A and B partners sharing profits in the ratio of 7 : 3. C is admitted for $$\frac{3}{7}$$ share in the profit. The new profit-sharing ratio of the partners will be:

The correct answer is A. 14 : 6 : 15.

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, he gets a share of $\frac{3}{7}$ of the profit. This means that the new profit-sharing ratio of the partners will be 7 : 6 : 15.

To arrive at this answer, we can use the following formula:

New profit-sharing ratio = Old profit-sharing ratio + New share

In this case, the old profit-sharing ratio is 7 : 3 and the new share is $\frac{3}{7}$. Therefore, the new profit-sharing ratio is:

7 : 3 + $\frac{3}{7}$ = 14 : 6 : 15

Here is a brief explanation of each option:

• Option A: 14 : 6 : 15. This is the correct answer. It is the new profit-sharing ratio of the partners after C is admitted.
• Option B: 7 : 6 : 7. This is not the correct answer. It is the old profit-sharing ratio of the partners before C is admitted.
• Option C: 7 : 3 : 3. This is not the correct answer. It is the old profit-sharing ratio of the partners before C is admitted.
• Option D: 5 : 3 : 3. This is not the correct answer. It is not a possible profit-sharing ratio for the partners.