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    Question

    Pipe β€˜A’ and pipe β€˜B’ can fill a cistern in 18

    minutes and 16 minutes respectively. Pipe β€˜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 14.4 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 = 144 units Then, efficiency of pipe β€˜A’ = 144/18 = 8 units/minute Efficiency of pipe β€˜B’ = 144/16 = 9 units/minute Efficiency of pipe β€˜C’ = 144/12 = 12 units/minute So, combined efficiency of pipes β€˜A’, β€˜B’ and β€˜C’ = 8 + 9 – 12 = 5 units/minute 50% of the cistern’s capacity = 72 units Therefore, time taken by all 3 pipes together to fill 50% of the cistern = 72/5 = 14.4 minutes

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