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One top can fill a cistern in 2 hours and another can empty the cistern in 3 hours. How long will they take to fill the cistern if both the taps are opened?

Correct answer: B. 6 Hours

  • A. 5 Hours
  • B. 6 Hours
  • C. 7 Hours
  • D. 8 Hours

Explanation

The filling tap supplies 1/2 cistern per hour and the emptying tap removes 1/3 cistern per hour. Their net rate is 1/2 - 1/3 = 1/6 cistern per hour, so the cistern fills in 6 hours. The likely mistake is choosing 5 hours by adding the two times or ignoring the emptying tap's opposing effect.

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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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