Explanation:

When an outgoing partner is compensated for parting with the firm's future profits, the remaining partners contribute to this compensation amount in a ratio known as the gaining ratio. The gaining ratio determines how the remaining partners will share the profits that were previously allocated to the outgoing partner.

Gaining Ratio:
The gaining ratio is the ratio in which the remaining partners acquire the share of the outgoing partner. It is calculated by taking into consideration the new profit-sharing ratio of the partners after the retirement or withdrawal of the outgoing partner. The gaining ratio represents the increase in the profit-sharing ratio of each remaining partner.

Calculation of the Gaining Ratio:
To calculate the gaining ratio, we need to determine the new profit-sharing ratio of the remaining partners after the retirement or withdrawal of the outgoing partner. This can be done by adjusting the profit-sharing ratio of the partners based on the agreed terms.

For example, let's say there are three partners in a firm: A, B, and C. The profit-sharing ratio before the retirement of partner A is 2:2:1. After the retirement of partner A, the remaining partners, B and C, agree to a new profit-sharing ratio of 3:2.

In this case, the gaining ratio for partner B would be 1/3 (increase in profit-sharing ratio from 2/5 to 3/5) and the gaining ratio for partner C would be 1/1 (increase in profit-sharing ratio from 1/5 to 2/5). The gaining ratio is always expressed in terms of the total gain of each partner.

Importance of Gaining Ratio:
The gaining ratio is important as it determines how the remaining partners will share the profits that were previously allocated to the outgoing partner. It ensures a fair distribution of profits among the remaining partners based on their increased share in the firm.

Conclusion:
In conclusion, when an outgoing partner is compensated for parting with the firm's future profits, the remaining partners contribute to this compensation amount in the gaining ratio. The gaining ratio represents the increase in the profit-sharing ratio of each remaining partner and ensures a fair distribution of profits among them.