Time & Work / Pipes & Cisterns

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

Sample questions

Sample Easy question 1

A pipe can fill a tank in 6 hours. What fraction of the tank is filled in 2 hours?

  1. 2/3
  2. 1/4
  3. 1/3
  4. 1/2
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Answer: C. Rate = 1/6 per hour. In 2 hours: 2 × 1/6 = 1/3 of the tank.

Sample Easy question 2

If 8 workers can complete a wall in 12 days, how many days will 12 workers take?

  1. 7 days
  2. 6 days
  3. 9 days
  4. 8 days
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Answer: D. Total man-days = 8×12 = 96. For 12 workers: 96/12 = 8 days.

Sample Easy question 3

A, B and C can complete a job in 10, 15 and 30 days respectively. If they all work together, in how many days will the job be completed?

  1. 7 days
  2. 4 days
  3. 5 days
  4. 6 days
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Answer: C. Combined rate = 1/10 + 1/15 + 1/30 = 3/30 + 2/30 + 1/30 = 6/30 = 1/5, so together they take 5 days.

Sample Medium question 4

A pipe can fill a tank in 6 hours. Because of a leak at the bottom, it takes longer. If the leak alone can empty the full tank in 24 hours, in how many hours will the tank be filled with the leak present?

  1. 18 hours
  2. 8 hours
  3. 9 hours
  4. 7 hours
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Answer: B. Net rate = 1/6 − 1/24 = 1/8 of the tank per hour, so the time = 8 hours.

Sample Medium question 5

A pipe can fill a tank in 10 hours. Because of a leak at the bottom, it takes longer. If the leak alone can empty the full tank in 40 hours, in how many hours will the tank be filled with the leak present?

  1. 14 1/3 hours
  2. 13 1/3 hours
  3. 12 1/3 hours
  4. 30 hours
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Answer: B. Net rate = 1/10 − 1/40 = 3/40 of the tank per hour, so the time = 13 1/3 hours.

Sample Medium question 6

Pipe A fills a tank in 6 hours, pipe B empties it in 12 hours. If both are opened together, how long will it take to fill the tank?

  1. 14 hrs
  2. 11 hrs
  3. 12 hrs
  4. 10 hrs
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Answer: C. Net rate = 1/6 - 1/12 = 1/12, so the tank fills in 12 hours.

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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