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Two pipes A and B can separately fill a tank in 12 and 15 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?

Correct answer: B. 540 liters

  • A. 480 liters
  • B. 540 liters
  • C. 600 liters
  • D. 675 liters

Explanation

The two filling pipes together work at 1/12 + 1/15 = 3/20 of the tank per minute. Since all three pipes fill the tank in 15 minutes, their net rate is 1/15, so the drain reduces the rate by 3/20 - 1/15 = 1/12. Therefore 45 litres per minute represents 1/12 of the tank, giving a capacity of 45 x 12 = 540 litres. Students may choose 600 litres by subtracting the rates incorrectly.

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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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