When a partner of a partnership firm decides to retire from the firm or when a partner is deceased, the profit sharing rate of the remaining partners changes. The share of the retiring/ deceased partner is divided between the continuing partners in the Gaining Ratio.

The common procedure adopted by partnership firms is to divide the retiring/ deceased partner share between the remaining partners in their old profit sharing ratio. In such a case, there is no requirement to separately compute the gaining ratio as it is the same as the old profit sharing ratio.

In certain circumstances, the proportion in which the share of the retiring/deceased partner is to be shared is already mentioned, therefore eliminating the need to calculate the gaining ratio.

However, in cases where the new profit sharing ratio of remaining partners is given we need to calculate the gaining ratio.

This can be computed with the following formula –

**Gaining Ratio = New profit sharing ratio of partner – Old profit sharing ratio of partner**

**Example 1 –**

A, B and C are partners in a partnership firm sharing profits in the ratio of 1:2:3. Partner A decides to retire and the remaining two partners agree to share the profits in the ratio 3:4. In this situation, it is necessary to calculate the gaining ratio using the formula –

**Explanation:**

Gaining Ratio = New profit sharing ratio of partner – Old profit sharing ratio of partner

B’s Gaining Ratio = 3/7 – 2/6 = 18-14/42 = 5/42

C’s Gaining Ratio = 4/7 – 3/6 = 24-21/42 = 3/42

So, gaining ratio of B and C is 5:3.

**Example 2 – **

M , N and O are partners sharing profits and losses in the ratio of 2/4 : 1/4 : 1/4 N died.what will be the gaining ratio

between M and O ?

**Explanation:**

New Ratio between M and O after retirement of N = 2/3 : 1/3

Gaining Ratio = New Ratio – Old Ratio

M s Gaining Ratio = (2/3) – (2/4)

= (8/12) – (6/12)

= 2/12

O s Gaining Ratio = (1/3) – (1/4)

= (4/12) – (3/12)

= 1/12

Gaining Ratio = 2 : 1

**Example 3 – **

G , H and I are partners sharing profits and losses in the ratio of 1 : 1 : 1. I retired from the firm and surrendered 2/3rd of his share of profit to G and remaining in favour of H . What will be the gaining ratio between G and H ?

**Explanation:**

Old ratio between G H and I = 1 : 1 : 1

Share surrendered by I in favour of G = (1/3) x (2/3) = 2/9

Share surrendered by I in favour of H = (1/3) – (2/9) = (3-2)/9 = 1

Gaining ratio = The ratio in which the continuing partners acquire the outgoing (retired ) partner share

New share – Old share

Gaining ratio between G and H = 2/9 : 1/9

= 2:1