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    One pipe can fill the tank in 9 minutes while another pipe can empty completely filled tank in 90 minutes. If both the pipes are operated togethe
    Question

    One pipe can fill the tank in 9 minutes while another pipe can empty completely filled tank in 90 minutes. If both the pipes are operated together on empty tank, how long (in minutes) will it take to fill the tank completely?

    A.

    13

    B.

    11

    C.

    12

    D.

    10

    Correct option is D

    Given

    Pipe A fills the tank in 9 minutes

    rate =19= \frac{1}{9}​ tank/min.

    Pipe B empties a full tank in 90 minutes

    rate =190= \frac{1}{90}​ tank/min (emptying).

    Both start together on an empty tank.

    Formula Used

    Net rate = filling rate - emptying rate

    Time to fill=1net rate =\dfrac{1}{\text{net rate}}​​

    Solution
    Net rate =19190=10190=990=110 \frac{1}{9}-\frac{1}{90}=\frac{10-1}{90}=\frac{9}{90}=\frac{1}{10}​ tank/min.

    Time to fill =1110=10\dfrac{1}{\frac{1}{10}}=10​ minutes.

    Alternate Method:
    Assume tank capacity = LCM(9,90) = 90 units.
    A fills 10 units/min; B empties 1 unit/min

    net = 9 units/min.
    Time =909=10 \dfrac{90}{9}=10​ minutes.

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