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    Question

    Pipes X and Y can fill a tank in 45 minutes and 60 minutes

    respectively. Another pipe Z can empty the tank in 1 hour 30 minutes. If X and Z are opened first and Y is opened after 20 minutes, in how much total time will the tank be filled?
    A 75 mins Correct Answer Incorrect Answer
    B 27 mins Correct Answer Incorrect Answer
    C 48 mins Correct Answer Incorrect Answer
    D 65 mins Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let tank capacity be 180 litres (LCM of 45, 60, 90)

    Efficiency of X = 180 ÷ 45 = 4 litres/minute

    Efficiency of Y = 180 ÷ 60 = 3 litres/minute

    Efficiency of Z = 180 ÷ 90 = -2 litres/minute

    Filled in 20 minutes = (4 - 2) × 20 = 40 litres

    Remaining = 180 - 40 = 140 litres

    Time for remaining = 140 ÷ (4 + 3 - 2) = 28 minutes

    Total time = 20 + 28 = 48 minutes

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