X and Y can complete a work in 9 days and 36 days, respectively. X begins to do the work and they work alternately one at a time for one day each. The whole work will be complete in:

A

$$12\frac{1}{2}$$ days

B

$$14\frac{1}{4}$$ days

C

$$13\frac{1}{3}$$ days

D

$$15\frac{1}{5}$$ days