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    A and B can do a piece of work in 9 days and 15 days, respectively. If they work together, then the work will be completed in:
    Question

    A and B can do a piece of work in 9 days and 15 days, respectively. If they work together, then the work will be completed in:

    A.

    3 38\frac 38 ​days

    B.

    2 18\frac 18​days

    C.

    558\frac 58​ days

    D.

    4 58\frac 58​days

    Correct option is C

    Given:
    A complete the work in 9 days
    B complete the work in 15 days
    Solution:
    A’s one day work = 19\frac{1}{9}​ unit
    B’s one day work = 115\frac{1}{15} ​unit
    A+B’s one day work = 19+115=5+345=845\frac{1}{9} + \frac{1}{15} = \frac{5+3}{45}=\frac{8}{45}​​
    A+B complete the total work in 458=558days\frac{45}{8} = 5\frac{5}{8} days 

    Alternate Solution:

    Efficiency of A = 3 unit
    Efficiency of B = 5 unit
    Time required to complete whole work by A+B together = 458=558days\frac{45}{8} = 5\frac{5}{8} days​​

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