Understanding Gaining Ratio in Partnership Retirement

When a partner retires from a partnership firm, their share of profit is taken over by the remaining partners. The proportion in which the remaining partners acquire the retiring partner's share is known as the gaining ratio. This ratio is important for calculating goodwill treatment and other adjustments upon retirement.

Calculating Gaining Ratio: Step-by-Step

The gaining ratio is calculated as the difference between the new profit share and the old profit share of the continuing partners. The formula is:

Gaining Share = New Share - Old Share

Let's apply this formula to the given problem:

Given Information:

• Old profit-sharing ratio of A, B, and C = 5:3:2
• Retiring partner = B
• New profit-sharing ratio of A and C = 3:2

Step 1: Determine the old shares of the continuing partners.

The total old share is $5 + 3 + 2 = 10$.

• A's old share = $\frac{5}{10}$
• C's old share = $\frac{2}{10}$

Step 2: Determine the new shares of the continuing partners.

The total new share is $3 + 2 = 5$.

• A's new share = $\frac{3}{5}$
• C's new share = $\frac{2}{5}$

Step 3: Calculate A's gain.

A's gain = New share - Old share

A's gain = $\frac{3}{5} - \frac{5}{10}$

To subtract these fractions, find a common denominator, which is 10.

A's gain = $\frac{3 \times 2}{5 \times 2} - \frac{5}{10} = \frac{6}{10} - \frac{5}{10} = \frac{6 - 5}{10} = \frac{1}{10}$

Step 4: Calculate C's gain.

C's gain = New share - Old share

C's gain = $\frac{2}{5} - \frac{2}{10}$

To subtract these fractions, find a common denominator, which is 10.

C's gain = $\frac{2 \times 2}{5 \times 2} - \frac{2}{10} = \frac{4}{10} - \frac{2}{10} = \frac{4 - 2}{10} = \frac{2}{10}$

Step 5: Determine the gaining ratio.

The gaining ratio is the ratio of the individual gains of the continuing partners.

Gaining Ratio (A:C) = A's gain : C's gain

Gaining Ratio = $\frac{1}{10} : \frac{2}{10}$

Multiply both parts by 10 to get the ratio in whole numbers:

Gaining Ratio = $1 : 2$

Therefore, the gaining ratio between A and C is 1:2.

Summary of Gaining Ratio Calculation

Gaining Ratio (A:C) = $\frac{1}{10} : \frac{2}{10} = 1 : 2$

Revision Table: Key Ratios in Partnership

Additional Information: Treatment of Goodwill on Retirement

The gaining ratio is crucial for the accounting treatment of goodwill when a partner retires. If the firm's goodwill is valued, the retiring partner is entitled to their share of goodwill because it was earned during their association with the firm. The remaining partners, who gain from the retirement (as reflected in their gaining ratio), compensate the retiring partner for their share of goodwill.

The journal entry typically involves debiting the Capital Accounts of the gaining partners in their gaining ratio and crediting the retiring partner's Capital Account with their share of goodwill.

Example Journal Entry (Illustrative):

• Gaining Partner's Capital A/c Dr. (in gaining ratio)
• Gaining Partner's Capital A/c Dr. (in gaining ratio)
•    To Retiring Partner's Capital A/c (with retiring partner's share of goodwill)

This adjustment ensures that the burden of compensating the retiring partner for goodwill is borne by the partners who benefit from the change in the profit-sharing arrangement.