Question
Pipe βGβ and pipe βHβ together can fill an empty
tank in 40 hours while pipe βHβ and pipe βIβ together take 25 hours to fill the same tank. If the efficiency of pipe βIβ is twice that of pipe βGβ, then find the time taken by pipe βHβ to fill the tank alone.Solution
ATQ, Let the total capacity of the tank = 200 units Efficiency of pipes (G + H) = 200/40 = 5 units/hour Efficiency of pipes (H + I) = 200/25 = 8 units/hour Let the efficiency of pipe βGβ = x units/hour Therefore, efficiency of pipe βIβ = 2x units/hour Therefore, 2x β x = 8 β 5 Or, x = 3 Therefore, efficiency of pipe βHβ = 5 β 3 = 2 units/hour Time taken by pipe βHβ to fill the tank alone = 200/2 = 100 hours
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