Question

    Pipe β€˜A’ can fill a tank in 30 hours whereas leak

    β€˜A’ can empty it in 40 hours. If they both operate along with pipe β€˜B’, then the given tank gets filled in 15 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
    E 16 hours Correct Answer Incorrect Answer

    Solution

    Let the capacity of the tank be 120 litres {LCM (30 and 40)} Efficiency of pipe β€˜A’ = 120 Γ· 30 = 4 litres/hour Efficiency of leak β€˜A’ = 120 Γ· 40 = 3 litres/hour Combined efficiency of pipe β€˜A’ and leak β€˜A’ = 4 – 3 = 1 litre/hour Combined efficiency of pipe β€˜A’, β€˜B’ and leak β€˜A’ = 120 Γ· 15 = 8 units/hour Efficiency of pipe β€˜B’ = 8 – 1 = 7 units/hour Time taken by pipe β€˜B’ and leak β€˜A’ to fill the tank = 120 Γ· (7 – 3) = 30 hours

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