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    P and Q can complete a job in 12 days and 16 days respectively. They work together for 4 days. What portion of work is left for completion?
    Question

    P and Q can complete a job in 12 days and 16 days respectively. They work together for 4 days. What portion of work is left for completion?

    A.

    34\frac{3}{4}​​

    B.

    67\frac{6}{7}​​

    C.

    512\frac{5}{12}​​

    D.

    712\frac{7}{12}​​

    Correct option is C

    Given: 

    P can complete the work = 12 days 

    Q can complete the work = 16 days 

    Solution:

    Let the total work be represented as 1 unit.

    P can complete the work in 12 days, so P's rate of work is: 112 \frac{1}{12}​  of the work per day.

    Q can complete the work in 16 days, so Q's rate of work is:  116\frac{1}{16}​ of the work per day.

    Together, P and Q's rate of work is:   112+116=4+348=748\frac{1}{12} + \frac{1}{16} = \frac{4 + 3}{48} = \frac{7}{48}​ of the work per day.

    In 4 days, P and Q together can complete:   4×748=2848=7124 \times \frac{7}{48} = \frac{28}{48} = \frac{7}{12}​ of the work.

    Thus, the portion of work left is: 1712=512 1 - \frac{7}{12} = \frac{5}{12}​.

    Hence, 512\frac{5}{12}​ of the work is left for completion.

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