Question
Pipe βAβ can fill a tank in 15 hours whereas leak
βAβ can empty it in 45 hours. If they both operate along with pipe βBβ, then the given tank gets filled in 9 hours. How much time is needed to fill the given tank if pipe βBβ and leak βAβ work together?Β ΒSolution
Let the capacity of the tank be 45 litres {LCM (15 and 45)} Efficiency of pipe βAβ = 45 Γ· 15 = 3 litres/hour Efficiency of leak βAβ = 45 Γ· 45 = 1 litres/hour Combined efficiency of pipe βAβ and leak βAβ = 3 β 1 = 2 litre/hour Combined efficiency of pipe βAβ, βBβ and leak βAβ = 45 Γ· 9 = 5 units/hour Efficiency of pipe βBβ = 5 β 2 = 3 units/hour Time taken by pipe βBβ and leak βAβ to fill the tank = 45 Γ· (3 β 1) = 22.5 hours
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