A and B together can complete a job in 8 days. Both B and C, working alone can finish the same job in 12 days, A and B commence work on the job, and work for 4 days, where upon A leaves, B continues for 2 more days, and then he leaves too, C now starts working, and finishes the job. How many days will C require to finish the remaining work ?

Solution(By Examveda Team)

L.C.M. of total days = 24
One day work of A + B = $$\frac{{24}}{8}$$ = 3 units/day
One day work of B = $$\frac{{24}}{12}$$ = 2 units/day
One day work of C = $$\frac{{24}}{12}$$ = 2 units/day
A and B work for 4 days they completed
$$\eqalign{ & = 3 \times 4 \cr & = 12{\text{ units}} \cr & \therefore {\text{Work left}} \cr & = 24 - 12 \cr & = {\text{12 units}} \cr & {\text{B's 2 days work}} \cr & = 2 \times 2 \cr & = {\text{4 units}} \cr & \therefore {\text{Work left}} \cr & = 12 - 4 \cr & = {\text{8 units}} \cr & {\text{Now, }} \cr & {\text{C's complete the work in}} \cr & = \frac{8}{2} \cr & = 4{\text{ days}} \cr} $$