Question
An inlet pipe can fill a cistern in 25 minutes when working alone. However, due to a leak, the fully filled cistern would empty in 87.5 minutes. If the leak is not fixed, how long will it take for the inlet pipe to fill 60% of the empty cistern?
Solution
Let the capacity of the cistern = L.C.M of 25 and 87.5 = 175 units
So, efficiency of the inlet pipe = 175 ÷ 25 = 7 units/minute
Efficiency of the leak = 175 ÷ 87.5 = 2 units/minute (outlet)
So, combined efficiency of the inlet pipe with the leakage = 7 - 2 = 5 units/minute
60% of the cistern = 175 X 0.6 = 105 units
Time taken for the inlet pipe to fill 60% of the cistern with the leakage = 105 ÷ 5 = 21 minutes
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