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    Pipe A can fill a tank in 5 hours. Pipe B can empty it in 12 hours. If both the pipes are opened simultaneously, how much time will it take to fi
    Question

    Pipe A can fill a tank in 5 hours. Pipe B can empty it in 12 hours. If both the pipes are opened simultaneously, how much time will it take to fill the tank?

    A.

    827 hours8 \frac{2}{7} \text{ hours} \quad​​

    B.

    847 hours8 \frac{4}{7} \text{ hours} \quad​​

    C.

    817 hours 8 \frac{1}{7} \text{ hours} \quad​​

    D.

    837 hours8 \frac{3}{7} \text{ hours}​​

    Correct option is B

    Given:

    Pipe A can fill the tank in 5 hours.

    Pipe B can empty the tank in 12 hours.

    Formula Used:

    Rate of work =1Time \frac{1}{\text{Time}}​​

    Time taken =1Net rate of work \frac{1}{\text{Net rate of work}}​​

    Solution:
    Rate of work of Pipe A =15=\frac{1}{5}​ (since it fills the tank in 5 hours)
    Rate of work of Pipe B = 112-\frac{1}{12}​ (since it empties the tank in 12 hours)

    Net rate of work =15112 \frac{1}{5} - \frac{1}{12}​​

    Net rate of work =1260560=760 \frac{12}{60} - \frac{5}{60} = \frac{7}{60}​​

    Now, time taken to fill the tank =1760=607=847= \frac{1}{\frac{7}{60}} = \frac{60}{7} = 8\frac 47 hours

    Alternate Method:

    Time taken to fill the tank = 60125=607=847\frac {60}{12-5}=\frac {60}7=8\frac47 hours​

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