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?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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