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A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?

Correct answer: D. 5 PM

  • A. 3 PM
  • B. 7 PM
  • C. 4 PM
  • D. 5 PM

Explanation

From 1 to 2 AM, A fills 1/4 tank; from 2 to 3 AM, A and B fill 1/4 + 1/5 = 9/20 tank, leaving 7/10 tank. With all three open, the net rate is 1/4 + 1/5 - 1/2 = -1/20 tank/hour, so emptying takes (7/10 tank) ÷ (1/20 tank/hour) = 14 hours after 3 AM, at 5 PM. The likely wrong choice is 4 PM, caused by using 13 hours instead of the required 14 hours.

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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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