Explanation:

- A, B, and C are partners with a profit-sharing ratio of 2:3:4.

- When A retires, his share is distributed between B and C according to their new profit-sharing ratio of 3:4.

- The calculation for the gaining ratio is:

- B’s new share is 3/7 and was 3/9, hence gain = (3/7 - 3/9) = 27 - 21/63 = 6/63

- C’s new share is 4/7 and was 4/9, hence gain = (4/7 - 4/9) = 36 - 28/63 = 8/63

- The gaining ratio comes out to be 6:8 or 3:4