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?

Answer 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

Answer 2

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

Answer 3

You are welcome, Happy New Years

Answer 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?