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Two pipes P and Q can fill a cistern in 12 minutes and 16 minutes respectively. Simultaneously both the pipes are opened together, then after how much time Q should be closed so that the tank is full in 9 min ?

Correct answer: C. 4 min

  • A. 2 min
  • B. 3 min
  • C. 4 min
  • D. 5 min

Explanation

If Q is closed after t minutes, P works for all 9 minutes and Q works for t minutes. The filled fraction is 9/12 + t/16 = 1, so 3/4 + t/16 = 1 and t/16 = 1/4, giving t = 4 minutes. The likely mistake is 3 minutes, which does not provide enough contribution from Q to complete the remaining quarter of the tank.

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About Time and Work

Problems measure work through rates, treating each person's or machine's contribution as work completed per unit time. Questions cover combined work, efficiency, wages, alternate working schedules, pipes and cisterns, and men-days relationships, with care needed to distinguish time taken by one worker from the time required when workers act together.

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