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    Question

    Pipe тАШAтАЩ and pipe тАШBтАЩ can fill a cistern in 20

    minutes and 15 minutes respectively. Pipe тАШCтАЩ 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

    Solution

    Let the capacity of the cistern = 60 units Then, efficiency of pipe тАШAтАЩ = 60/20 = 3 units/minute Efficiency of pipe тАШBтАЩ = 60/15 = 4 units/minute Efficiency of pipe тАШCтАЩ = 60/12 = 5 units/minute So, combined efficiency of pipes тАШAтАЩ, тАШBтАЩ and тАШCтАЩ = 3 + 4 тАУ 5 = 2 units/minute 50% of the cisternтАЩs capacity = 30 units Therefore, time taken by all 3 pipes together to fill 50% of the cistern = 30/2 = 15 minutes

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