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A leak in the bottom of a tank can empty the full tank in 6 hrs. An inlet pipe fills water at the rate of 4 lit. a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 8 hrs. The capacity of the tank in liters is_________?

Correct answer: B. 5,760 litres

  • A. 5,750 litres
  • B. 5,760 litres
  • C. 6,890 litres
  • D. None of these

Explanation

Let the tank capacity be V litres. The leak removes V/6 litres per hour, while the inlet supplies 4 litres per minute = 240 litres per hour; when both operate, the net emptying rate is V/8 litres per hour. Hence V/6 - 240 = V/8, so V(1/6 - 1/8) = 240 and V/24 = 240, giving V = 5,760 litres. The likely mistake is 5,750 litres, caused by inaccurate subtraction or division.

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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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