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    Question

    Pipes X and Y can fill a tank in 48 minutes and 80 minutes

    respectively. Another pipe Z can empty the tank in 2 hours. X and Z are opened together. If after 36 minutes, Y is also opened, then how long will it take to fill the tank completely?
    A 75 mins Correct Answer Incorrect Answer
    B 27 mins Correct Answer Incorrect Answer
    C 58 mins Correct Answer Incorrect Answer
    D 65 mins Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the capacity of the tank be 240 litres (LCM of 48, 80 and 120)

    Efficiency of X = 240 ÷ 48 = 5 litres/minute

    Efficiency of Y = 240 ÷ 80 = 3 litres/minute

    Efficiency of Z = 240 ÷ 120 = -2 litres/minute (since it is an outlet pipe)

    Tank filled in 36 minutes = (5 - 2) × 36 = 108 litres

    Remaining tank to be filled = 240 - 108 = 132 litres

    Time to fill remaining = 132 ÷ (5 + 3 - 2) = 132 ÷ 6 = 22 minutes

    Total time taken = 36 + 22 = 58 minutes

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