A, B and C are partners in a firm sharing profits in the ratio $$\frac{2}{5}:\,\frac{2}{5}:\,\frac{1}{5}.$$   C retires from the firm and his share is bought by A and B in equal ratio. New profit sharing ratio will be.

A. $${\text{A}} = \frac{1}{2}:{\text{B}} = \frac{1}{2}$$

B. $${\text{A}} = \frac{3}{5}:{\text{B}} = \frac{2}{5}$$

C. $${\text{A}} = \frac{2}{5}:{\text{B}} = \frac{3}{5}$$

D. $${\text{A}} = \frac{1}{3}:{\text{B}} = \frac{2}{3}$$

Answer: Option A