Explanation:

- Current Ratio: A, B, and C are sharing profits in a ratio of 3:2:1.

- B's Retirement: With B retiring, A and C need to adjust the ratio.

- New Ratio after B's exit: A and C agree on a future sharing ratio of 3:2.

- Calculation of Gaining Ratio:

- A's share before B retires: 3/6 = 1/2

- C's share before B retires: 1/6

- A's share after B retires: 3/5

- C's share after B retires: 2/5

- Gain for A: (3/5) - (1/2) = 1/10 = 2/20

- Gain for C: (2/5) - (1/6) = 7/30 = 14/60

- Gaining Ratio Calculation:

- A's gain: 2/20 = 6/60

- C's gain: 14/60

- Gaining Ratio: 6:14 = 3:7