Calculation of Gaining Ratio: Retirement of a Partner

Last Updated : 05 Apr, 2023

What is Gaining Ratio?

When a partner retires from a firm, his share of the profit is acquired by the continuing partners in a certain ratio, and a new profit-sharing ratio is determined. A Gaining Ratio is a ratio in which the remaining partners take over the share of the retiring partner. The purpose of calculating the Gaining Ratio is to determine the amount of goodwill or premium for goodwill payable to the retiring partner by the continuing partners as compensation for the acquisition of his/her shares. The Gaining ratio helps in adjusting the share of goodwill of the retiring partner. The Gaining Ratio is calculated by deducting the old share of a partner from his/her new share.

Gaining Ratio = New Ratio − Old Ratio

Computation:

Case 1: When the New Profit-Sharing Ratio of the remaining partner is not given:

In the absence of the new profit-sharing ratio, it is presumed that the remaining partners shall continue to share the future profits and losses in their old ratio. As an effect of this, the share of the retiring partner is acquired by the remaining partner in their old profit-sharing ratio.

Illustration 1:

Om, Jay, and Jagdish were partners sharing profits in the ratio of 9: 6: 3. Jay retires from the firm on 30th April, 2022. Find the Gaining Ratio of Om and Jagdish.

Solution:

Since there is no information given about the new profit-sharing ratio between Om and Jagdish (Continuing Partners), it is assumed that they acquire the share of Jay in their old profit-sharing ratio.

The Gaining Ratio of Om and Jagdish is in the ratio of 9: 3 i.e., 3:1.

Illustration 2:

Seema, Reena, and Neetu were partners sharing profits and losses in the proportion of $\frac{1}{8},\frac{1}{16},\frac{10}{32}.$ Calculate their gaining ratio if Seema retires from the firm.

Solution:

The Profit Sharing Ratio of Seema, Reena, and Neetu can be written in the simplest form by taking 32 as L.C.M.

Therefore, the Profit Sharing Ratio of Seema, Reena, and Neetu = 4: 2: 10 = 2: 1: 5.

Now, when Seema retires, her share of profit is acquired by Reena and Neetu in their old ratio, i.e., 1: 5.

Case 2: When the new profit-sharing ratio of the remaining partner is given:

Whenever the New Profit-Sharing Ratio among the remaining partners is given, the Gaining Ratio will be different from the new ratio. The following Formula is used to calculate the Gain of each remaining partner:

Gain of a Partner = New Share − Old Share

Illustration 1:

Kamal, Indu, and Rocky were partners in a firm sharing profit in a ratio of 4: 3: 2. Indu retires, and Kamal and Rocky decide to share the future profits and losses in the ratio of 5: 4. Calculate the Gaining ratio of the remaining partners.

Solution:

Old Ratio of Kamal, Indu, and Rocky = 4: 3: 2

New Ratio of Kamal and Rocky = 5: 4.

So, Gain of a Partner = New Share − Old Share

Gaining Ratio of Kamal = $\frac{5}{9}-\frac{4}{9}=\frac{1}{9}$

Gaining Ratio of Rocky = $\frac{4}{9}-\frac{2}{9}=\frac{2}{9}$

Therefore, the Gaining Ratio between Kamal and Rocky = 1 : 2

Illustration 2:

Ikkat, Imli, and Chamma were partners sharing profit in the ratio of 2: 2: 1, respectively. Chamma retires, Ikkat and Imli decide to share future profits and losses in the ratio of 2: 1. Calculate the Gaining Ratio.

Solution:

Old Ratio of Ikkat, Imli, and Chamma = 2: 2: 1

New Ratio of Ikkat, and Imli = 2:1

So, Gain of a Partner = New Share − Old Share

Gaining Ratio of Ikkat = $\frac{2}{3}-\frac{2}{5}=\frac{4}{15}$ (Gain)

Gaining Ratio of Imli = $\frac{1}{3}-\frac{2}{5}=\frac{-1}{15}$ (Sacrifice)

Therefore, the Gaining Ratio between Ikkat and Imli = 4: -1

Case 3: When the gaining ratio of the remaining partner is given clearly:

In this case, the gaining ratio of the remaining partners is specified in the question. There is no need to calculate the gaining ratio, rather the Gaining Ratio mentioned shall be taken into consideration.

Illustration 1:

Hamza, Hala, and Sameen were partners in the firm sharing profits equally. Hamza retires, and Hala and Sameen decide to take over the share of Hamza in a ratio of 1: 1. Calculate the New Profit-Sharing Ratio and also mention the Gaining Ratio.

Solution:

Old Ratio of Hamza, Hala, and Sameen = 1: 1: 1

Gain of Hala = $\frac{1}{2}$ of $\frac{1}{3}$ i.e., $\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}$

Gain of Sameen = $\frac{1}{2}$ of $\frac{1}{3}$ i.e., $\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}$

New Ratio of Partner = Old Ratio + Gain

Therefore, New Share of Hala = $\frac{1}{3}+\frac{1}{6}=\frac{3}{6}=\frac{1}{2}$

New Share of Sameen = $\frac{1}{3}+\frac{1}{6}=\frac{3}{6}=\frac{1}{2}$

Thus, the New Ratio of Hala and Sameen = 1: 1, and the Gaining Ratio of Hala and Sameen = 1: 1

Illustration 2:

Ravi, Sankar, and Prakash were partners sharing profits and losses in the ratio of $\frac{2}{6},\frac{1}{2},\frac{1}{6}.$ Ravi retires and surrenders $\frac{2}{3}rd$ of his share in favour of Sankar and remaining in the favour of Prakash. Calculate the Gaining Ratio and New Ratio.