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A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?

Correct answer: D. 7.2 hrs

  • A. 4.5 hrs
  • B. 5 hrs
  • C. 6.5 hrs
  • D. 7.2 hrs

Explanation

The filling rate is 1/4 tank per hour and the emptying rate is 1/9 tank per hour, so the net rate is 1/4 - 1/9 = 5/36 tank per hour. The time required is 1 divided by 5/36 = 36/5 = 7.2 hours. The likely mistake is choosing 4.5 hours by combining the times directly instead of subtracting the 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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