A and B can do a piece of work in 10 days, B and C in 15 days and A and C in 12 days. A,B and C work together to finish the work. If they are paid 15000, find the share of each?

Answer 1

1/a + 1/b = 1/10
1/b + 1/c = 1/15
1/a + 1/c = 1/12

subtract 2 from 1
1/a - 1/c = 1/30
1/a + 1/c = 1/12

add them
2/a = 7/60
1/a = 7/120
similarly, 1/b = 1/24 and 1/c = 1/40

1/a is the share of the work a can do in a day.
Now set up a proportion to allocate the money

1/a : 1/b : 1/c = 7/120 : 1/24 : 1/40
= 7:5:3 = 7000:5000:3000
and those are the shares of the $15000

Answer 2

Thankyou very much sir.