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    Question

    Pipe β€˜A’ can fill a tank in 15 hours whereas leak

    β€˜A’ can empty it in 45 hours. If they both operate along with pipe β€˜B’, then the given tank gets filled in 9 hours. How much time is needed to fill the given tank if pipe β€˜B’ and leak β€˜A’ work together?Β Β 
    A 37.5 hours Correct Answer Incorrect Answer
    B 60 hours Correct Answer Incorrect Answer
    C 30 hours Correct Answer Incorrect Answer
    D 22.5 hours Correct Answer Incorrect Answer

    Solution

    Let the capacity of the tank be 45 litres {LCM (15 and 45)} Efficiency of pipe β€˜A’ = 45 Γ· 15 = 3 litres/hour Efficiency of leak β€˜A’ = 45 Γ· 45 = 1 litres/hour Combined efficiency of pipe β€˜A’ and leak β€˜A’ = 3 – 1 = 2 litre/hour Combined efficiency of pipe β€˜A’, β€˜B’ and leak β€˜A’ = 45 Γ· 9 = 5 units/hour Efficiency of pipe β€˜B’ = 5 – 2 = 3 units/hour Time taken by pipe β€˜B’ and leak β€˜A’ to fill the tank = 45 Γ· (3 – 1) = 22.5 hours

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