Understanding Gaining Ratio in Partnership Retirement

When a partner retires from a partnership, the remaining partners usually acquire the retiring partner's share of profit. The ratio in which the remaining partners gain this share is called the Gaining Ratio. This ratio is important for adjusting capital accounts, goodwill, and revaluation accounts.

Calculating Gaining Ratio

The Gaining Ratio is calculated as the difference between the new profit share and the old profit share for each remaining partner.

\text{Gaining Ratio} = \text{New Share} - \text{Old Share}

Given Information:

• Partners: Lal, Bal, and Pal
• Old Profit Sharing Ratio (Lal : Bal : Pal): 5 : 3 : 2
• Total Old Share: $5 + 3 + 2 = 10$
• Old Share of Lal: $\frac{5}{10}$
• Old Share of Bal: $\frac{3}{10}$ (Bal retires)
• Old Share of Pal: $\frac{2}{10}$
• Remaining Partners: Lal and Pal
• New Profit Sharing Ratio (Lal : Pal): 2 : 1
• Total New Share: $2 + 1 = 3$
• New Share of Lal: $\frac{2}{3}$
• New Share of Pal: $\frac{1}{3}$

Step-by-Step Calculation of Gaining Ratio:

Calculate Lal's Gain:

Lal's Gain = New Share of Lal - Old Share of Lal

Lal's Gain = $\frac{2}{3} - \frac{5}{10}$

To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 3 and 10 is 30.

Lal's Gain = $\frac{2 \times 10}{3 \times 10} - \frac{5 \times 3}{10 \times 3}$

Lal's Gain = $\frac{20}{30} - \frac{15}{30}$

Lal's Gain = $\frac{20 - 15}{30} = \frac{5}{30}$

Calculate Pal's Gain:

Pal's Gain = New Share of Pal - Old Share of Pal

Pal's Gain = $\frac{1}{3} - \frac{2}{10}$

Again, we use the common denominator 30.

Pal's Gain = $\frac{1 \times 10}{3 \times 10} - \frac{2 \times 3}{10 \times 3}$

Pal's Gain = $\frac{10}{30} - \frac{6}{30}$

Pal's Gain = $\frac{10 - 6}{30} = \frac{4}{30}$

Determine the Gaining Ratio:

The Gaining Ratio between Lal and Pal is the ratio of their individual gains:

Gaining Ratio (Lal : Pal) = Lal's Gain : Pal's Gain

Gaining Ratio = $\frac{5}{30} : \frac{4}{30}$

Since both fractions have the same denominator, the ratio is simply the ratio of the numerators.

Gaining Ratio = 5 : 4

Thus, the Gaining Ratio between Lal and Pal is 5:4.

Revision Table: Key Concepts in Partnership Retirement

Additional Information on Partner Retirement

When a partner retires, the partnership firm is reconstituted. Several adjustments are required in the accounts of the firm. These typically include:

• Calculation of the new profit sharing ratio and the gaining ratio.
• Treatment of goodwill. Goodwill may be valued and adjusted through the capital accounts of the remaining and retiring partners based on the gaining ratio.
• Revaluation of assets and liabilities. Profits or losses on revaluation are distributed among all partners (including the retiring one) in the old profit sharing ratio.
• Adjustment of reserves and accumulated profits/losses. These are also distributed among all partners in the old ratio.
• Calculation of the amount due to the retiring partner. This amount includes their capital, share of reserves, accumulated profits, revaluation profit, and goodwill adjustment, less any accumulated losses, revaluation loss, or drawings.
• Settlement of the retiring partner's dues. The amount due can be paid immediately or transferred to a loan account, payable over time.

The gaining ratio specifically determines how the burden of compensating the retiring partner for their share of goodwill will be borne by the continuing partners.