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    Question

    Pipe X can fill a tank on its own

    in 12 hours, while Pipe Y can fill the same tank individually in 20 hours. Both pipes X and Y operate together for 4 hours, after which Pipe P is introduced. Pipe P, when working alone, can drain the fully filled tank in 15 hours. Determine the total time required to fill the tank under these conditions.
    A 24 hrs Correct Answer Incorrect Answer
    B 18 hrs Correct Answer Incorrect Answer
    C 5 hrs Correct Answer Incorrect Answer
    D 11 hrs Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the capacity of the tank be 60 litres. {LCM (12, 20 and 15)} Efficiency of pipe 'X' = (60/12) = 5 litres/hour Efficiency of pipe 'Y' = (60/20) = 3 litres/hour Efficiency of outlet pipe 'Z' = (60/15) = 4 litres/hour Quantity of water filled by pipe 'X' and 'Y' together in 4 hours = (5 + 3) × 4 = 32 litres Combined efficiency of all three pipes = 5 + 3 - 4 = 4 litres/hour So, time taken to fill the remaining tank = {(60 - 32)/4} = 7 hours So, total time taken = 7 + 4 = 11 hours

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