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    A and B complete a work in 2 days. If A alone can do it in 38 days, then B alone can do 9 times of the same work in ______________ days.
    Question

    A and B complete a work in 2 days. If A alone can do it in 38 days, then B alone can do 9 times of the same work in ______________ days.

    A.

    10

    B.

    9

    C.

    20

    D.

    19

    Correct option is D

    Given:

    A and B together complete the work in 2 days.

    A alone can complete the work in 38 days.

    Solution:

    Total work = LCM of ( 2, 38) = 38

    Efficiency of A  + B = 382=19\frac{38}{2} = 19  unit per day 

    Efficiency of A =  3838\frac{38}{38} = 1 unit per day 
    Efficiency of B = 19 - 1 = 18 unit per day

    9 times of the work = 9×38\times 38  

    B alone complete the work = 9×3818=19\frac{9×38 }{18} = 19  days

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