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    A and B together can do a piece of work in 10 days. A alone can do it in 30 days. The time in which B alone can do it is:
    Question

    A and B together can do a piece of work in 10 days. A alone can do it in 30 days. The time in which B alone can do it is:

    A.

    20 days

    B.

    15 days

    C.

    12 days

    D.

    10 days

    Correct option is B

    Given:

    A and B together can do a piece of work in 10 days. A alone can do it in 30 days. 

    Concept:

    Ram is work in X days, then, 

    Ram is work in one day = 1X\frac{1}{X}

    solution:

    A and B together can do a piece of work = 10 days

    A can alone work = 30 days

    Let B can alone work = x days

    130+1x=110\frac{1}{30} + \frac{1}{x} = \frac{1}{10}

    1x=110130\frac{1}{x} = \frac{1}{10} - \frac{1}{30}

    ​​​​1x=3130\frac{1}{x} = \frac{3-1}{30}

    1x=230 \frac{1}{x} = \frac{2}{30}

    1x=115 \frac{1}{x} = \frac{1}{15}

    x =15 days

    So, The time in which B alone can do it is 15 days.

    Thus, the correct answer is (b).

    Alternative method:

    B = 302\frac{30}{2}

    B = 15 days

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