A and B have been in partnership sharing profits in the ratio of 7 : 3. C is admitted as a partner. A surrender $$\frac{1}{7}$$ of his share and B surrenders $$\frac{1}{3}$$ of his share in favour of C. The new profit sharing ratio will be-

The correct answer is $\boxed{\text{C}}$.

Initially, A and B share the profits in the ratio of 7 : 3. This means that A gets 7 parts of the profit and B gets 3 parts of the profit. When C is admitted as a partner, A surrenders $\frac{1}{7}$ of his share and B surrenders $\frac{1}{3}$ of his share in favour of C. This means that A now gets $\frac{6}{7}$ of the profit and B now gets $\frac{4}{3}$ of the profit. The total profit is now shared by A, B, and C in the ratio of $\frac{6}{7} : \frac{4}{3} : 1 = 1 : 3 : 1$.

Here is a step-by-step solution:

1. Calculate the new share of A:

$$\frac{7}{10} – \frac{1}{7} = \frac{6}{7}$$

1. Calculate the new share of B:

$$\frac{3}{10} – \frac{1}{3} = \frac{4}{10} = \frac{2}{5}$$

1. Calculate the new profit sharing ratio:

$$\frac{6}{7} : \frac{4}{10} : 1 = 1 : 3 : 1$$