A,B and C can do a piece of work in 30 days, 40 days and 50 days, respectively. Beginning with A, if A, B and C do the work alternatively then in how many days will the work be finished?

A

$$38\frac{1}{12}$$

B

$$36\frac{1}{2}$$

C

36

D

$$39\frac{1}{12}$$