Sacrificing Ratio in Partnership Accounts: Meaning, Formula and Examples

Sacrificing Ratio in Partnership Accounts: Meaning, Formula and Examples

When a new partner joins a firm, they don't create profit share from thin air — they receive it from existing partners, who each give up a portion of what they held. Measuring exactly how much each old partner gives up is the job of the sacrificing ratio, a concept that appears in almost every admission-of-partner numerical in CBSE Class 12 Accountancy.

What Is Sacrificing Ratio?

The sacrificing ratio is the ratio in which old partners agree to give up, or "sacrifice," a portion of their profit share in favour of the incoming partner. It answers a very specific question: who is giving up how much, and in what proportion?

The formula is simple:

Sacrifice by a partner = Old Share of Profit − New Share of Profit

Whatever fraction is left over after this subtraction represents that partner's contribution to the new partner's share.

Why Is Sacrificing Ratio Calculated?

The sacrificing ratio isn't calculated for its own sake — it has one primary, very practical purpose: distributing the premium for goodwill that the new partner brings into the firm. Since the new partner is compensating the old partners for the share of future super-profits they're giving up, that compensation must be split in exact proportion to how much each partner actually sacrificed — not equally, and not in the old profit ratio, unless those happen to be the same thing.

When Is the Sacrificing Ratio the Same as the Old Profit Sharing Ratio?

If a question states that the new partner acquires their share from the old partners "in their old ratio" or doesn't specify anything at all, the sacrificing ratio will automatically turn out to be the same as the old profit sharing ratio. This is the most common scenario in textbook problems.

However, when partners agree to sacrifice unequally, or when a new profit sharing ratio is given directly (without stating how the new partner acquired the share), the sacrificing ratio must be worked out separately using the formula above.

Worked Example 1: Deriving Sacrificing Ratio From a Given New Ratio

Example: Rohit and Mohit share profits in the ratio 5:3. They admit Bijoy for a 1/7 share, and the new profit sharing ratio is agreed at 4:2:1. Find the sacrificing ratio of Rohit and Mohit.

Step 1: Rohit's old share = 5/8; Rohit's new share = 4/7
Rohit's sacrifice = 5/8 − 4/7 = 35/56 − 32/56 = 3/56

Step 2: Mohit's old share = 3/8; Mohit's new share = 2/7
Mohit's sacrifice = 3/8 − 2/7 = 21/56 − 16/56 = 5/56

Sacrificing ratio of Rohit and Mohit = 3 : 5

Notice how the sacrificing ratio (3:5) is completely different from the old profit sharing ratio (5:3) — this is exactly why you can't assume they're the same unless the question tells you the new partner acquired their share in the old ratio.

Worked Example 2: When the New Ratio Isn't a Simple Split of the Old Ratio

Example: Amar and Bahadur share profits 3:2. They admit Mary for a 1/4 share. The new ratio between Amar and Bahadur is agreed at 2:1.

Mary's share = 1/4; remaining 3/4 is split 2:1, giving Amar's new share = 1/2 and Bahadur's new share = 1/4. Amar's sacrifice = 3/5 − 1/2 = 1/10; Bahadur's sacrifice = 2/5 − 1/4 = 3/20. Converting to a common denominator of 20: Amar = 2/20, Bahadur = 3/20.

Sacrificing ratio of Amar and Bahadur = 2 : 3

What If a Partner's Share Increases Instead of Decreases?

This is an important twist examiners love to test. If, after admission, a partner's new share is actually greater than their old share, that partner hasn't sacrificed at all — they've gained. This can happen when the new profit sharing ratio is restructured in a way that benefits one of the old partners even as a new partner joins.

Example: Ramesh and Suresh share profits 4:3. They admit Mohan, and the new ratio is fixed at 2:3:1. Ramesh's sacrifice = 4/7 − 2/6 = 10/42. Suresh's new share (3/6 = 21/42) is actually greater than his old share (3/7 = 18/42), so Suresh has gained 3/42 instead of sacrificing. Here, the entire compensation for Mohan's share is effectively funded by Ramesh alone, and Suresh may even need to compensate Ramesh separately for his own gain.

Sacrificing Ratio vs Gaining Ratio: Don't Mix Them Up

Keeping this distinction clear prevents one of the most common mix-ups in board exam answer sheets.

Quick Recap

Sacrificing ratio (Old Share − New Share) determines how a new partner's goodwill premium is split among old partners. If the new partner acquires their share in the old ratio, the sacrificing ratio equals the old profit sharing ratio; if a partner's new share exceeds their old share, they've gained, not sacrificed.

Related Reading on ChampionsPrep

• Link "new profit sharing ratio" to New Profit Sharing Ratio on Admission of a Partner
• Link "premium for goodwill" to Accounting Treatment of Goodwill on Admission of a Partner
• Link "reconstitution" to Reconstitution of a Partnership Firm: Meaning and Modes
• Add a link to ChampionsPrep's sacrificing ratio practice worksheet

Sharpen This Concept With Guided Practice

Sacrificing ratio questions reward speed and accuracy, and both come from repetition. ChampionsPrep gives Class 12 Commerce students pay-per-use practice sets on sacrificing ratio, new profit sharing ratio, and goodwill — pay only for what you need before your board exam.

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