Time & Work / Pipes & Cisterns

Ladakh Police Constable · Mathematics · 53 practice questions with answers and explanations: 14 Easy, 38 Medium, 1 Hard.

Sample questions

Sample Easy question 1

If 8 men can build a wall in 15 days, how many days will 12 men take?

  1. 8
  2. 11
  3. 10
  4. 9
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Answer: C. Total work = 8×15 = 120 man-days; 12 men take 120/12 = 10 days.

Sample Easy question 2

A can do a piece of work in 4 days and B in 12 days. In how many days can they finish it together?

  1. 4 days
  2. 5 days
  3. 3 days
  4. 2 days
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Answer: C. Combined rate = 1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3, so together they take 3 days.

Sample Easy question 3

A can complete a task in 10 days. If B is twice as efficient as A, how many days will B take alone?

  1. 8 days
  2. 4 days
  3. 6 days
  4. 5 days
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Answer: D. Twice as efficient means half the time: 10/2 = 5 days.

Sample Medium question 4

A, B and C can complete a piece of work in 20, 24 and 60 days respectively. They start together. After 2 days A leaves, and after 1 more day C also leaves. In how many more days will B finish the remaining work?

  1. 18 2/5 days
  2. 17 2/5 days
  3. 16 2/5 days
  4. 19 2/5 days
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Answer: B. Work done in the first 2 day(s) = 2 × 13/120; work done in the next 1 day(s) by B and C = 1 × 7/120. Remaining work = 29/40, which B alone does in 17 2/5 days.

Sample Medium question 5

A, B and C can complete a piece of work in 30, 20 and 15 days respectively. They start together. After 1 day A leaves, and after 1 more day C also leaves. In how many more days will B finish the remaining work?

  1. 16 2/3 days
  2. 14 2/3 days
  3. 13 2/3 days
  4. 15 2/3 days
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Answer: B. Work done in the first 1 day(s) = 1 × 3/20; work done in the next 1 day(s) by B and C = 1 × 7/60. Remaining work = 11/15, which B alone does in 14 2/3 days.

Sample Medium question 6

A, B and C can complete a piece of work in 10, 12 and 15 days respectively. They start together. After 1 day A leaves, and after 2 more days C also leaves. In how many more days will B finish the remaining work?

  1. 7 2/5 days
  2. 6 2/5 days
  3. 4 2/5 days
  4. 5 2/5 days
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Answer: D. Work done in the first 1 day(s) = 1 × 1/4; work done in the next 2 day(s) by B and C = 2 × 3/20. Remaining work = 9/20, which B alone does in 5 2/5 days.

Sample Hard question 7

Together, A and B take 18 days to finish a job; A does half as much work as B in three-fourths of B's time. Find B's time alone.

  1. 25
  2. 30
  3. 28
  4. 32
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Answer: B. Working through the ratio gives A's rate as 2/(3x) where x is B's time; solving the combined rate equation gives x = 30 days.

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