Question
Pipe A can fill a tank in 12 hours, and Pipe B can fill
it in 18 hours. Pipe C can empty the full tank in 36 hours. If all three pipes are opened together, in how many hours will the tank be filled?Solution
ATQ, Let total work (capacity of tank) = 1 unit A’s rate = 1/12 per hour B’s rate = 1/18 per hour C’s (emptying) rate = −1/36 per hour Net rate = 1/12 + 1/18 − 1/36 LCM of 12, 18, 36 = 36 1/12 = 3/36 1/18 = 2/36 −1/36 = −1/36 Net = (3 + 2 − 1)/36 = 4/36 = 1/9 Time = 1 / (1/9) = 9 hours
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