Explanation:

- Before B retires, the profit-sharing ratio is 5:3:2 for A, B, and C.

- After B retires, A and C agree on a new profit-sharing ratio of 3:2.

- To find the gaining ratio, calculate how much of B’s share each partner has taken.

- A's initial share is 5/10 and becomes 3/5.

- C's initial share is 2/10 and becomes 2/5.

- Calculate the gain:

- A gains: \( \frac{3}{5} - \frac{5}{10} = \frac{1}{10} \).

- C gains: \( \frac{2}{5} - \frac{2}{10} = \frac{2}{10} \).

- Since both A and C gain equally, the gaining ratio is 1:2.