Question
Pipe βPβ alone can fill a tank in 12 hours. When
pipe βPβ and βQβ are opened together, they can fill 75% of the same tank in 9 hours. Find the time taken by pipe βQβ alone to fill 60% of the same tank.Solution
ATQ; Time taken by pipes βPβ and βQβ together to fill 100% of the tank = 9 Γ· 0.75 = 12 hours Let the capacity of the tank be 60 litres. {LCM (12 and 12)} Efficiency of pipe βPβ = (60/12) = 5 litres/hour Efficiency of pipe βPβ and βQβ together = (60/12) = 5 litres/hour Efficiency of pipe βQβ = 5 β 5 = 0 litres/hour Time taken by pipe βQβ to fill 60% of the tank = (60 Γ 0.6)/0 = Undefined (This scenario is not possible, as pipe βQβ has no efficiency.)
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