Question
Pipe βXβ and pipe βYβ together can fill an empty
tank in 24 hours while pipe βYβ and pipe βZβ together take 15 hours to fill the same tank. If the efficiency of pipe βZβ is twice that of pipe βXβ, then find the time taken by pipe βYβ to fill the tank alone.Solution
ATQ, Let the total capacity of the tank = 120 units Efficiency of pipes (X + Y) = 120/24 = 5 units/hour Efficiency of pipes (Y + Z) = 120/15 = 8 units/hour Let the efficiency of pipe βXβ = x units/hour Therefore, efficiency of pipe βZβ = 2x units/hour Therefore, 2x β x = 8 β 5 Or, x = 3 Therefore, efficiency of pipe βYβ = 5 β 3 = 2 units/hour Time taken by pipe βYβ to fill the tank alone = 120/2 = 60 hours
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