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A cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?

Correct answer: D. 90 hrs

  • A. 45 hrs
  • B. 60 hrs
  • C. 75 hrs
  • D. 90 hrs

Explanation

Without the leak, the filling rate is 1/9 tank/hour, while with the leak the net rate is 1/10 tank/hour. Thus the leak removes 1/9 - 1/10 = 1/90 tank/hour, so it alone empties a full cistern in 90 hours. The likely mistake is choosing 45 hours by doubling the net filling time rather than subtracting the two 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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