Accountancy · Ch 4 — Reconstitution of a Partnership Firm — Retirement/Death of a Partner
Gaining Ratio
Gaining Ratio
What is Gaining Ratio?
When a partner retires or dies, the remaining (continuing) partners take over that partner's share of profit. The gaining ratio is the ratio in which the continuing partners acquire the share of the retiring/deceased partner.
In simple terms, it tells us who gains how much of the outgoing partner's profit share.
When Do We Need to Calculate Gaining Ratio?
There are three common situations:
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Continuing partners take the retiring partner's share in their old profit-sharing ratio.
In this case, the gaining ratio is exactly the same as their old profit-sharing ratio among themselves. No separate calculation is needed.
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The proportion in which they acquire the share is specifically agreed upon.
For example, they may decide that A will take 2/3 of the retiring partner's share and B will take 1/3. Here, the gaining ratio is simply that agreed proportion (2:1). Again, no calculation is required.
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The new profit-sharing ratio of the continuing partners is given.
This is the only situation where we must calculate the gaining ratio. The formula is:
Gaining Share of a Continuing Partner = New Share – Old Share
The gaining ratio is then the ratio of these individual gains.
How to Calculate Gaining Ratio (Step-by-Step)
Step 1: Write down the old profit share of each continuing partner (as a fraction of the total profit).
Step 2: Write down the new profit share of each continuing partner (as a fraction of the total profit).
Step 3: For each continuing partner, subtract the old share from the new share. The result is their gaining share.
Step 4: Express these gaining shares in the simplest ratio.
A common mistake is to forget that the old and new shares must be expressed with a common denominator before subtracting. Always convert them to equivalent fractions with the same denominator.
Example from the Textbook
Amit, Dinesh, and Gagan share profits in the ratio 5:3:2. Dinesh retires. Amit and Gagan decide to share future profits in the ratio 3:2.
Old shares (as fractions of 10):
Amit = 5/10, Gagan = 2/10
New shares (as fractions of 5):
Amit = 3/5 = 6/10, Gagan = 2/5 = 4/10
Gaining share:
Amit = 6/10 – 5/10 = 1/10
Gagan = 4/10 – 2/10 = 2/10
Gaining ratio = 1/10 : 2/10 = 1:2
This means Amit gains 1/3 of Dinesh's share and Gagan gains 2/3 of Dinesh's share.
Distinction Between Gaining Ratio and Sacrificing Ratio
| Aspect | Gaining Ratio | Sacrificing Ratio |
|---|---|---|
| Meaning | Ratio in which continuing partners acquire the share of the retiring/deceased partner | Ratio in which existing partners give up their share in favour of a new partner |
| Effect on Partner's Share of Profit | Increases the share of continuing partners | Decreases the share of existing partners |
| Mode of Calculation | New share – Old share (for each continuing partner) | Old share – New share (for each existing partner) |
| When to Calculate | At the time of retirement or death of a partner | At the time of admission of a new partner |
Key Points to Remember
- Gaining ratio is relevant only at the time of retirement or death of a partner. …