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Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?

Correct answer: C. 17 1/7 min

  • A. 19 1/7 min
  • B. 15 1/7 min
  • C. 17 1/7 min
  • D. 7 1/7 min

Explanation

The combined filling rate after allowing for the drain is 1/20 + 1/30 - 1/40. Using denominator 120 gives 6/120 + 4/120 - 3/120 = 7/120 of the tank per minute. The filling time is therefore 120/7 = 17 1/7 minutes. The likely trap is 15 1/7 minutes, which does not correctly subtract the drain rate.

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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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