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    Question

    Pipe ‘A’ and pipe ‘B’ can fill a cistern in 20 minutes and 10 minutes respectively. Pipe ‘C’ alone can empty the cistern in 12 minutes. If all three pipes are opened together then what is the time taken to fill 50% of the cistern?

    A 15 minutes Correct Answer Incorrect Answer
    B 5 minutes Correct Answer Incorrect Answer
    C 22.5 minutes Correct Answer Incorrect Answer
    D 7.5 minutes Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the capacity of the cistern = 60 units Then, efficiency of pipe ‘A’ = 60/20 = 3 units/minute Efficiency of pipe ‘B’ = 60/10 = 6 units/minute Efficiency of pipe ‘C’ = 60/12 = 5 units/minute So, combined efficiency of pipes ‘A’, ‘B’ and ‘C’ = 3 + 6 – 5 = 4 units/minute 50% of the cistern’s capacity = 30 units Therefore, time taken by all 3 pipes together to fill 50% of the cistern = 30/4 = 7.5 minutes

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