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If two pipes function together, the cistern will be filled in 6 hrs. One pipe fills the cistern 5 hrs. faster than the other. How many hours it take the second pipe to fill the cistern?

Correct answer: C. 15 hrs

  • A. 5 hrs
  • B. 10 hrs
  • C. 15 hrs
  • D. 20 hrs

Explanation

Let the slower pipe take t hours, so the faster takes t - 5 hours. Since together they fill 1/6 cistern per hour, 1/t + 1/(t - 5) = 1/6, which gives t² - 17t + 30 = 0 and the valid root t = 15 hours. The likely mistake is 10 hours, from treating the 5-hour difference as a direct part of the combined time.

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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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