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    Question

    Pipes 'P' and 'Q' can fill a tank in 36 minutes and 72

    minutes respectively. A third pipe 'R' can empty it in 1 hour 48 minutes. 'P' and 'R' are turned on together. After 30 minutes, 'Q' is also started. Find how long in total it takes to fill the tank.
    A 75 mins Correct Answer Incorrect Answer
    B 27 mins Correct Answer Incorrect Answer
    C 46 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 tank be 432 litres (LCM of 36, 72 and 108)

    Efficiency of 'P' = 432 ÷ 36 = 12 litres/minute

    Efficiency of 'Q' = 432 ÷ 72 = 6 litres/minute

    Efficiency of 'R' = 432 ÷ 108 = -4 litres/minute

    Filled in 30 minutes = (12 - 4) × 30 = 240 litres

    Remaining = 432 - 240 = 192 litres

    Time for remaining = 192 ÷ (12 + 6 - 4) = 16 minutes

    Total time = 30 + 16 = 46 minutes

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