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    Two taps can fill a cistern in 2 hours and 54 hours respectively. A third tap can empty it in 54 hours. How long (in hours) will it take to fill the e
    Question

    Two taps can fill a cistern in 2 hours and 54 hours respectively. A third tap can empty it in 54 hours. How long (in hours) will it take to fill the empty cistern, if all of them are opened together?

    A.

    3

    B.

    5

    C.

    2

    D.

    4

    Correct option is C

    Given:

    First tap can fill the cistern in 2 hours,

    Second tap can fill the cistern in 54 hours

    Third tapcan empty the cistern in 54 hours 

    Formula Used:  

    If a Pipe fill a tank in x hours , 

    Then work rate of pipe = 1x\frac{1}{x} ​

    Solution: 

    Work rate of first tap = 12\frac 1 2 

    Work rate of second tap = 154\frac{1} {54} 

    Work rate of third tap(empty) = 154\frac{1} {54}

    Filling rate of the first and second taps:

    Total filling rate=12+154.\text{Total filling rate} = \frac{1}{2} + \frac{1}{54}.​​​​

    When all three taps are open, the combined rate of filling is:

    Effective rate = 12+154154\frac{1}{2} + \frac{1}{54} - \frac{1}{54}​​

    Effective rate = 12\frac{1}{2} 

    Now , 

    Time taken  to fill the tank =112 \frac{1}{\frac{1}{2}}​ = 2  hours.

    It will take 2 hours to fill the empty cistern when all three taps are opened together.

    Thus, the correct answer is option (c) 2

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