Question
Pipe βPβ and pipe βQβ together can fill an empty
tank in 18 hours while pipe βQβ and pipe βRβ together take 12 hours to fill the same tank. If the efficiency of pipe βRβ is twice that of pipe βPβ, then find the time taken by pipe βQβ 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 βPβ = x units/hour Therefore, efficiency of pipe βRβ = 2x units/hour Therefore, 2x β x = 6 β 4 Or, x = 2 Therefore, efficiency of pipe βQβ = 4 β 2 = 2 units/hour Time taken by pipe βQβ to fill the tank alone = 72/2 = 36 hours
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