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A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?

Correct answer: A. 6 min. to empty

  • A. 6 min. to empty
  • B. 6 min. to full
  • C. 9 min. to empty
  • D. 9 min. to full

Explanation

The filling rate is 1/10 tank/minute and the emptying rate is 1/6 tank/minute, so the net emptying rate is 1/6 - 1/10 = 1/15 tank/minute. Since the tank initially contains 2/5 of its capacity, the emptying time is (2/5 tank) ÷ (1/15 tank/minute) = 6 minutes. The likely mistake is choosing 9 minutes by using only the emptying pipe's rate and ignoring the filling pipe.

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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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