Q.X and Y are partners sharing profit and loss in the ratio of 3 : 2. They decided to admit Z for 1/5th share in profit. Calculate the new profit-sharing ratio of X, Y, and Z.
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🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Sacrificing Ratio Definition
Let’s start with something you already know from everyday life.
Suppose you and your friend share a pizza equally — half each. One day, your friend says, “I’m not that hungry, you can have a bigger slice today.” So you take 60% and your friend takes 40%. Your friend has sacrificed 10% of the pizza in your favour. That 10% is the sacrificing ratio — the share your friend gave up so you could have more.
Now bring this into a partnership firm. Partners share profits in a fixed ratio (say 3:2). When a new partner is admitted, the old partners have to give up a part of their share to make room for the newcomer. The proportion in which they give up their shares is called the sacrificing ratio.
Precise meaning
Sacrificing ratio = Old ratio – New ratio (for each old partner).
If the result is positive, that partner has sacrificed. If negative, that partner has gained (which is called the gaining ratio, used at retirement).
For example, if A and B share profits 3:2, and they admit C for a 1/5th share, the new ratio might become 2:2:1. Then:
- A’s sacrifice = 3/5 – 2/5 = 1/5
- B’s sacrifice = 2/5 – 2/5 = 0
So A alone sacrifices 1/5th of the total profit. That 1/5th is the sacrificing ratio between A and B — here it’s simply 1:0.
Why does it matter?
Because the new partner brings in goodwill (a premium) to compensate the old partners for the share they gave up. That goodwill is distributed among the sacrificing partners in their sacrificing ratio. If you don’t calculate the sacrificing ratio correctly, you’ll distribute the goodwill unfairly — and that’s a serious accounting error.
Accounting treatment
When the new partner brings in his share of goodwill in cash:
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Journal entry:
- Debit: Cash/Bank A/c (with the amount brought in)
- Credit: Premium for Goodwill A/c (with the same amount)
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Then the premium is distributed to the sacrificing partners:
- Debit: Premium for Goodwill A/c
- Credit: Old Partners’ Capital A/cs (individually, in sacrificing ratio)
If the new partner does not bring in cash, the adjustment is done through the capital accounts directly (the new partner’s capital is debited, and the old partners’ capitals are credited).
Format: Capital Accounts (showing goodwill adjustment) …
Z gets 1/5th share, so X and Y keep the remaining 4/5th in their old ratio 3:2. X's new share = 4/5 × 3/5 = 12/25, Y's = 4/5 × 2/5 = 8/25, and Z's = 1/5 = 5/25. The new profit-sharing ratio of X : Y : Z = 12 : 8 : 5. This is a TS Inter 2nd-year (Telangana Intermediate) Accountancy admission-of-a-partner sum; the TS treatment aligns with the NCERT/CBSE commerce curriculum. ## Working - Z's share = 1/5 - Remaining share for X and Y = 1 − 1/5 = 4/5 - X and Y share this 4/5 in their old ratio 3 : 2 - X's new share = 4/5 × 3/5 = 12/25 - Y's new share = 4/5 × 2/5 = 8/25 - Z's share = 1/5 = 5/25 - Expressing all over 25: X = 12/25, Y = 8/25, Z = 5/25 …
Z gets 1/5th share, so X and Y keep the remaining 4/5th in their old ratio 3:2. X's new share = 4/5 × 3/5 = 12/25, Y's = 4/5 × 2/5 = 8/25, and Z's = 1/5 = 5/25. The new profit-sharing ratio of X : Y : Z = 12 : 8 : 5.
This is a TS Inter 2nd-year (Telangana Intermediate) Accountancy admission-of-a-partner sum; the TS treatment aligns with the NCERT/CBSE commerce curriculum.
Working
- Z's share = 1/5
- Remaining share for X and Y = 1 − 1/5 = 4/5
- X and Y share this 4/5 in their old ratio 3 : 2
- X's new share = 4/5 × 3/5 = 12/25
- Y's new share = 4/5 × 2/5 = 8/25
- Z's share = 1/5 = 5/25 …
Showing the 12 most recent of 78 on this concept.
- CBSE 2026Set MARCH1 markQ.Old Ratio – New Ratio = __________ Ratio.
›Reveal solutionSolution
Old Ratio - New Ratio = Sacrificing Ratio.
On admission of a partner, the existing partners surrender a portion of their profit share in favour of the incoming partner. The proportion in which they surrender is the sacrificing ratio, calculated as the difference between each old partner's old share and new shar …
- CBSE 2026Set ANNUAL1 markMCQQ.Consider the following statements: Statement (I): Sacrificing Ratio = Old Profit and Loss sharing ratio – New Profit and Loss sharing ratio. Statement (II): Super profit = Average profits – Normal profits. Choose the correct answer from the following options: A) Only statement (I) is wrong B) Only statement (II) is correct C) Statement (I) is wrong and statement (II) is correct D) Both statements (I) and (II) are correct
›Reveal solutionSolution
Both definitions are standard and correct, so option (D) applies.
Statement (I): Sacrificing Ratio = Old profit-sharing ratio - New profit-sharing ratio. This is the correct formula; it measures the share old partners give up to the incoming/gaining partner.
…
- CBSE 2026Set ANNUAL1 markMCQQ.If Nisha and Komal are sharing profits in the ratio of 4 : 3. They decided to distribute profits equally in future. The sacrifice of Nisha will be A) 1/14 B) 4/14 C) 4/7 D) 3/7
›Reveal solutionSolution
Nisha's sacrifice on moving from a 4:3 ratio to an equal ratio is 1/14 — option (A).
Old ratio of Nisha and Komal = 4 : 3, so Nisha's old share = 4/7.
New ratio = equal = 1 : 1, so Nisha's new share = 1/2.
Sacrifice = Old share - New share
= 4/7 - 1/2
= 8/14 - 7/14
= 1/14
…
- CBSE 2026Set ANNUAL1 markQ.Mahaveer and Jitendra are partners in a firm sharing profits in the ratio of 4 : 3. They admitted Vaibhav for 1/5th share in profit, which he received from Jitendra. Calculate the sacrificing ratio.
›Reveal solutionSolution
Only Jitendra sacrifices his 1/5th share, so the sacrificing ratio is entirely Jitendra's (Mahaveer nil).
Mahaveer and Jitendra share profits 4 : 3. Vaibhav is admitted for a 1/5th share, which he takes wholly from Jitendra.
- Mahaveer's sacrifice = 0 (his share is unchanged).
- Jitendra's sacrifice = 1/5 (he alone gives up the share). …
- CBSE 2026Set ANNUAL1 markQ.Fill in the blank: Sacrificing ratio is always ________ to gaining ratio.
›Reveal solutionSolution
Answer: Opposite / reverse.
Sacrificing ratio = Old ratio - New ratio (share given up), while gaining ratio = New ratio - Old ratio (share acquired). They are computed in opposite directions, so a sacrificing ratio is always the opposite (reverse) of a gaining r …
- CBSE 2026Set ANNUAL1 markQ.Answer in one word/sentence: The amount of goodwill brought by new partner is distributed to old partners in which ratio?
›Reveal solutionSolution
Answer: Sacrificing ratio.
The premium (goodwill) brought in by a new partner compensates the old partners for the share of profit they give up, so it is distributed among the …
- CBSE 2026Set ANNUAL1 markMCQQ.Case study: Pawan and Ritesh are partners in Vision Tech Solutions, a partnership business sharing profit-loss in the ratio of 3:2. Capital invested by Pawan was ₹1,00,000 and by Ritesh ₹1,20,000 in the business. Their business involves developing software and providing related services according to market demand. Considering the potential for increased demand in the future, they plan to expand their business. To expand their business, they decide to bring in Sundar, a software investor, as a new partner to provide the necessary additional capital. Sundar contributed ₹80,000 as his capital. Pawan and Ritesh surrender 1/2 of their respective profit shares in favor of Sundar. Upon Sundar's admission, the firm's goodwill is to be valued at 2 years' purchase of the average profits of the last three years. The profits for the last three years were: I year ₹10,000 (loss); II year ₹40,000; III year ₹60,000. Sundar did not bring his share of goodwill in cash, and goodwill of ₹30,000 already existed in the firm's books. Based on the above information, answer the following question: What will be the sacrificing ratio of Pawan and Ritesh?(a) 1:1(b) 3:2(c) 2:1(d) 2:3(a) 1:1(b) 3:2(c) 2:1(d) 2:3
›Reveal solutionSolution
Sacrificing ratio of Pawan and Ritesh = 3:2.
Pawan and Ritesh share profit-loss in the ratio 3:2, so Pawan's share = 3/5 and Ritesh's share = 2/5. Each of them surrenders exactly 1/2 of their OWN respective share in favour of Sundar:
Pawan's sacrifice = 1/2 × 3/5 = 3/10
Ritesh's sacrifice = 1/2 × 2/5 = 2/10 (= 1/5)
Sacrificing Ratio = Pawan's sacrifice : Ritesh's sacrifice
= 3/10 : 2/10
= 3 : 2
…
- CBSE 2026Set ANNUAL1 markMCQQ.Case study (same as above — Pawan and Ritesh are partners in Vision Tech Solutions sharing profit-loss 3:2; capitals ₹1,00,000 and ₹1,20,000; they admit Sundar as a new partner who contributes ₹80,000 capital, with Pawan and Ritesh each surrendering 1/2 of their respective profit shares in favor of Sundar). Based on the above information, answer the following question: What will be the new profit sharing ratio of Pawan, Ritesh and Sundar?(a) 3:2:5(b) 3:2:1(c) 1:1:1(d) 5:2:3(a) 3:2:5(b) 3:2:1(c) 1:1:1(d) 5:2:3
›Reveal solutionSolution
New profit-sharing ratio of Pawan, Ritesh and Sundar = 3:2:5.
Step 1 — Old shares
Pawan = 3/5, Ritesh = 2/5
Step 2 — Sacrifice by each (from Q29)
Pawan sacrifices 3/10, Ritesh sacrifices 2/10
Step 3 — New shares of Pawan and Ritesh
Pawan's new share = 3/5 − 3/10 = 6/10 − 3/10 = 3/10
Ritesh's new share = 2/5 − 2/10 = 4/10 − 2/10 = 2/10
Step 4 — Sundar's share
Sundar receives exactly what both partners sacrificed:
Sundar's share = 3/10 + 2/10 = 5/10
Step 5 — New Ratio
…
- CBSE 2026Set ANNUAL1 markQ.How can the gaining partner compensate the sacrificing partner in case of change in profit sharing ratio?
›Reveal solutionSolution
The gaining partner compensates the sacrificing partner by paying him the value of goodwill corresponding to the share he has gained, usually through an adjustment in the partners' capital accounts.
When partners decide to change their profit-sharing ratio, some partners' shares increase (gaining partners) while others' shares decrease (sacrificing partners). Since goodwill represents the value of the firm's reputation and future profit-earning capacity built up by all partners together, it is only fair that a partner whose share of future profits increases (the gaining partner) compensates the partner whose share decreases (the sacrificing partner).
The compensation is calculated as:
Compensation = Gaining Partner's Gain in Share × Firm's Goodwill
This amount is adjusted by passing a journal entry:
Gaining Partner's Capital A/c Dr.To Sacrificing Partner's Capital A/c…
- CBSE 2026Set ANNUAL1 markMCQQ.P and Q are partners in a firm sharing profits and losses in the ratio of 3 : 2. They admit R, a new partner for 1/5th share in profit. What is the sacrificing ratio of P and Q?(a) 3 : 1(b) 2 : 1(c) 3 : 2(d) 1 : 1
›Reveal solutionSolution
With no new ratio specified, P and Q are assumed to sacrifice in their existing old ratio of 3:2 to make room for R's 1/5th share.
Sacrificing Ratio = Old Share − New Share, for each existing partner. It tells us in what proportion the old partners give up their share of profit to accommodate the incoming partner.
Here, P and Q share profits in the ratio 3:2, and they admit R for a 1/5th share. The question does not state that P and Q will share the remaining profit in any ratio different from their old one. Whenever the new partner's share is simply carved out and the old partners' mutual ratio is left unchanged, the sacrificing ratio equals the old profit-sharing ratio itself — because both partners give up a share of their own profit proportionate to what they used to hold.
…
- CBSE 2026Set ANNUAL1 markQ.State one point of difference between Sacrificing Ratio and Gaining Ratio.
›Reveal solutionSolution
Sacrificing Ratio belongs to admission (old partners give up share); Gaining Ratio belongs to retirement/death (continuing partners gain share) — the two ratios serve opposite purposes at opposite events.
Both ratios compare a partner's old share of profit with their new share after reconstitution, but they are used in entirely different situations and for opposite reasons:
Basis Sacrificing Ratio Gaining Ratio When computed At the time of admission of a new partner At the time of retirement or death of a partner Formula Old Share − New Share New Share − Old Share Purpose To find how much of their share the existing partners give up to accommodate the new partner, so that the new partner's goodwill premium can be fairly distributed among them To find how much of the retiring/deceased partner's share is picked up by each continuing partner, so that the continuing partners can compensate for the retiring/deceased partner's share of goodwill - CBSE 2025Set MARCH1 markMCQQ.When only old profit-loss sharing ratio is given; sacrificing ratio of old partners = ______.(a) equal(b) old ratio(c) old share - new share(d) cannot be calculated
›Reveal solutionSolution
If only the old profit-sharing ratio is given (new ratio not specified), the sacrificing ratio equals the old ratio. Correct option: (b).
In GSEB Class-12 Commerce Accountancy (admission of a partner):
- Sacrificing ratio = Old share − New share, when the new ratio is given. …
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