A and B are partners sharing profits and losses in the ratio of 1 : 2. They admit c and agree to give him $$\frac{1}{5}$$ of the share. The new profit sharing ratio will be:

The correct answer is C.

Initially, A and B share the profits in the ratio of 1 : 2. This means that A gets 1 share and B gets 2 shares. When C is admitted, he gets $\frac{1}{5}$ of the share. This means that the new profit sharing ratio will be 1 + $\frac{1}{5}$ : 2 + $\frac{1}{5}$ : $\frac{1}{5}$. This simplifies to 8 : 3 : 4.

Option A is incorrect because it does not take into account the fact that C gets $\frac{1}{5}$ of the share.

Option B is incorrect because it does not take into account the fact that A and B share the profits in the ratio of 1 : 2.

Option D is incorrect because it does not take into account the fact that C gets $\frac{1}{5}$ of the share.