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wo pipes X and Y fill a tank in 15 hrs. and 20 hrs. respectively, while a third pipe 'Z' can empty the full tank in 25 hrs. All the three pipes are opened in the beginning. After 10 hrs. Z is closed. In how much time, will the tank be full ?

Correct answer: A. 12 hrs

  • A. 12 hrs
  • B. 14 hrs
  • C. 16 hrs
  • D. 18 hrs

Explanation

The combined filling rate of X and Y is 1/15 + 1/20 = 7/60 of the tank per hour, and Z empties 1/25 of the tank per hour, giving an initial net rate of 23/300 of the tank per hour. In 10 hours they fill 10 x 23/300 = 23/30 of the tank, leaving 7/30; after Z closes, the remaining time is (7/30) ÷ (7/60 per hour) = 2 hours, so the total time is 10 hours + 2 hours = 12 hours. Students may choose 14 hours by adding 2 hours to the wrong stage or treating Z as open throughout.

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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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