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    Question

    Pipes A and B can fill a cistern in 48 and 80 minutes

    respectively. Another pipe C can empty the cistern in 1 hour 36 minutes. A and C are opened first. After 30 minutes, B is turned on. Find the total time taken to fill the cistern.
    A 75 mins Correct Answer Incorrect Answer
    B 27 mins Correct Answer Incorrect Answer
    C 60 mins Correct Answer Incorrect Answer
    D 65 mins Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let capacity = 480 litres (LCM of 48, 80, 96)

    Efficiency of A = 480 ÷ 48 = 10 litres/minute

    Efficiency of B = 480 ÷ 80 = 6 litres/minute

    Efficiency of C = 480 ÷ 96 = -5 litres/minute

    Filled in 30 minutes = (10 - 5) × 30 = 150 litres

    Remaining = 480 - 150 = 330 litres

    Time = 330 ÷ (10 + 6 - 5) = 330 ÷ 11 = 30 minutes

    Total time = 30 + 30 = 60 minutes

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