Time and work
- 12 men or 18 women can complete a piece of work in 14 days. In how many days will 8 men and 16 women together complete the same work? Answer: D. 9 days Answer: (D) 9 days 12 men = 18 women, so 1 man = 1.5 women. 8 men + 16 women = 12 + 16 = 28 women. Work = 18 × 14 = 252 wo... 1
- A can do a piece of work in 16 days and B can do it in 24 days. They work together for 6 days and then A leaves. In how many more days will B finish the remaining work? Answer: B. 9 days Answer: (B) 9 days In 6 days together: 6(1/16 + 1/24) = 6 × 5/48 = 5/8 . Remaining 3/8 ; B needs 3/8 × 24 = 9 days. 1
- A and B together can finish a work in 12 days, B and C in 15 days, and C and A in 20 days. In how many days can A, B and C together finish it? Answer: C. 10 Answer: (C) 10 2(A + B + C) = 1/12+1/15+1/20 = 12/60 = 1/5 . So A + B + C = 1/10 : 10 days. 1
- A can finish a work in 12 days and B in 18 days. They work together for 4 days, after which A leaves. In how many more days will B finish the remaining work? Answer: D. 8 Answer: (D) 8 In 4 days they do 4(1/12+1/18) = 5/9 . Remaining 4/9 at B's rate 1/18 takes 8 days. 1
- A can finish a piece of work in 12 days and B in 18 days. How many days will they take working together? Answer: D. 7.2 days Answer: (D) 7.2 days Shortcut: together = ab/a+b = 12 × 18/30 = 7.2 days. LCM method: work = 36 units; A does 3/day, B 2... 1
- 15 men can finish a job in 20 days. How many days will 25 men take to finish the same job? Answer: D. 12 days Answer: (D) 12 days Shortcut: M₁D₁ = M₂D₂. 15 × 20 = 25 × D, so D = 12 days. 1
- A can do a piece of work in 10 days. What fraction of the work is left after A works for 4 days? Answer: A. 3/5 Answer: (A) 3/5 A does 1/10 per day, so 4/10 in 4 days. Work left = 1 - 2/5 = 3/5 . 1
- A and B together can do a work in 8 days. A alone can do it in 12 days. How many days will B alone take? Answer: A. 24 days Answer: (A) 24 days Shortcut: B = 8 × 12/12 - 8 = 96/4 = 24 days. LCM: work = 24 units; A+B = 3/day, A = 2/day, so B = 1/... 1
- A is twice as efficient as B. Together they finish a work in 14 days. How many days will A alone take? Answer: D. 21 days Answer: (D) 21 days Efficiencies A : B = 2 : 1. Total work = (2 + 1) × 14 = 42 units. A alone = 42 ÷ 2 = 21 days. 1
- A can do a work in 20 days and B in 30 days. They work together for 6 days. What fraction of the work is left? Answer: B. 1/2 Answer: (B) 1/2 Together per day = 1/20 + 1/30 = 1/12 . In 6 days they do 6/12 = 1/2 . Work left = 1/2 . 1
- A is 25% more efficient than B. If B takes 20 days to do a work, how many days will A take? Answer: A. 16 days Answer: (A) 16 days Time is inversely proportional to efficiency. A's time = 20 ÷ 1.25 = 16 days. Trap: 25% less time (15... 1
- A, B and C can finish a work in 10, 12 and 15 days respectively. How many days will they take working together? Answer: C. 4 days Answer: (C) 4 days LCM method: work = 60 units. A = 6, B = 5, C = 4 units/day; together 15 units/day. Days = 60 ÷ 15 = 4. 1
- A and B together can do a work in 10 days, B and C in 15 days, and C and A in 12 days. How many days will A, B and C take working together? Answer: B. 8 days Answer: (B) 8 days Work = 60 units. (A+B) = 6, (B+C) = 4, (C+A) = 5 units/day. Adding: 2(A+B+C) = 15, so A+B+C = 7.5 units... 1
- A can do a work in 15 days. B is 50% more efficient than A. How many days will they take working together? Answer: A. 6 days Answer: (A) 6 days B takes 15 ÷ 1.5 = 10 days. Together = 15 × 10/25 = 6 days. Efficiency method: A : B = 2 : 3, work = 2... 1
- 4 men or 6 women can finish a work in 12 days. How many days will 3 men and 3 women take to finish it? Answer: C. 9.6 days Answer: (C) 9.6 days 4 men = 6 women, so 1 woman = 2/3 man. 3 men + 3 women = 3 + 2 = 5 men. 4 men take 12 days, so 5 me... 1
- 12 men working 8 hours a day finish a job in 10 days. In how many days will 15 men working 6 hours a day finish it? Answer: A. 102/3 days Answer: (A) 102/3 days Shortcut: M₁D₁H₁ = M₂D₂H₂. 12 × 10 × 8 = 15 × D × 6, so D = 960/90 = 102/3 days. 1
- A can do a work in 20 days and B in 30 days. They start together, but A leaves after 5 days. In how many days in all is the work finished? Answer: A. 22.5 days Answer: (A) 22.5 days Work = 60 units; A = 3, B = 2 units/day. In 5 days together they do 25 units; 35 units remain. B... 1
- A can do a work in 6 days and B in 8 days. Working together they finish it and are paid ₹1,400. What is A's share? Answer: C. ₹800 Answer: (C) ₹800 Wages are shared in the ratio of work done, i.e. efficiencies. A : B = 1/6 : 1/8 = 4 : 3. A's share = 4/7 ×... 1
- A and B can do a work in 6 days. With the help of C they finish it in 4 days. How many days will C alone take? Answer: C. 12 days Answer: (C) 12 days Shortcut: C = 6 × 4/6 - 4 = 12 days. 1
- A can do a work in 10 days and B in 15 days. They work on alternate days, with A starting on the first day. In how many days will the work be finished? Answer: B. 12 days Answer: (B) 12 days Work = 30 units; A = 3 units/day, B = 2 units/day. Every 2 days, 5 units are done. 30 units need 6 su... 1
- 10 men can finish a job in 15 days. After they have worked for 5 days, 5 more men join them. In how many more days will the job be finished? Answer: D. 62/3 days Answer: (D) 62/3 days Remaining work = 10 men × 10 days = 100 man-days. Now 15 men work, so days = 100 ÷ 15 = 62/3 . 1
- A is four times as efficient as B and takes 45 days less than B to finish a work. How many days will they take working together? Answer: C. 12 days Answer: (C) 12 days If A takes x days, B takes 4x days. 4x − x = 45, so x = 15. B takes 60 days. Together = 15 × 60/75 =... 1
- A can do a work in 16 days and B in 12 days. With C's help they finish it in 4 days and are paid ₹3,600 in all. What is C's share? Answer: A. ₹1500 Answer: (A) ₹1500 In 4 days A does 4/16 = 1/4 of the work and B does 4/12 = 1/3 . C does 1 - 1/4 - 1/3 = 5/12 . C's share =... 1
- A can do a work in 15 days. He works for 5 days and then B finishes the rest in 9 days. How many days would B alone take to do the whole work? Answer: C. 13.5 days Answer: (C) 13.5 days A does 5/15 = 1/3 . B does the remaining 2/3 in 9 days, so B alone needs 9 × 3/2 = 13.5 days. 1