , 5  18, = 3 days, 30, , Number of men required to finish the work in 14 days, =, , (a) 8 × 20 men ≡ 8 × 32 women, ⇒ 5 men ≡ 8 women, , 5, m, 12, , 15 , , 35, =  10 +  m =, men, 2, 2, , , , ⇒ 5 × 18 = 30 D2, , 14, , 2 5, 5, m,  m=, 3 8, 12, , ⇒ 10m + 18w, , ∴ 1 men ≡ 5 women, , ⇒ D2 =, , 12  7, = 14 days, 6, , ∴ B’s 6 day’s work, , 18 men will do the same in 4 days., , 13, , 9800, = 28, 350, , 19, , 35 12, = 15 men, , 2 14, , (b) 2 men = 3 women

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , 1 men + 1 woman, , ⇒ D2 =, , 3 , 5, =  + 1  woman = women, 2, 2 , , 22, , 60, = 4 days, 15, , (d) (A + B)’s 1 day’s work =, , M1D1 = M2D2, ⇒3×4=, ⇒ D2 =, 20, , 5, × D2, 2, , 3  4  2 24, days, =, 5, 5, , (c) Examiners, 4, , 2, , work, Hours/day, , days, , 1 10, , , 2 20, , 5, , x, , 1, 40, , =, , 1, 1, 1, +, +, 20 30 40, , =, , 6 + 4 + 3 13, =, 120, 120, , ∴ (A + B + C)’s 1 day’s work =, , ⇒ 2 × 20 × x = 4 × 10 × 5 × 2, , =, , Aliter:, , 5, 1, =, 240 48, , C’s 1 day’s work, , M1D1H2 M2D2H2, =, W1, W2, , =, , 4  10  5 2  20  x, =, 1, 2, , 13, 1 13 − 12, 1, −, =, =, 240 20, 240, 240, , ∴ Required ratio = 48 : 240 or 1 : 5, Aliter :, , 4  10  5  2, ⇒x=, = 10 hrs., 2  20, , Total work Efficiency, , MD MD, (e) 1 1 = 2 2, W1, W2, , 6×6 9×10, =, W1, 1, , A + B – 20, , 6, , B + C – 30 120, , 4, , C + A – 40, , 3, , ∴ efficiency of A + B + C, , 66 2, =, 9  10 5, , ∴ Part of work done by 6 women in 6 days =, , =, , 6 + 4 + 3 13, = 6.5, =, 2, 2, , ∴ efficiency of A = 6.5 – 4 = 2.5, , 2, 5, , efficiency of B = 6.5 – 3 = 3.5, , ∴ Part of work done by 6 men in 6 days, , efficiency of C = 6.5 – 6 = 0.5, , 2 3, =1- =, 5 5, , ⇒ Time taken y A alone :, Time taken by C alone :, , M1D1 M2D2, =, W1, W2, , ⇒, , 13, 240, , ∴ A’s 1 day’s work, , 4  10  5  2, ⇒x=, = 10 hours, 2  20, , ⇒ W1 =, , (C + A)’s 1 day’s work =, , 2(A + B + C)’s 1 day’s work, , , , 1:2  : : 5 : x, 20:10, , 21, , 1, 30, , On adding,, , 2:4, , ⇒, , (B + C)’s 1 day’s work =, , 1, 20, , 6×6 15×D2, =, 3, 1, 5, , ⇒ 15 × D2 =, , 665, = 60, 3, , ⇒, , 1, :, efficiency of A, , 1, efficiency of C, , =, , 1, 2.5, , :, , 1, 0.5

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Edited with the trial version of, Foxit Advanced PDF Editor, , SOE COMPETITIVE CLASSES, , To remove this notice, visit:, www.foxitsoftware.com/shopping, , = 0.5 :, , 2.5, , ⇒ 5 boys ≡ 1 men, , =1, , :, , 5, , ∴ Required ratio = 1 : 5, , 23, , (c) (A + B + C)’s 1 day’s work, =, , 1, 1, +, 10 50, , =, , 5+1 6, 3, =, =, 50, 50 25, , 26, , (c), Working, Workers hours, Days, 13, , 18, , 24, , 36, , Time taken by A = x days (let), ∴ Time taken by (B + C), , 50, 2 3, ⇒x=, =, 3, x 25, , 50, days, 3, , 52, , 64, , = 24 × 13 × 432 × 21 × 64 × 32, , 3, 1, 2, 1, −, , , 50 50 50 25, , ⇒x=, , 24  13  432  21  64  32, 36  18  224  16  52, , = 48 days, , Aliter :, Time, , Total, , Efficiency =, , taken, , work, ,  Total work , , ,  Time taken , , A + B – 10, , 5, 50, , C - 50, , 27, , (e) ∵ 28 men’s day’s work =, , =5+1=6, , 1, 15, , ∴ 1 man’s 1 day’s work, =, , 1, 28  15, , ∴ 20 men’s 1 day’s work, , 1, , =, , ∴ efficiency of A + B + C, … (i), , 20, 1, =, 28  15 21, , ∴ 20 men’s, , from equation, we have, , 42, day’s work, 5, , 42 1 2, , =, 5 21 5, , a can do a certain work in the same time in which B & C, together can do it., , =, , ⇒A=B+C, , Remaining work = 1 -, , … (ii), , From (i) & (ii), we get, 2 (B + C) = 3, , Now, 36 women do, , We have efficiency of C = 1, ∴B+1=3, , ∴, , ⇒B=3–1=2, ∴ Time taken by B to complete the work, , 24, , 16, , 21, , ∴ 36 × 18 × 224 × 16 × 52 × x, , ∴ Required time = 25 days, , =, , 224, , 432, , , , 18 : 13 , , 224 : 432 : : 32 : x, 16 : 21 , , 52 : 64 , , ∴ B’s 1 day’s work, =, , Height, ,  36 : 24, , ∴ Time taken by (B + C), =, , Width, , 32, , x, , = x days, ∴, , Length, , Total work 50, = 25 days, =, efficiency, 2, , (b) 9 boys + 3 men ≡ 4 boys + 4 men, , ⇒, , 2 3, =, 5 5, , 3, 42, work in, days., 5, 5, , M1D1 M2D2, =, W1, W2, , 36×42 40×7, =, 3, W2, ×5, 5, , ⇒ 12 × 42 × W2 = 40 × 7

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , ⇒ W2 =, , 40  7 5, =, 12  42 9, , ⇒ W2 =, , ∴ Remaining work, =128, , 28  9, 7, =, 24  18 12, , ∴ Remaining work, , 5 4, =, 9 9, , =1-, , 7, 5, =, 12 12, , (c) 16 men + 12 women complete the work in 8 days., , This part of work is done by 10 men., , 20 men complete the work in 16 days., , M1D1 M2D2, =, W1, W2, , ∴ 16 × 8 men + 12 × 8 women, ≡ 20 × 16 men, , ⇒, , ⇒ 128 men + 96 women ≡ 320 men, ⇒ 96 women ⇒ 192 men, ⇒ 1 women = 2 men, , 12  20 10  D2, =, 5, 1, 12, , ⇒ 10 × D2 = 12 × 20 ×, , ∴ 16 women = 32 men, ⇒ D2 =, , ∴ M1D1 = M2D2, ⇒ 20 × 16 = 32 × D2, ⇒ D2 =, 29, , 20  16, = 10 days, 32, , 31, , 3 1, = :, 4 4, , ⇒ 36 × 40 = M2 × 32, ⇒ M2 =, , 30, , 36  40, = 45, 32, , 15  28, = 14 days, 30, , ∵ 15 women do the work in 24 days., ∴ Time taken by 18 women, 15  24, = 20 days, 18, , =, , M1D1 M2D2, =, W1, W2, , 36×40 M2  8, ⇒, =, 1, 1, 4, , (a) ∵ 28 men do 1 work in 15 days., , =, , Remaining time = 8 days, ∴, , 100, = 10 days, 10, , ∴ Time taken by 30 men, , (c) Remaining work, =1-, , ∴ Required ratio =, , 32, , (a) 24 men complete 1 work in 18 days., What part of work will 27 men do in 8 days?, , ∴ Additional men = 45 – 36 = 9, (b) According to the equation,, , ⇒, , 18 × 16 women, , = (12 + 16) children, = 28 Children, , 24  18 27  8, =, 1, W2, , ⇒ W2 =, , ⇒ 2 women ≡ 3 children, ∴ 8 women + 16 children, , 1 1, :, 14 20, , = 20 : 14 = 10 : 7, , M1D1 M2D2, =, W1, W2, , ≡ 24 × 18 children, , 5, = 100, 12, , 27  8 1, =, 24  18 2, , Remaining work = 1 -, , 1 1, =, 2 2, , This part of work is to be done by 14 women, M1D1 M2D2, =, W1, W2, , ∴, , M1D1 M2D2, =, W1, W2, , ∴, , ⇒, , 24  18 28  9, =, 1, W2, , ⇒, , 12  28 14  D2, =, 1, 1, 2

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , ⇒ 14 × D2 =, , 36, , ∴ B’s 1 day’s work =, , (e) Work done by 15 men in 9 days = W2 (let), ∴, , ⇒, , 18  30 15  9, =, 1, W2, , ⇒ 18 × 30 × W2 = 15 × 9, , ⇒, , 1 3, =, 4 4, , ⇒, , 15 + 30 − 2x, =1, 36, , According to the question, if efficiency of A = 1, then, efficiency of B = 2, ∵ A completes a job in 36 days and its efficiency is 1 then,, total work, = 1 × 36 = 36, , 3, × 16 × 36, 4, , Now,, , = 27 × 16, , Work done by A in 15 days, = 1 × 15 = 15, , 27  16, = 24 days, 18, , ∴ remaining work = 36 – 15 = 21, , 34Sol.(c) Work done by 8 women in 18 days = 144 unit, , ∴ Time taken by B to complete the 21 work, , work done by 12 women in 16 days = 192 unit, , =, , Remaining work = 192- 144 ⇒ 48 unit, 12 women will do this work in =, , 9, 1, = 4 days, 2, 2, , Aliter:, , 16  36 18  D2, =, 3, 1, 4, , ⇒ D2 =, , 15 15 − x, =1, +, 36, 18, , ⇒x=, , M1D1 M2D2, =, W1, W2, , ⇒ 18 × D2 =, , ∴, , ⇒ 2x = 45 – 36 = 9, , Again, 16 women complete the projects in 36 days., ∴, , 1, 18, , ⇒ 45 – 2x = 36, , 15  9 1, =, 18  30 4, , Remaining work = 1 -, , 1, 36, , Let B join with A after x days., , M1D1 M2D2, =, W1, W2, , ⇒ W2 =, , (a) A’s 1 day’s work =, , ∵ B is twice as efficiency as A., , 6  28, = 12 days, 14, , ⇒ D2 =, 33, , 1, × 12 × 28, 2, , 48, = 4 days, 12, , So total days = 18 + 4 = 22 days35, question,, , ⇒ 15 – 10.5 = 4.5 = 4, , (a) According to the, , (15 × 6) men + (16 × 6) women, , 21, = 10.5 days, 2, , ∴ after 4, 37, , 1, days, 2, , 1, days B joins with A., 2, , (d) According to the question,, , ≡ (12 × 32) women, , 15 × 8 men ≡ 18 × 10 women, , ⇒ 90 men + 96 women, , ⇒ 2 men ≡ 3 women, , ≡ 384 women, , ∴ 6 men + 6 women, , ⇒ 90 women ≡ (384 - 96) women, , ≡ (6 + 4) men = 10 men, , = 288 women, , ∴ M1D1 = M2D2, , ⇒ 10 men ≡ 32 women, , ⇒ 15 × 8 = 10 × D2, , ∴ M1D1 = M2D2, , ⇒ D2 = 12 days, , ⇒ 12 × 32 = 32 × D2, , or additional men = 0, , ⇒ D2 =, , 12  32, = 12 days, 32, , 38, , (a) According to the question,, 48 Children ≡ 16 women

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Edited with the trial version of, Foxit Advanced PDF Editor, , SOE COMPETITIVE CLASSES, ⇒ 3 children ≡ 1 woman, , ∵ A completes, , ∴ 28 women + 24 children, , ∴ Time taken by A in doing 1 work, , ≡ 36 women, , =, , ⇒ D2 =, =6, , 28  8 56, days, =, 36, 9, , = 24 ×, , 2, day, 9, , =, , 10×3, W1, , =142, , 10  3, 1, =, 15  24 12, , 1 1 2+1 1, +, =, =, 6 24 12, 4, , =, , 10  5, = 25 days, 2, , ∴ Remaining work, , (24 girls + 20 boys)’s 1 day’s work =, 5+3 8, =, 75 75, 75 2, , 8 5, , 15, 3, =3, 4, 4, , (d) B is, , 4, times as efficient as A., 3, , ∴ A and B worked together for 4 days., 43, , (e) Ratio of the time taken by each of A, B and C in doing, 1 work = 5 : 4 : 3, Time taken by A = 5x days, , 1 2, 3 2, − =1- =, 5 5, 5 5, , Time taken by C = 3x days, 1, 1, +, 15 25, , 2, 2, rd work = × 6, 3, 3, , = 4 days, , Similarly,, Time taken by 20 boys in doing 1 work =, , 1, 1 2+3 5 1, +, =, =, =, 15 10 30 30 6, , ∴ Time taken by A and B in doing, , ∴ Time taken by 24 girls in doing 1 work = 15 days, , 41, , 2, of work., 3, , (A + B)’s 1 day’s work, , (e) Time taken by 24 girls in doing one-fifth work = 3, days, , =, , 100, × 15 = 10 days, 150, , A and B together completed, , 1 3, =1- =, 4 4, , ∴ Required time =, , (c) A complete 1 work in 15 days., , ∴ Time taken by B =, , ∴ Remaining work, , =, , 5 4, =, 9 9, , B is 50% more efficient than A., , ∴ Total work done, , =1-, , 10 5, =, 18 9, , ∴ Remaining work, , ∴ M1D1 = M2D2, , =, , 1, 18, , ∴ B’s 10 day’s work, , 3 1, =, 18 6, , Work done by 10 women in 3 days = W1, , ⇒ W1 =, , 3, = 18 days, 4, , ∵ B’s 1 day’s work =, , (a) Work done by 14 men in 3 days =, , ⇒ 15 × 24 =, , 15  8, = 24 days, 5, , ∴ Time taken by in doing whole work, , ⇒ 28 × 8 = 36 × D2, , 40, , 5, th work in 15 days., 8, , ≡ (28 + 8) women, ∴ M1D1 = M2D2, , 39, , To remove this notice, visit:, www.foxitsoftware.com/shopping, , According to the questions,, 1, 1, 4, +, =, 5x 3x 45, , ⇒, , 3+5 4, =, 15x 45, , ⇒, , 8 4, =, x 3, , ⇒ 4x = 8 × 3, ⇒x=, , 83, =6, 4

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , ∴ Time taken by B = 6 × 4 = 24 days44, = 12 : 15, , (e) A : B = 4 : 5, , 50, ×D2, 8×25 3, =, ⇒, 7, 1, 15, , B : C = 3 : 4 = 15 : 20, ∴ A : B : C = 12 : 15 : 20, , ⇒ 8 × 25 =, , Time taken by A and C in doing 1 work = 15 days, ∴, , 1, 1, 1, +, =, 12x 20x 15, , ⇒ D2 =, , ⇒, , 5+3 1, =, 60x 15, , = 5 days, , ⇒, , 8, =1, 4x, , 8  25  7 28, =, 50  5, 5, , 3, 5, , 46, , ⇒ 4x = 8, , (d) B is, , 100, % more efficient than A., 3, , Time taken by A = 36 days, , 8, ⇒x= =2, 4, , ∴ Time taken by B, , ∴ Time taken by B = 15x, , = 36 ×, , = 15 × 2 = 30 days, 45, , 50 15, × D2, , 3 7, , (d) 8 men can do 1 work in 25 days., , = 36 ×, , 15 women can do the same work in 16 days., ∴ (8 × 25) men ≡ (15 × 16) women, ∴ 5 men ≡ 6 women, , = 36 ×, , ∴ 4 men + 8 women, , =, , 20 , , ≡ 4+,  men, 3 , , , =, , =, , 32,  10, 8  25 3, ⇒, =, 1, W2, , 105, 108, , 3, 1, =, 108 36, , ∴ Total time taken = 30 + 1 = 31 days, , 32  10, 8, =, 3  8  25 15, , 47, 8, 7, =, 15 15, , Again, 6 men join the team., , M1D1 M2D2, =, W1, W2, , 15  7 105, =, 108 108, , Now this part of work is done by A in 1 day., , Remaining work = 1 -, , ∴, , 1, 1 4 +3, 7, +, =, =, 27 36 108 108, , Remaining work = 1 -, , MD MD, ∵ 1 1= 2 2, W1, W2, , ∴ Number of men =, , 3, = 27 days, 4, , (A + B)’s 30 day’s work, , 32, men, 3, , ⇒ W2 =, , 1,  400 ,  3 %, , , , (A + B)’s 2 day’s work, , 5 , , ≡  4 +  8  men, 6 , , , ≡, , 1, 100 , ,  100 + 3  %, , , , 32, 50, +6=, 3, 3, , (c) ∵ 24 girls do, , 1, th of project in 4 days., 9, , ∴ 24 girls will do 1 work in 36 days., Again, remaining work, =1=, , 1 1, −, 9 3, , 9 −1 −3 5, =, 9, 9, , ∵ (24 girls + 30 boys) do, , 5, 20, work in, days., 9, 3

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , ∵ (24 girls + 30 boys) will do 1 work in, , 20 9,  = 12 days., 3 5, , =, , 48, days., 5, , ∴ One day’s work of 30 boys, =, , 2. SBI PO (Solution), 1, , 1, 1, −, 12 36, , 3−1 2, 1, =, =, =, 36, 36 18, , ∴ Required time = 18 days, 48, , (c) B’s 1 day’s work =, C’s 1 day’s work =, , 1, 2, =, 0.5x x, , (b) 2 men = 1 woman, ⇒ 1 man =, , 1, woman, 2, , ⇒ 3 men =, , 3, women, 2, , Again, 2 children = 1 man =, , 1, 8, , ⇒ 1 child =, , ∴ (B + C)’s 3 day’s work, =, , 1∴, ⇒, ⇒, , =, , 13, 13, day’s work =, 2x, 2, , Remaining work, , 2, , cases, 1 woman’s daily work =, , 2x − 13 6 3, − =, 2x, x 8, , =, , 2x − 13 − 12 3, =, 2x, 8, , = 16 men’s daily work., 12 men can do the work is 36 days, ∴ 16 men can do the work is 36 ×, , 100, = 20, 5, , ∴ Time taken by B in doing 1 work = 16 days, , 3, × 8 = 6 men’s daily work, 4, , = (10 men + 6 men), , ⇒ 8x – 3x = 100 ⇒ 5x = 100, , ∴ Time taken by A in doing 1 work = 24 days, , 3, , (c) A’s 1 day’s work =, , ∴ B’s 1 day’s work, , 1, 1, =, +, 24 16, , =, , 2+3 5, =, 48, 48, , ∴ Required time, , 12, = 27 days., 16, , 1, 12, , (A + B)’s 1 day’s work =, , ∴ (A + B)’s 1 day’s work, , =, , 3, th of 1 man’s daily work, 4, , (10 men + 8 womens daily work), , 3, 3x, × 2x =, 8, 4, , (d) Time taken by A in doing one-third work = 8 days, , 3, th of the work, 4, , Since time and the no. of persons is the same is both, , ⇒ 8x – 100 = 3x, , 49, , (b) In 36 days, 12 men can do 1 complete work., & in 36 days, 12 women can do, , 2 x − 13 6 3, = +, x 8, 2x, , ⇒x=, , 3, 3, + 4 + = 7 women, 2, 2, , Hence, 7 women complete the work in 7 days., , 13 2 x − 13, =, 2x, 2x, , ⇒ 2x – 25 =, , 6 3, = women, 4 2, , Now, three men, four women and six children, , 1, A’s 1 day’s work =, x, , ∴ A’s, , 1, woman, 4, , ⇒ 6 children =, , 6 3, +, x 8, , 1, woman, 2, , 1, 8, , 1 1 3−2 1, − =, =, 8 12 24 24, , ∴ B alone can do the work in 24 days., Aliter :, Total work Efficiency

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , A – 12, , 2, , ∴ 5x + 5 ×, , 24, A+B–8, , ⇒ 9x = 576000, , 3, , ⇒x=, , ∴ efficiency of B – 2 = 1, ∴ time taken by B alone, =, 4, , =, , (e) Days, , Men, , 10, , 8, , 12, , x, , 8, , (c) Time taken by Shruti in doing the work = 10 days, ∴ Time taken by Harish, , Where x = number of men, , = 5 days, , ∴ 8 : 10 :: 12 : x, , Time taken by Shankar, , ⇒ 8 × x = 10 × 12, , = 15 days, , 10  12, = 15, 8, , (e) (A + B)’s 1 day’s work =, , ∴ Work done by all three in 1 day, , 1, T, , =, , 1 1 1, + +, 10 5 15, , =, , 3 + 6 + 2 11, =, 30, 30, , Hence, the work will be finished in, , 1, B’s 1 day’s work =, T + 12, , ∴, , 1, 1, 1, +, =, (T + 3) (T + 12) T, , ⇒, , T + 12 + T + 3 1, =, (T + 3)(T + 12) T, , =, , 1, (Time taken by Shruti), 2, , ⇒, , 2T 15, 1, =, T + 15T + 36 T, , =, , 1, × 10 = 5 days, 2, , ∵ Harish works twice as fast as Shruti., ∴ Time taken by Harish, , 2, , Total work Efficiency, , ⇒ T2 =36, , Shruti – 10, , 3, , ⇒ T = 6 days, , Shanakar – 15 30, , 2, , Harish – 5, , 6, , (a) Tricky Approach, 4 × 2 men ≡ 4 × 4 women ≡ 20 children, ⇒ 2 men ≡ 4 women ≡ 5 children, ∴ 2 men + 4 women + 10 children, , ∴ Time taken by all of them together, =, , Total work, Total efficiency, , =, , 30, 3+2+6, , =, , 30, 8, =2, days, 11, 11, , = 20 children, M1D1 = M2D2, ⇒ 5 × 4 = 20 × D2 ⇒ D2 = 1 day, (c) Let Amit’s speed be x key depressions per day., ∴ Sujit’s speed =, , 4x, key depressions per day, 5, , 30, days., 11, , Aliter :, , ⇒ 2T2 + 15T = T2 + 15T + 36, , 7, , 64000, = 8000 per hour, 8, , The efficiency of Harish is twice to that of Shruti., , 1, A’s 1 day’s work =, T +3, , 6, , 576000, = 64000, 9, , ∴ Amit’s speed per hour, , 24, = 24 days, 1, , ⇒x=, 5, , 4x, = 576000, 5, , 9, , (a) B is 25% more efficient than C., ∴ Ratio of time taken by B and C

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , = 100 : 125 = 4 : 5, Time taken by B = 4x days, , ∴, , M1D1 M2D2, =, W1, W2, , ⇒, , 10  20 14  5, =, 1, W2, , Time taken by C = 5x days, ∴, , 1, 1, 3, +, =, 4 x 5x 40, , ⇒ W2 =, , 5+ 4 3, =, ⇒, 20 x 40, , Remaining work = 1 -, , 9, 3, =, ⇒, 20x 40, , ⇒, , ∴ Required time, =, , ⇒x=6, 11, , 13, × 20 = 13 days., 20, , (c) Remaining work, , Time taken by C = 30 days, =1-, , If the time taken by A be y days, then, , 1 1, 7, +, =, y 24 72, ⇒, =, , ∴, , 1 7 1 7 −3, = −, =, y 72 24 72, , ⇒, , 4, 1, , 72 18, , M1D1 M2D2, =, W1, W2, 16  30 M2  8, =, 5, 4, 9, 9, , ⇒ M2 × 8 × 5 = 16 × 30 × 4, ∴ Additional men, , ∴ (A + C)’s 1 day’s work, , = 48 – 16 = 32, , 1 1 5+3, +, =, 18 30 90, , =, , 8, 4, =, 90 45, , 12, , =, , (e) According to the questions,, 10 men complete the work in 6 days., 6 women complete the same work in 12 days., ∴ 10 × 6 men ≡ 6 × 12 women, , ∴ Time taken by A and C together, , 10, , 5 4, =, 9 9, , ∴ y = 18, , =, , ⇒ 5 men ≡ 6 women, ∴ 15 men + 10 women, , 1, 45, = 11 days, 4, 4, , ≡ (18 + 10) women, , (b) 10 × 15 men, , ≡ 28 women, , ≡ 8 × 25 women, , ∴ M1D1 = M2D2, , ⇒ 3 men ≡ 4 women, , ⇒ 6 × 12 = 28 × D2, , 3 men + 10 women, , ⇒ D2 =, , ≡ (10 + 4) women ≡ 14 women, 8 women’s 1 day’s work, =, , =, , =2, , 1, 25, , ∴ 10 women’s 1 day’s work, 10, 1, =, part, 25  8 20, , 7, 13, =, 20 20, , ∴ This part of work is done by 10 women., , 3 1, =, x 2, , Time taken by B = 24 days, , 14  5, 7, =, part, 10  20 20, , 13, , 6  12 18, =, 28, 7, , 4, days, 7, , 1 ,  1, (b) Work done by A and B in 20 days = 20  +, ,  80 120 ,  3+2  5, = 20 , =,  240  12, Work done by B in 12 days

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , =, , 12, 1, =, 120 10, , =, , Remaining work, =1=, , (10 men + 15 women)’s 1 day’s work =, , 5 1, −, 12 10, , 60 − 25 − 6 29, =, 60, 60, , =, , ∴, , 28 28 29, +, =, 120 x 60, , ⇒, , 28 29 28, =, −, x 60 120, , 1 10 1 1, −, = −, 6 100 6 10, , ∴ 1 woman’s day’s work, =, , 1, 225, , ∴ Required time = 225 days, 15, , According to the question,, A’s 4 day’s work + B’s 15 day’s work =, , Aliter :, Total work Efficiency, , A – 80, , 3, 240, , B – 120, , (d) Time taken by A = x days, ∴ Time taken by B = 3x days, , 58 − 28 30, 28 1, =, ⇒, =, 120, 120, x 4, , ⇒ x = 28 × 4 = 112 days, , ⇒, , 4 15 3, +, =, x 3x 4, , ⇒, , 4 5 3, + =, x x 4, , ⇒, , 9 3, =, x 4, , 2, , Now, according to question,, A works 20 days, , ⇒x=, , B works (20 + 12 + 28) = 60 days, , 9 4, = 12 days, 3, , C works 28 days., , Time taken by B alone, , ∴ Works done by A in 20 days, , ∴ Time taken by B = 3 × 12, , = 20 × 3 = 60, , = 36 days, , Work done by B in 60 days, , = 3x = 3 × 12 = 36 days, , = 60 × 2 = 120, , 16, , (d) Time taken by = x days, , ∴ Remaining work, , C is 40% less efficiency than A., , = 240 – 120 – 60 = 60, , ∴ Time taken by A, , 60 15, =, ∴ Efficiency of C =, 28 7, , = 0.6x days, , ∴ Time taken by C to complete the whole work alone, =, , 240, 15, 7, , = 240 ÷, , 15, 15, = 240 ×, 7, 70, , = 112 days, 14, , 1, 6, , 15 women’s 1 day’s work, , Let C alone do the work in x days., , =, , 1, 100, , (A + B)’s 1 day’s work =, , 1, 10, , … (i), , (B + C)’s 1 day’s work =, , 1, 15, , … (ii), , Equation (i) – (ii), (A - C)’s 1 day’s work, =, , 1 1, −, 10 15, , =, , 3−2 1, =, 30 30, , (e) 1 man’s 1 day’s work, , 3, 4

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , ⇒, , 1, 1 1, − =, 0.6 x x 30, , 5 17 3, +, =, x y 4, , ⇒, , 10 1 1, − =, 6x x 30, , Equation (ii) – 5 × (i) :, , 12 3 5 3 1 1, = −, = − =, y 4 20 4 4 2, , 5 1 1, − =, 3x x 30, , ⇒, , ⇒, , 5−3 1, =, 3x 30, , ⇒, , ⇒, , 5−3 1, =, 3x 30, , ⇒, , 2 1, =, x 10, , ∴ B alone can do the remaining, , ∵ 1 work is done by A & B together in 20 hrs., ∴, , 6, × 20 = 12 days, 10, , Let, efficiency of A = a and that of B = b, ∴ (a + b) 15 = a × 5 + b × 17, ⇒ 15a + 15b = 5a + 17b, , ⇒ 12 days, , ⇒ 10a = 2b, , (b) C is 20% more efficient than A., , a 2 1, =, =, b 10 5, , ∴ Time taken by A = 6x days, , ⇒, , Time taken by C = 5x days, , ⇒a:b=1:5, , (B + C)’s 1 day’s work =, , 1, 16, , Total work, , … (i), , = (Total efficiency) × time taken, , 1, … (ii), 15, , = (1 + 5) × 20 = 120, ∴ Remaining work, , ∴ By equation (ii) – (i),, ,  3, = 120 ×  1 − ,  4, , (C - A)’s 1 day’s work, =, , 1 1, −, 15 16, , ∴, , 1 1, 1 1, −, = −, 5x 6x 15 16, , = 120 ×, , 1, = 30, 4, , ∴ time taken by B to finish the remaining work, =, , 6 − 5 16 − 15, =, ⇒, 30x, 240, , 19, , ⇒ 30x = 240, , 18, , 3, 3, th work is done by A & B together in 20 × = 15 hrs., 4, 4, , ∴ Time taken by A = 0.6 × 20, , (A + B)’s 1 day’s work =, , 30, = 6 hrs., 5, , (b) C is twice as good as B., ∴ If time taken by B be 2x days,, , 240, ⇒ 6x =, × 6 = 48 days, 30, , Time taken by C = x days, , = Time taken by A, , ∴, , 1 1 3, + =, 2x x 40, , (b) Let A and B do the work alone in x and y hours, respectively., , ⇒, , 1+2 3, =, 2x, 40, , ⇒, , 3, 3, =, 2x 40, , So,, , 1 1 1, + =, x y 20, , 1, 24, work in, = 6 hours, 4, 4, , Aliter :, , Time taken by A to finish the work alone, , 17, , 1, 1, 1, =, =, y 2  12 24, , ∴ B alone can do the whole work in 24 hours., , ⇒ x = 2 × 10 = 20 days, , = 0.6x =, , … (ii), , … (i), , ⇒ 2x = 40 ⇒ x = 20

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Edited with the trial version of, Foxit Advanced PDF Editor, , SOE COMPETITIVE CLASSES, ∴ Time taken by B = 40 days, , 2 1 1, − =, [A is twice as efficient as C]., x x 60, , ∴ Time taken by B = 40 days, If A takes y days, then, , 21, , ⇒, , y, 8y, =, 8 40 + y, , (c) work done by A =, Work done by B =, , , ,  1  8, , ⇒ y=,  40 + y  5,  40 y , , , , 5, 5, y=, 8, 8, , 1 1, ⇒ x = 60 days, =, x 60, , ⇒, , , ,  1  160, , y= ,  1 + 1  100,  y 40 , , , , ⇒, , 2, 5, , Time taken by B in doing 1 work =, , 5( x + 8 ), , ∴, , 3, , 3, , 5x, days, 2, , =, , 5x 120, , 2 100, , x + 8 3x, =, 3, 5, , ⇒, , OR, , ⇒ 9x = 5x + 40, , B:C=2:1, Time taken by both in doing work =, ∴ Time taken by B =, , ⇒ 4x = 40 ⇒ x = 10, , 40, 3, , ∴ Time taken by A =, , 40, × 3 = 40 days, 3, , Time taken by B = 25 days, , 40 3, × = 20 days, 3 2, , ∴ Work done by both in 1 day, =, , A+B 160 8, =, =, A 100 5, , 1 1 5 + 6 11, +, =, =, 30 25 150 150, , ∴ Required time =, , ⇒ 5A + 5B = 8A, ⇒ 3A = 5B, ⇒A:B=5:3, ∴ Time taken by A =, , 3, × 40, 5, , 5  18, 3, , = 30 days, , Again,, , 150, 7, = 13, days, 11, 11, , 3. RBI GRADE-B NABARD, GRADE-A OFFICER EXAMS, 1, , (a), , = 24 days (inverse ratio), , Men, , Hours/day, , Days, , 1, (d) (A + B)’s 1 day’s work =, 20, , 9, , 6, , 7, , 9, , 15, , x, , (B + C)’s day’s work =, , 1, 30, , ∴ (A - C)’s 1 day’s work, =, , 5( x + 8 ), , B is 20% more efficient than A., , ⇒ y = 64 – 40 = 24 days., , 20, , 3, 5, , ∴ Time taken by A in doing 1 work =, , ⇒ 40 + y = 64, , Time taken by C =, , To remove this notice, visit:, www.foxitsoftware.com/shopping, , 1, 1 3−2 1, −, =, =, 20 30 60 60, , If time taken by C be x days, then, , Where x = number of days, ∴, , 6 : 9,  : : 15 : x, 9 : 7, , ⇒ 6 × 9 × x = 9 × 7 × 15, ⇒x=, , 9  7  15 35, 1, = 17 days, =, 69, 2, 2

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Edited with the trial version of, Foxit Advanced PDF Editor, , SOE COMPETITIVE CLASSES, 2, , (b) 12 boys = 15 girls, , ⇒, , ⇒ 24 boys = 30 girls, ∴ 24 boys + 6 girls, , ⇒ 24D2 = 180 ⇒ D2 =, , M1D1 M2D2, =, W1, W2, , =, , 15  48 36  D2, =, 1, 2, , 5, , 1 child will complete the work in, = 18 × 10 = 180 days, 4 men + 120 women + 20 children’s 2 days work, , 9 + 4 + 3 16 2, =, =, 72, 72 9, ,  4 12 20 , +, = 2 +, ,  72 144 180 , , 9, 2, ,  1 1 1, = 2 + + ,  18 12 9 , , = 1656 minutes = 27.6 hours, 4, , (e) According to the question,, , =, , (18 × 10) men ≡ (16 × 12) women, ⇒ 15 men ≡ 16 women, , 2(2 + 3 + 4 ), 36, , =, , 1, 2, , ∴ Remaining work =, , 8 women + 6 men, , 1, 2, , ∴ Required number of men, ,  15 , =  + 6  men,  2, , , = 72 ×, ,  15 + 12 , =,  men,  2 , , 6, , 1, = 36, 2, , (c) According to the question,, 15 × 4 women ≡ 32x children, , 27, men, 2, , =, , (a) 1 man will complete the work in, , = 8 × 18 = 144 days, , 1 1, 1, = +, +, 8 18 24, , ∴ Time taken = 368 ×, , 15, 1, = 7 days, 2, 2, , 1 woman will complete the work in, , (b) Page printed in one minute, , =, , 180, 24, , = 6 × 12 = 72 days, , 15  48, ⇒ D2 =, = 40 days, 18, , 3, , 18  10 8  D2, =, 1, 1, 3, , 30 girls + 6 girls = 36 girls, , ⇒, , ⇒ 15 women ≡ 8x children, , ∵ 18 men do the work in 10 days., , ∴ 10 women + 20 children, , ∴, , M1D1 M2D2, =, W1, W2, ,  8x, , ≡   10 + 20  children,  15, , , ⇒, , 18  10 27, 80, = , 1, 2 9  W2, ,  16 x, , + 20  children, = , 3, , , , ⇒ 180 =, ⇒ W2 =, , 120, W2, , If work done by 3 women in, , = work done by 8 men, , M1D1 M2D2, =, W1, W2, , 15, days be W2, then, 2, , 15  4 3  15, =, W1, W2  2, , 120 2, =, 180 3, , Remaining work = 1 -, , ∴, , To remove this notice, visit:, www.foxitsoftware.com/shopping, , 2 1, =, 3 3, , ⇒ 15 × 4 × 2 × W2 = 3 × 15, ⇒ W2 =, , 3, 8, ,  16 x, , 5, + 20  children in 3 days =, ∴ Work done by , 8,  3, 

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , ⇒ W2 =, , 5, ⇒ 32x × = 16x + 60, 8, , =1-, , 7 1, =, 8 8, , 9, , (a) Time taken in completing the project = x days (let), , ⇒ 20x = 16x + 60, , ∴ Remaining work, , According to the question,, , ⇒ 20x – 16x = 60 ⇒ 4x = 60, , x − 10 x, =1, +, 20, 30, , ⇒ x = 15 days, 7, , (b) M1 D1 = M2 D2, ⇒ 8 × 9 = 12 D2, ⇒ D2 =, , 89, = 6 days, 12, , ⇒, , x 1 x, =1, − +, 20 2 30, , ⇒, , 1 3, x, x, =1+ =, +, 2 2, 20 30, , ⇒, , 3x + 2x 3, =, 60, 2, , ∴ Time taken by 18 women, = 10 days, ∴ 18 × 10 women ≡ 12 × 6 men, ≡ (6 + 12) men ≡ 18 men, ∴, , M1D1 M2D2, =, W1, W2, , ⇒, , 8  9 18  3, =, 1, W2, , ⇒x=, 10, , 90, = 18 days, 5, , (b) For men,, , M1D1 M2D2, =, W1, W2, , ∴ Remaining work, =1-, , 3, × 60 = 90, 2, , ⇒ 5x =, , ⇒ 5 women ≡ 2 men, , 8, , 63  6 7, =, 18  24 8, ,  16x, , + 20   3, 32x  3, , ∴, =, 5, 1, 8, , ⇒ 32 × 12 =, , 3 1, =, 4 4, , ⇒ W1 =, , (a) According to the question,, , 24  4, W2, , 24  4 1, =, 32  12 4, , M1D1 = M2D2, , For women,, , 12 × 20 = 15 × D2, , M1D1 M2D2, =, W1, W2, , ⇒ D2 =, , 12  20, = 16 days, 15, , ⇒ 20 × 18 =, , ∴ Time taken by 18 women = 24 days, ∴ (15 × 16) men, , ⇒ W2 =, , ≡ (18 × 24) women, ⇒ 5 men ≡ 9 women, , 36  5 1, =, 20  18 2, , Required ratio =, , ∴ 15 men + 36 women, ≡ (27 + 36) women, , 36  5, W2, , 11, , (e) 15 men do, , ≡ 63 women, ∴, , M1D1 M2D2, =, W1, W2, , ⇒, , 18  24 63  6, =, 1, W2, , ∴, , 1 1, : =1:2, 4 2, , 1, th of work, 8, , M1D1 M2D2, =, W1, W2, , ⇒ 24 × 20 = 15 × D2 × 8, ⇒ D2 =, , 24  20, = 4 days, 15  8

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , Now 18 men do, , ∴, , 7, th of work., 8, , =, , M1D1 M3D3, =, W1, W3, , ⇒ 24 × 20 =, , ⇒ 18 × D3 =, ⇒ D3 =, , 1, 5+6, 11, 1, =, +, ⇒, 8  12 8  10, 60  8 60  8, , ∴ (P + Q)’s 1 day work working 8 hours a day, =, , 18  D3, 7, 8, , 11  8 11, =, 60  8 60, , ∴ No. of days required =, , 7, × 24 × 20, 8, , 3, , 7 24  20, ×, 18, 8, , (b) Let the man worked overtime for x, hours., Basic pay of 40 hours, = Rs. 200, , 200, ∴ Basic pay of 1 hour = 40, , 70, =, days, 3, , = Rs. 5, , ∴ Required time, , According to the question,, , 70 , , =  4 +  days, 3 , , , 200 + x ×, , 1, , 1, =  4 + 23  days = 27 days, 3, 3, , , ⇒, , ⇒x=, , (e) According to the question,, A’s one day work =, , = 40 + 16 = 56, , 1, B’s one day work =, 8, , 4, , Less efficiency, more days, (Indirect), , 12 : 9, Men, , 15 , Hrs/day 6 :,  : : 20 : x, 2 , 1 1, : , Efficiency, 2 3, , Similarly,, (A + B + C)’s one day work =, , 7, 16, , 7 3 1, − =, 16 8 16, , ∴ 12 × 6 ×, , Therefore, C can complete the whole work in 16 days., (d) P can complete a work in 12 days working 8 hours a, day, ∴ P can do a work in 12 days working 1 hour a day =, ∴ P’s 1 day work working 1 hour a day =, , 1, 8  12, , Similarly, Q’s 1 day work working 1 hour a day, =, , (c) More men, less days (Indirect), Less hrs/day, more days (Indirect), , 1 1 3, (A + B)’s one day work = + =, 4 8 8, , 2, , 100  4, = 16, 25, , ∴ Total hours of work, , 1, 4, , ∴ C’s one day work =, , 5  125, = 300, 100, , 25, x = 300 – 200, 4, , 4. INSURANCE EXAMS, 1, , 5, 60, =5, days., 11, 11, , 1, 8  10, , ∴ (P + Q)’s 1 day work working 1 hour a day, , ⇒x=, , 1, 8, , 1, 15 1, × x = 9 ×  × 20, 2, 2 3, , 9  15  2  20 25, 1, =, = 12, 2  3  12  6, 2, 2, , ∴ Required number of days = 12, 5, , 1, 2, , (c) Let the number of books distributed by a man, a, woman and a child per day be 5x, 4x and 2x respectively., Books distributed on the first day, = 7 × 5x + 5 × 4x + 8 × 2x, = 35x + 20x + 16x = 71x, Books distributed on the second day

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , = 7 × 5x + 3 × 4x + 5 × 2x, , Aliter :, , = 35x + 12x + 10x = 57x, , Let efficiency of B = 1, , Books distributed on the third day, , Then efficiency of A = 2, , = 4 × 5x + 5 × 4x + 3 × 2x = 46x, , ∴ total work = (1 + 2) × 14 = 42, , ∴ 71x + 57x + 46x = 2000, , ∴ time taken by A alone to finish the work, , ⇒ 174x = 2000, ∴ 57x =, 6, , =, , 2000, × 57x = 650, 174x, , 10, , (d) 3 women ≡ 2 men, , hours/day, , 15, , 14, ∴, , 8, , 6, , 11, , days, , 21, , x, , 15  8  21, = 30 days, 14  6, , 12, , 30, , x, , 30  16, = 24, 20, , (c) (P + Q)’s 1 day’s work =, , (c) Tricky Approach :∴ If A completes a work in 30 days. B will complete it in, 90 days., ∴ (A + B)’s day work, =, , (Q + R)’s 1 day’s work =, , 1, 15, , (R + P)’s 1 day’s work =, , 1, 20, , 2 (P + Q + R)’s 1 day’s work, 1, 45, = 22 days., 2, 2, , =, , 1 1 1 5+ 4+3 1, + +, =, =, 12 15 20, 60, 5, , (c) Men, , Days, , (P + Q + R)’s 1 day’s work, , x, , x − 10, , 100, , 110, , =, , ⇒, , x − 10 100, , , x, 110, , =, , ⇒ x = 110 men, (b) If time taken by B be 2x days, then time taken by A =, x days., , 1, 10, , ∴ P’s 1 day’s work =, , ⇒ 11x – 110 = 10x, , 1 1, −, 10 15, , 3−2 1, =, 30 30, , Hence, P alone will complete the work in 30 days., 13, , (c) M1D1 = M2D2, , ∴, , 1 1, 1, +, =, x 2x 14, , ⇒ x × 30 = (x + 6) × 20, , ⇒, , 2+1 1, 3 1, =, ⇒ =, 2x, 14, x 7, , ⇒ x = 12 men, , ⇒ x = 3 × 7 = 21 days, , 1, 12, , On adding,, , 1, 1 3+1 2, +, =, =, 30 90 90 45, , ∴ Hence, both will complete the work in, , 9, , 16, , 20, , ⇒x=, , A is three times as good a workman as B., , 8, , Men, , ⇒ 20 × x = 16 × 30, , ∴ 14 × 6 × x = 15 × 8 × 21, , 7, , (d) Days, , ∴ 20 : 16 = 30 : x, , 14 : 15,  : : 21 : x, 6:8 , , ⇒x=, , 1 1 3+2 1, + =, =, 10 15 30 6, , ∴ Number of days to complete the work = 12, , Working, Men, , (b) work done in 1st two days, =, , ⇒ 21 women ≡ 14 men, , 42, = 21 days., 2, , ⇒ 3x = 2x + 12, , 14, , (a) (1 man + 1 woman + 1 boy) 1 day work =, , 1, 3

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , ∴ Woman’s 1 day’s work, , =1-, , 1 1 1, = − −, 3 6 18, , =, , According to the question,, , 6 −3−1 1, =, 18, 9, , M1D1 M2D2, =, W1, W2, , ∴ The woman alone will complete the work in 9 days., 15, , ⇒, , (b) M1D1 = M2D2, ⇒ 8 × 40 = 10 × D2, ⇒ D2 =, , 16, , 8  40, 10, , 20  16 ( 20 − x )  55, =, 11, 1, 3, 16, , ⇒ 20 × 16 =, , (20 − x )  55 16, 11  3, , = 32 days, , ⇒ 20 × 3 = (20 - x) × 5, , (c) 10 women complete the work in 7 days., , ⇒ 60 = 100 – 5x, , 10 children complete the same work in 14 days, , ⇒ 5x = 100 – 60 = 40, , ∴ 1 woman ≡ 2 children, , ⇒x=, , ⇒ 5 women + 10 children = 20 children, 20, , By M1D1 = M2D2., 10 × 14 = 20 × D2, ⇒ D2 =, 17, , 5 11, =, 16 16, , 40, =8, 5, , (d) Part of work done by 8 men in 10 days = W, ∴ M1D1 =, , 10  14, = 7 days., 20, , M2D2, W, , ⇒ 12 × 20 =, , (b) According to the question,, 9 × 360 children = 18 × 72 men, , ⇒W=, , = 12 × 162 women, ⇒ 5 children =2 men = 3 women, , 8  10, W, , 8  10 1, =, 12  20 3, , Remaining work = 1 -, , ∴ 4 men + 12 women + 10 children, = 10 children + 20 children + 10 children, , 1 2, =, 3 3, , ∵ Time taken by 18 women in doing, , = 40 children, M1D1 = M2D2, , ∴ Time taken by them in doing whole work =, , ⇒ 9 × 360 = 40 × D2, 21, , (d) Part of work done by 14 men in 3 days = W2, W1 = 1, , (a) M D = M1D1 + M2D2 + M3 × D3, ⇒ 24 × 14 = 24 × 2 + 28 × 2 + 22 × D3, , ∴, , M1D1 M2D2, =, W1, W2, , ⇒, , 8  21 14  3, =, 1, W2, , ⇒ 336 = 48 + 56 + 22 × D3, ⇒ 22 × D3 = 336 – 104 = 232, ⇒ D3 =, ⇒ 10, 19, , 232 116, =, 22, 11, , ⇒ 8 × 21 × W2 = 14 × 3, , 6, days, 11, , ⇒ W2 =, , (c) Let the number of men who left be x., Part of work done by 20 men in 5 days =, ∴ Remaining work, , 16  3, = 24, 2, , days, , 9  360, ⇒ D2 =, = 81 days., 40, , 18, , 2, work = 16 days, 3, , 14  3 1, =, 8  21 4, , ∴ Remaining work = 1 5, 16, , 1 3, =, 4 4, , ∵ Time taken by 9 women in doing, , 3, th work = 24 days, 4

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , ∴ Time taken by them in doing whole work, =, 22, , 24  4, = 32 days, 3, , (a) Time taken by A = 24 days, B is 20% more efficient than A., ∴ Time taken by B, =, , 24  100, = 20 days, 120, , Similarly,, Time taken by C = 20 ×, , 100, 125, , = 16 days, ∴ (B + C)’s 1 day’s work, =, , 1, 1 4+5 9, +, =, =, 20 16 80 80, , ∴ Required time =, , 80, 8, = 8 days., 9, 9, , SOE COMPETITIVE CLASSES, SAFAKHANA ROAD DUMRAON, cont- 9931878918