A and B can do a piece of work in 10 days, B and C in 15 days, A and C in 12 days. A,B and C work together to finish the work. If they are paid $1500, how should the money be divided?

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  1. Let their times to do the job alone be A, B, and C days respectively

    A and B can do a piece of work in 10 days -->
    1/A + 1/B = 1/10
    A + B = AB/10
    10A + 10B = AB

    B and C in 15 days:
    1/B + 1/C = 1/15
    B+C = BC/15
    15B + 15C = BC

    A and C in 12 days
    12A + 12C = AC

    Not the nicest triplet of equations to solve, but how about
    A = 120/7
    B = 24
    C = 40

    so the ratio of their times
    = (7/120) : 1/24 : 1/40
    = 7 : 5 : 3

    So the cost should be split in that ratio, or

    (7/15)(1500) : (5/15)(1500) : (3/15)(1500)
    = $700 : $500 : $300

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  2. Thank you so much. :D :D . I am very grateful towards you... :)

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  3. You are welcome, Happy New Years

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  4. Thanks... can you help me with this question as well?

    A and B take 18 days to complete a work. A left the work after 10 days and B takes 12 days more to complete the work. In how many days can A complete the whole work?

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