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    Two pipes can fill a tank in 30 minutes and 60 minutes respectively. Another pipe at the bottom will empty it in 120 minutes. If all the pipes are ope
    Question

    Two pipes can fill a tank in 30 minutes and 60 minutes respectively. Another pipe at the bottom will empty it in 120 minutes. If all the pipes are open, in what time will the tank get filled?

    A.

    24 minutes

    B.

    40 minutes

    C.

    50 minutes

    D.

    52 minutes

    Correct option is A

    Given:

    Pipe 1 can fill the tank in 30 minutes.

    Pipe 2 can fill the tank in 60 minutes.

    Pipe 3 at the bottom can empty the tank in 120 minutes.

    Solution:

    Work done by each pipe in 1 minute:

    Work done by Pipe 1 in 1 minute = 130\frac{1}{30}​​

    Work done by Pipe 2 in 1 minute = 160\frac{1}{60}​​

    Work done by Pipe 3 in 1 minute (emptying) = 1120 \frac{1}{120}​​

    Net work done in 1 minute = 130+1601120 \frac{1}{30} + \frac{1}{60} - \frac{1}{120}​​

    Net work done in 1 minute = 4120+21201120=5120 \frac{4}{120} + \frac{2}{120} - \frac{1}{120} = \frac{5}{120}​​

    Time required to fill the tank = 1205=24 minutes\frac{120}{5} = 24 \text{ minutes}​​

    Therefore, the tank will get filled in 24 minutes.

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