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A cistern has two taps which fill it in 12 min. and 15 min.respectively There is one outlet pipe in the cistern. When all the taps & pipe are opened, the empty cistern is full in 20 min. How long will the waste pipe (outlet) take to empty the full cistern ?

Correct answer: A. 10 min

  • A. 10 min
  • B. 20 min
  • C. 30 min
  • D. 40 min

Explanation

The two inlet taps fill at 1/12 + 1/15 = 3/20 cistern per minute, while the net rate with the outlet open is 1/20 cistern per minute. Thus the outlet rate is 3/20 - 1/20 = 1/10 cistern per minute, so it empties the cistern in 10 minutes. The likely mistake is 20 minutes, which treats the net filling time as the outlet's emptying time.

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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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