Hello! Welcome to the first lesson in our module on the Retirement and Death of a Partner.
In our previous module, you mastered the accounting for the admission of a new partner. We finished by tackling comprehensive problems where you learned the importance of the sacrificing ratio for distributing goodwill. Today, we shift our focus to the opposite scenario: a partner leaving the firm.
This lesson addresses the learning outcome: Calculate the new profit-sharing ratio and gaining ratio upon a partner's retirement or death. Just as the sacrificing ratio was fundamental to admission, the gaining ratio is the cornerstone of accounting for retirement and death. Understanding these calculations is the essential first step before we can handle adjustments for goodwill and other items.
From Sacrificing to Gaining: The Core Concept
When a new partner is admitted, the old partners sacrifice a portion of their profit share. When an existing partner retires or passes away, the opposite happens: the remaining (or continuing) partners gain the outgoing partner's share of profit. The proportion in which they gain this share is called the gaining ratio.
This chart provides a clear comparison between the two ratios.
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The fundamental formula to remember is:
This is the reverse of the sacrificing ratio formula, which you'll recall was Old Share - New Share.
Calculating the New and Gaining Ratios
The calculation method depends entirely on the information provided in the problem. There are two primary scenarios you will encounter.
Case 1: The "Simple Case" (No Information Given)
This is the most straightforward scenario. The problem states that a partner is retiring but provides no further details about how the continuing partners acquire their share.
The Rule: In this case, you simply remove the retiring partner's share from the old ratio. The ratio that remains among the continuing partners is both their new profit-sharing ratio and their gaining ratio.
Retirement of a Partner | New Ratio and Gaining Ratio | Basics | Part 1
To understand this simple case and the core concept of the gaining ratio, let's watch this segment from a video by Rajat Arora. He explains the logic and the shortcut very effectively.
Please watch the following clips: 04:20 to 07:15: This explains why we calculate a 'gaining' ratio in retirement instead of a sacrificing ratio. 07:15 to 08:35: Focus on the first case he presents, where no information about the gain is given. Note the simple shortcut. 12:50 to 14:15: This confirms that in this simple case, the new ratio and the gaining ratio are the same.
Why does this shortcut work? The underlying assumption is that the continuing partners gain the outgoing partner's share in their existing profit-sharing ratio. The following video provides an excellent conceptual breakdown of this logic.
Retirement of a Partner | Part 1 | New Ratio and Gaining ratio | Class 12 Accounts | Session 2025-26
The shortcut is easy, but it's important to know why it works. This video from Sunil Panda explains the detailed calculation behind the simple case, proving that the shortcut is mathematically sound.
Watch the section from 32:20 to 36:56. The instructor demonstrates how the retiring partner's share is distributed in the old ratio of the remaining partners, and how this leads to the same result as the shortcut. Understanding this will deepen your conceptual clarity.
Test your understanding!
X, Y, and Z are partners sharing profits in the ratio 5:3:2. Y retires from the firm. No other information is provided. What are the new profit-sharing ratio and the gaining ratio of X and Z?
Show answer
Since no information is given, we simply remove Y's share (3) from the ratio.
- New Profit-Sharing Ratio of X and Z = 5:2
- Gaining Ratio of X and Z = 5:2
Case 2: The "Acquire Case" (Specific Information Given)
This is the more common scenario in exam questions. The problem explicitly states how the retiring partner's share is taken over by the continuing partners.
The Rule:
- The ratio in which the continuing partners acquire the share is the gaining ratio.
- To find the new profit-sharing ratio, you must first calculate the actual share each partner gains and add it to their old share.
This video demonstrates how to handle these calculations with several clear, step-by-step examples covering different variations.
Retirement of a Partner | Part 1 | New Ratio and Gaining ratio | Class 12 Accounts | Session 2025-26
Let's explore the 'acquire case' with its different variations. This video provides comprehensive examples that are very similar to what you'll see in your exams.
Watch from 16:55 to 32:20. Pay close attention to how the instructor solves problems where the retiring partner's share is: Acquired in a specific new ratio (e.g., 3:2). Taken entirely by only one partner. Taken as a specific fraction of the retiring partner's share (e.g., X takes 1/9th of Y's share, and the balance is taken by Z).
Calculating Gaining Ratio When the New Ratio is Given
Sometimes, a problem will give you both the old profit-sharing ratio of all partners and the new profit-sharing ratio of the continuing partners. In this situation, you must use the primary formula to find the gaining ratio.
To see how this is applied, let's refer to your NCERT textbook.
Retirement/Death of a Partner - NCERT Textbook
The NCERT textbook provides a clear, formal explanation for this scenario. We'll look at an example where you are given both old and new ratios and must calculate the gain.
Please read section 3.3 Gaining Ratio on pages 109-110. Focus on the example of Amit, Dinesh, and Gagan. Their old ratio was 5:3:2. Dinesh retires, and the new ratio for Amit and Gagan is 3:2. Notice how the formula New Share - Old Share is applied to each continuing partner to calculate the gaining ratio of 1:2.
Test your understanding!
P, Q, and R are partners sharing profits in the ratio 5:4:1. P retires. The new profit-sharing ratio between Q and R is 3:2. Calculate the gaining ratio.
Show answer
Let's apply the formula: Gaining Share = New Share - Old Share.
Old Shares:
- P = 5/10
- Q = 4/10
- R = 1/10
New Shares:
- Q = 3/5
- R = 2/5
Calculation:
- Q's Gain:
- R's Gain:
The gaining ratio is the ratio of their gains, which is 2:3.
Conclusion
You have now learned the foundational calculation for the entire topic of a partner's retirement and death. Mastering these ratio calculations is non-negotiable, as they directly impact the accounting treatment that follows.
Key Takeaways:
- Gaining Ratio is the ratio in which continuing partners acquire the profit share of an outgoing partner. Its formula is New Share – Old Share.
- Simple Case (No info given): The new ratio and gaining ratio are the same as the old ratio of the remaining partners.
- Acquire Case (Info given): The ratio in which the share is acquired is the gaining ratio. The new ratio is calculated as
Old Share + Gained Share. - If both Old and New Ratios are given: You must apply the formula
New Share – Old Shareto find the gaining ratio.
Preview of the Next Lesson:
Now that you can calculate the gaining ratio, our next step is to apply it. In the next lesson, we will focus on how to account for the outgoing partner's share of goodwill by adjusting it through the continuing partners' capital accounts. You will see exactly why the gaining ratio is so crucial in this process.