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    Pipe X can fill a tank 7 times faster in comparison to pipe Y. It takes 49 minutes for pipe X and Y to fill the tank together. How much time will pipe
    Question

    Pipe X can fill a tank 7 times faster in comparison to pipe Y. It takes 49 minutes for pipe X and Y to fill the tank together. How much time will pipe Y alone take to fill the tank?

    A.

    392 minutes

    B.

    393 minutes

    C.

    391 minutes

    D.

    390 minutes

    Correct option is A

    Given:

    Pipe X is 7 times faster than pipe Y

    Time taken by X and Y together = 49 minutes

    Formula Used:
    Let the time taken by pipe Y alone = y minutes
    Then pipe X alone will take y7\frac{y}{7} minutes​
    Combined rate of work = sum of individual efficiency

    Efficiency (Work Done Per Minute) = Total WorkTotal time\frac{\text{Total Work}}{\text{Total time}}​​

    Solution:

    Combined Efficiency​​1y+1y/7=1y+7y=8y \frac{1}{y} + \frac{1}{y/7} = \frac{1}{y} + \frac{7}{y} = \frac{8}{y}

    Time taken together=1Combined Efficiency=y8\text{Time taken together} = \frac{1}{\text{Combined Efficiency}} = \frac{y}{8}

    =>y8=49\Rightarrow\frac{y}{8} = 49​​​

    =>y=49×8=392\Rightarrow y = 49 \times 8 = 392 minutes​

    Time taken by pipe Y alone = 392 minutes

    Thus, the correct option is (a) 392 minutes

    Alternate:

    XY\frac{X}{Y} = 71\frac{7}{1}

    Total work = (7 + 1) ×\times 49

    =  8 ×\times 49

    = 392

    Time taken by pipe Y alone = 3921\frac{392}{1}

    = 392 minutes.

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