Question
Pipe ‘P’ and pipe ‘Q’ together can fill an empty
tank in 18 hours while pipe ‘Q’ and pipe ‘R’ together take 12 hours to fill the same tank. If the efficiency of pipe ‘R’ is twice that of pipe ‘P’, then find the time taken by pipe ‘Q’ to fill the tank alone.Solution
ATQ, Let the total capacity of the tank = 72 units Efficiency of pipes (P + Q) = 72/18 = 4 units/hour Efficiency of pipes (Q + R) = 72/12 = 6 units/hour Let the efficiency of pipe ‘P’ = x units/hour Therefore, efficiency of pipe ‘R’ = 2x units/hour Therefore, 2x – x = 6 – 4 Or, x = 2 Therefore, efficiency of pipe ‘Q’ = 4 – 2 = 2 units/hour Time taken by pipe ‘Q’ to fill the tank alone = 72/2 = 36 hours
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