Question
Pipes 'X' and 'Y' can fill a tank in 15 hours and 10
hours respectively, while pipe 'Z' can empty it in 30 hours. All pipes are opened together when the tank was empty. After 6 hours, pipe 'X' is closed. Find the total time taken to fill the tank.Solution
ATQ, Tank capacity = 30 units (LCM of 15, 10, 30) Efficiency of pipe 'X' = 30 / 15 = 2 units/hour Efficiency of pipe 'Y' = 30 / 10 = 3 units/hour Efficiency of pipe 'Z' = 30 / 30 = 1 units/hour Tank filled in 6 hours = (2 + 3 - 1) × 6 = 24 units Time taken by pipes 'Y' and 'Z', together to fill the remaining part of tank = (30 - 24)/(3 - 1) = (6/2) = 3 hours Total time taken = 6 + 3 = 9 hours
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