A, B, and C can do a piece of work in 36 days, 54 days and 108 days, respectively. They started the work together but A left 9 days after the start of the work and B left 3 days before the work was completed. For how many days did C work?

29

A = 36 days, B = 54 days, C = 108 days, 

⇒ A worked for 9 days and then left = 3 x 9 = 27 units,

⇒ B left before 3 days of completion of work = 2 x 3 = 6

⇒ So, 27- 6 = 21 units,

⇒ Remaining work = 108 - 21 = 87 units,

⇒ Time required for 87 units to be completed by B+C = \(\frac{87}{2+1}\) = \(\frac{87}{3}\) = 29 days.

As, C was working since day 1, so he worked 29 days since day 1.