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    Question

    Pipe P can fill a tank in 12 hours, while pipe Q can

    fill the same tank in 20 hours. Both pipes are initially opened to fill an empty tank, but after 5 hours, pipe Q is closed. To figure out how much less time would have been required to fill the tank if pipe Q had not been closed, considering the dynamic flow rates of both pipes, you need to determine the alternative completion time.
    A 2 hrs Correct Answer Incorrect Answer
    B 5 hrs Correct Answer Incorrect Answer
    C 1.5 hrs Correct Answer Incorrect Answer
    D 3 hrs Correct Answer Incorrect Answer
    E 12 hrs Correct Answer Incorrect Answer

    Solution

    We can say that Let the total capacity of the tank = 60 units (L.C.M of 12 & 20) Efficiency of P = 60/12 = 5 units/hr Efficiency of Q = 60/20 = 3 units/hr Time taken to fill the tank when both the pipes work together = 60/(5 + 3) = 7.5 hours According to the question, Tank filled in 5 hours = (5 + 3) × 8 = 40 units Remaining capacity of tank = 60 – 40 = 20 units Time taken by Pipe P to fill the remaining part = 20/5 = 4 hours Total time taken = 5 + 4 = 9 hours Extra time taken = 9 – 7.5 = 1.5 hrs

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