A and B are partners sharing profits and losses in the ratio 3 : 1. They decided to admit C. C will be given $${\frac{1}{4}^{{\text{th}}}}$$ share in future profits of the firm which he takes from A and B in ratio 2 : 1. New profit sharing ratio will be:

The correct answer is $\boxed{\text{B) 7 : 2 : 3}}$.

Initially, A and B share the profits in the ratio 3 : 1. This means that A gets 3 parts of the profit and B gets 1 part of the profit.

When C is admitted, he is given $\frac{1}{4}$ share of the future profits. This means that C gets $\frac{1}{4}$ of the total profit that A and B would have shared.

C takes $\frac{1}{4}$ share from A and B in the ratio 2 : 1. This means that C takes $\frac{2}{3}$ of $\frac{1}{4}$ share from A and $\frac{1}{3}$ of $\frac{1}{4}$ share from B.

Therefore, the new profit sharing ratio is 3 + $\frac{2}{3}$ : 1 + $\frac{1}{3}$ : $\frac{1}{4}$ = 7 : 2 : 3.