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Two pipes A and B can separately fill a cistern in 60 min and 75 min respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 min. In how much time, the third pipe alone can empty the cistern?

Correct answer: B. 100 min

  • A. 90 min
  • B. 100 min
  • C. 110 min
  • D. 120 min

Explanation

The two filling pipes together work at 1/60 + 1/75 = 3/100 tank/minute. Since the net rate is 1/50 tank/minute, the emptying pipe's rate is 3/100 - 1/50 = 1/100 tank/minute, so it alone empties the cistern in 100 minutes. The likely mistake is choosing 120 minutes by combining the filling times rather than their rates.

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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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