Question
Pipe βAβ can fill a tank in 40 hours whereas leak
βAβ can empty it in 50 hours. If they both operate along with pipe βBβ, then the given tank gets filled in 20 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 200 litres {LCM (40 and 50)} Efficiency of pipe βAβ = 200 Γ· 40 = 5 litres/hour Efficiency of leak βAβ = 200 Γ· 50 = 4 litres/hour Combined efficiency of pipe βAβ and leak βAβ = 5 β 4 = 1 litre/hour Combined efficiency of pipe βAβ, βBβ and leak βAβ = 200 Γ· 20 = 10 units/hour Efficiency of pipe βBβ = 10 β 1 = 9 units/hour Time taken by pipe βBβ and leak βAβ to fill the tank = 200 Γ· (9 β 4) = 40 hours
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