Question
Pipe ‘X’ and pipe ‘Y’ can fill a tank alone in 36 hours and 18 hours, respectively. If both pipes are opened together and pipe ‘Y’ is closed after 6 hours, then find the time taken by pipe ‘X’ to fill the remaining portion of the tank alone.
Solution
Let the capacity of the tank be 36 units (LCM of 36 and 18) Efficiency of pipe ‘X’ = 36 ÷ 36 = 1 unit/hour
Efficiency of pipe ‘Y’ = 36 ÷ 18 = 2 unit/hour Let pipe ‘X’ fill the remaining portion in x hours. ATQ, 6 × (1 + 2) + 1x = 36 Or, 18 + x = 36 Or, x = 18 Therefore, required time taken = 18 hours
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