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    A, B and C together can do a piece of work in 14 days, whereas C alone can do the same work in 42 days. How long will A and B together take to finish
    Question

    A, B and C together can do a piece of work in 14 days, whereas C alone can do the same work in 42 days. How long will A and B together take to finish it?

    A.

    28 days

    B.

    35 days

    C.

    21 days

    D.

    7 days

    Correct option is C

    Given:

    A, B, and C together can complete the work in 14 days

    C alone can complete the work in 42 days

    Formula Used:

    Work per day = 1Number of days \frac{1}{\text{Number of days}} ​​

    Solution:

    A + B + C's 1 day work = 114\frac{1}{14}​​

    C's 1 day work = 142\frac{1}{42}​​

    Then,

    A + B = 114142 \frac{1}{14} - \frac{1}{42}​​

    =3142= \frac{3 - 1}{42}​​

    =242= \frac{2}{42}​​

    =121= \frac{1}{21}​​

    So, A and B together can complete the work in 21 days.

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