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      Question

      A cistern has a leak that can empty it in 12 hours. A

      tap is turned on, which fills water at the rate of 15 liters per hour. Now, the cistern gets emptied in 20 hours. What is the capacity of the cistern?
      A 720 liters Correct Answer Incorrect Answer
      B 600 liters Correct Answer Incorrect Answer
      C 450 liters Correct Answer Incorrect Answer
      D 960 liters Correct Answer Incorrect Answer

      Solution

      Let the capacity of the cistern be x liters. Leak empties x liters in 12 hours: Rate = x/12 liters/hour Tap fills at 15 liters/hour. Net rate = (x/12 - 15) liters/hour Time to empty = x / (x/12 - 15) = 20 hours 1 / (1/12 - 15/x) = 20 1/12 - 15/x = 1/20 Solve: x = 450 liters Correct answer: c) 450 liters

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