Question
Pipe βMβ and pipe βNβ together can fill an empty
tank in 30 hours while pipe βNβ and pipe βOβ together take 20 hours to fill the same tank. If the efficiency of pipe βOβ is twice that of pipe βMβ, then find the time taken by pipe βNβ to fill the tank alone.Solution
ATQ, Let the total capacity of the tank = 120 units Efficiency of pipes (M + N) = 120/30 = 4 units/hour Efficiency of pipes (N + O) = 120/20 = 6 units/hour Let the efficiency of pipe βMβ = x units/hour Therefore, efficiency of pipe βOβ = 2x units/hour Therefore, 2x β x = 6 β 4 Or, x = 2 Therefore, efficiency of pipe βNβ = 4 β 2 = 2 units/hour Time taken by pipe βNβ to fill the tank alone = 120/2 = 60 hours
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