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A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?

Correct answer: A. 480 liters

  • A. 480 liters
  • B. 600 liters
  • C. 720 liters
  • D. 800 liters

Explanation

Let the capacity be C litres. The leak removes C/20 litres per minute, while the tap adds 4 litres per minute; because the tank empties in 24 minutes, 4 - C/20 = -C/24. Therefore 4 = C(1/20 - 1/24) = C/120, giving C = 480 litres. The likely mistake is 600 litres, which results from using the leak's 20-minute emptying time alone.

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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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