Anik alone can do a piece of work in 6 days and Bishal alone in 8 days. Anik and Bishal undertook to do it for Tk. 5400. With the help of Dinesh, they completed the work in 3 days. How much is to be paid to Dinesh?

Question: Anik alone can do a piece of work in 6 days and Bishal alone in 8 days. Anik and Bishal undertook to do it for Tk. 5400. With the help of Dinesh, they completed the work in 3 days. How much is to be paid to Dinesh?

Solution:
Anik's 1day work = 1/6
Bishal's 1 day work = 1/8

∴ (Anik + Bishal + Dinesh)'s 1 day work = 1/3

∴ Dinesh's 1 day work = (1/3) - (1/6) - (1/8) = (8 - 4 - 3)/24 = 1/24

So, Dinesh's 3 day work = 3 × (1/24) = 1/8
If Dinesh contributed 8th part of work then he will receive 8th part of total payment

∴ Dinesh should be paid = 5400 × (1/8) = Tk. 675