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A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full the leak will empty it in.

Correct answer: D. 40 hrs

  • A. 16 hrs
  • B. 20 hrs
  • C. 25 hrs
  • D. 40 hrs

Explanation

Without the leak, the filling rate is 1/8 tank per hour, while with the leak the net rate is 1/10 tank per hour because filling takes 10 hours. Therefore, the leak's rate is 1/8 - 1/10 = 1/40 tank per hour, so it empties a full cistern in 40 hours. The likely mistake is choosing 20 hours by subtracting the times instead of 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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