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    Question

    Pipes 'X' and 'Y' can fill a tank in 15 hours and 10 hours respectively, while pipe 'Z' can empty it in 30 hours. All pipes are opened together when the tank was empty. After 6 hours, pipe 'X' is closed. Find the total time taken to fill the tank.

    A 5 hrs Correct Answer Incorrect Answer
    B 9 hrs Correct Answer Incorrect Answer
    C 12 hrs Correct Answer Incorrect Answer
    D 20 hrs Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, Tank capacity = 150 units (LCM of 15, 10, 30) Efficiency of pipe 'X' = 150 / 15 = 10 units/hour Efficiency of pipe 'Y' = 150 / 10 = 15 units/hour Efficiency of pipe 'Z' = 150 / 30 = 5 units/hour Tank filled in 6 hours = (10 + 15 - 5) × 6 = 120 units Time taken by pipes 'Y' and 'Z', together to fill the remaining part of tank = (150 - 120) / (15 - 5) = 3 hours Total time taken = 6 + 3 = 9 hours

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