A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for tk. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for tk. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

Solution:
C's 1 day's work = (1/3) - {(1/6) + (1/8)}
= (1/3) - (7/24)
= 1/24

Now,
A's wages : B's wages : C's wages = (1/6) : (1/8) : (1/24)
= (1/6) × 24 : (1/8) × 24 : (1/24) × 24
= 4 : 3 : 1

∴ C's share (for 3 days) = 3 × (1/24) × 3200
= 400 tk