Question
A pipe, working by itself, can fill an empty cistern in 36(4/11) minutes. However, due to a leak, the same pipe now takes 50 minutes to fill the cistern completely. Based on this, determine how long it would take for the leak alone to empty 30% of the cistern.
Solution
Let the capacity of the tank = L.C.M of 36(4/11) and 50 = 400 units Then, efficiency of the pipe alone = 400 ÷ 36(4/11) = 400 ÷ (400/11) = 11 units/minute Combined efficiency of the pipe and the leakage = 400 ÷ 50 = 8 units/minute So, efficiency of the leak alone = 8 - 11 = 3 units/minute (outlet) 30% of the cistern = 400 X 0.3 = 120 units Time taken by the leak alone to empty 30% of the cistern = 120 ÷ 3 = 40 minutes
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