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    If 9 men and 12 boys can do a piece of work in 4 days and 4 men and 16 boys can do the same piece of work in 6 days, how long will 6 men and 24 boys t
    Question

    If 9 men and 12 boys can do a piece of work in 4 days and 4 men and 16 boys can do the same piece of work in 6 days, how long will 6 men and 24 boys take to complete the same work?

    A.

    7 days

    B.

    4 days

    C.

    6 days

    D.

    5 days

    Correct option is B

    Given:
    9 men + 12 boys =4 days.
    4 men + 16 boys = 6 days.
    Solution:
    Let the work done by 1 man in 1 day = M, and by 1 boy in 1 day = B.
    (9M + 12B) 4 = (4M + 16B) 6

    36M + 48 B = 24M + 96B

    12M = 48B

    M/B = 4/1 

    Total Work = (9M + 12B) 4 = (9×\times  4 + 12×\times 1)4 = 48×\times  4
    Time for 6 men and 24 boys =  48×46×4+24×1=48×448=4days\frac{48× 4}{6\times4+ 24\times1} =\frac{48× 4}{48} = 4 \text{days}​​

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