Question
Pipe ‘P’ and pipe ‘Q’ can fill a tank alone in
40 hours and 60 hours, respectively. If pipe ‘P’ and pipe ‘Q’ were opened together and pipe ‘P’ was closed after 20 hours, then find the time taken by pipe ‘Q’ to fill the remaining portion of the tank alone.Solution
Let the capacity of the tank be 120 units (LCM of 40 and 60) Efficiency of pipe ‘P’
= 120 ÷ 40
= 3 unit/hour Efficiency of pipe ‘Q’
= 120 ÷ 60
= 2 unit/hour Let the pipe ‘Q’ fill the remaining portion of the tank in x hours. ATQ, 20 × (3 + 2) + 2x = 120 Or, 20 × 5 + 2x = 120 Or, 100 + 2x = 120 Or, 2x = 20 Or, x = 10 Therefore, required time taken by pipe ‘Q’ = 10 hours
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