A can complete a work in 20 days, B in 30 days, and C in 60 days. A stops working 4 days before the completion of the work, and B stops 6 days before completion. C continues working alone till the end. What was the total number of days taken to complete the entire work?

Question: A can complete a work in 20 days, B in 30 days, and C in 60 days. A stops working 4 days before the completion of the work, and B stops 6 days before completion. C continues working alone till the end. What was the total number of days taken to complete the entire work?

Solution:
Let the total work be completed in y days.

∴ A worked for (y - 4) days
So his contribution = (y - 4)/20

B worked for (y - 6) days
So his contribution = (y - 6)/30

C worked full y days, so his contribution = y/60

Therefore,
(y - 4)/20 + (y - 6)/30 + y/60 = 1
⇒ 3(y - 4) + 2(y - 6) + y = 60
⇒ 3y - 12 + 2y - 12 + y = 60
⇒ 6y - 24 = 60
⇒ 6y = 84
⇒ y = 14

∴ The total work was completed in 14 days.