A and B can complete a piece of work in 10 and 16 days respectively. A begins to do the work and they work alternatively one at a time for one day each. The whole work will be completed in :

A

$$12\frac{1}{4}$$ days

B

$$13\frac{1}{4}$$ days

C

$$15\frac{1}{4}$$ days

D

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