Q.A, B and C were partners in a firm sharing profits and losses in the ratio of 4 : 3 : 2. B retired and his share was taken over by A and C equally. Calculate the gaining ratio.
Concept understanding — Admission Partner Adjustments
Let’s start with something you already know from daily life. Suppose you and a friend run a small tiffin service together. After a year, a third friend wants to join. You both agree to let her in. But the business has grown — you have a reputation, some regular customers, and maybe a little cash saved. She can’t just walk in and claim equal share of everything you built before she arrived. That wouldn’t be fair to you and your original partner.
So you sit down and decide: what is the business worth today? How much should the new partner bring in as her share of that past effort? And once she comes in, how do we rewrite the partnership deed so everyone’s rights are clear from Day 1?
That’s the heart of Admission of a Partner — and the adjustments that follow.
What does “Admission Partner Adjustments” mean?
When a new partner is admitted into an existing partnership, the old partnership is dissolved in the eyes of accounting, and a new one begins. The new partner brings in capital (cash or assets) and also buys a share of the goodwill — the value of the business’s reputation and past efforts. But that’s not all. Several things need to be revalued or adjusted so that the new partner doesn’t unfairly gain or lose from past decisions.
These adjustments are:
- Revaluation of Assets and Liabilities – because the balance sheet values may be outdated.
- Treatment of Goodwill – the new partner compensates old partners for their past efforts.
- Adjustment of Reserves and Accumulated Profits/Losses – these belong to old partners only.
- Adjustment of Capital Accounts – to bring all partners’ capitals in proportion to the new profit-sharing ratio.
Each of these has a clear accounting treatment. Let’s go through them one by one.
1. Revaluation of Assets and Liabilities
Why? The balance sheet shows assets at book value (historical cost minus depreciation). But the new partner should not benefit from an undervalued asset (like land that has appreciated) nor suffer from an overvalued one. Similarly, liabilities may be understated or overstated.
Accounting treatment:
We open a Revaluation Account (also called Profit & Loss Adjustment Account).
- Increase in asset value → debit Asset, credit Revaluation A/c
- Decrease in asset value → credit Asset, debit Revaluation A/c
- Increase in liability → credit Liability, debit Revaluation A/c
- Decrease in liability → debit Liability, credit Revaluation A/c
The net profit or loss on revaluation is transferred to the old partners’ capital accounts in their old profit-sharing ratio.
The new partner does not share in revaluation profit/loss — it belongs entirely to the old partners.
Example format (Revaluation Account):
| Particulars | ₹ | Particulars | ₹ |
|---|---|---|---|
| To Building (decrease) | 10,000 | By Land (increase) | 20,000 |
| To Provision for Doubtful Debts (increase) | 5,000 | By Creditors (decrease) | 8,000 |
| To Profit transferred to: | |||
| A’s Capital A/c (3/5) | 7,800 | ||
| B’s Capital A/c (2/5) | 5,200 | ||
| Total | 28,000 | Total | 28,000 |
2. Treatment of Goodwill
Why? The new partner is buying a share of the business’s earning power built by old partners. She must compensate them for this.
Accounting treatment (as per NCERT):
The new partner brings her share of goodwill in cash. That cash is then withdrawn by the old partners (or left in the business). The journal entry:
-
When new partner brings goodwill in cash:
Cash/Bank A/c Dr.
To Goodwill A/c (or Premium for Goodwill A/c)
-
Then, distribute that amount to old partners in their sacrificing ratio:
Goodwill A/c Dr.
To Old Partners’ Capital A/cs (individually)
The sacrificing ratio is the ratio in which old partners give up their share in favour of the new partner. It is not the same as the old ratio unless the new partner’s share is taken equally from all.
Sacrificing Ratio = Old Ratio – New Ratio
If the new partner does not bring cash for goodwill, we adjust through capital accounts (debit the new partner, credit the old partners).
3. Adjustment of Reserves and Accumulated Profits/Losses
Why? Any accumulated profits (like General Reserve, Profit & Loss A/c credit balance) belong to the old partners. The new partner should not get a share of past profits.
Accounting treatment:
Transfer the entire reserve/accumulated profit to old partners’ capital accounts in their old profit-sharing ratio.
Journal entry:
General Reserve A/c Dr.
To Old Partners’ Capital A/cs
Similarly, accumulated losses (debit balance of P&L A/c) are debited to old partners’ capital accounts.
4. Adjustment of Capital Accounts
Why? After all adjustments, the partners’ capitals may not be in the new profit-sharing ratio. The partnership deed may require capitals to be proportionate to profit shares.
Accounting treatment:
Calculate the total capital of the new firm based on the new partner’s capital contribution. Then determine each partner’s required capital. The difference is adjusted by bringing in or withdrawing cash.
Journal entry for excess capital withdrawn:
Partner’s Capital A/c Dr.
To Cash/Bank A/c
For deficiency (partner brings in more):
Cash/Bank A/c Dr.
To Partner’s Capital A/c
Putting it all together: A proforma Capital Account
Here’s how a Partner’s Capital Account looks after admission adjustments (NCERT format):
| Particulars | A (₹) | B (₹) | C (₹) | Particulars | A (₹) | B (₹) | C (₹) |
|---|---|---|---|---|---|---|---|
| To Revaluation Loss (if any) | By Balance b/d | 50,000 | 40,000 | — | |||
| To Goodwill (if written off) | By Cash (capital brought) | — | — | 30,000 | |||
| To Drawings | By Revaluation Profit | 7,800 | 5,200 | — | |||
| To Balance c/d | 65,800 | 49,200 | 30,000 | By Goodwill (premium) | 8,000 | 4,000 | — |
| By General Reserve | 10,000 | 6,000 | — | ||||
| Total | 65,800 | 49,200 | 30,000 | Total | 65,800 | 49,200 | 30,000 |
The final balances in capital accounts (Balance c/d) should be in the new profit-sharing ratio after all adjustments. If not, partners bring in or withdraw cash.
Why does this matter for your exam?
NCERT Class 12 Accountancy (Part II, Chapter 3 – Admission of a Partner) treats this as a step-by-step process. You will be asked to:
- Prepare Revaluation Account
- Prepare Partners’ Capital Accounts
- Calculate sacrificing ratio
- Pass journal entries for goodwill
The key is to never skip a step. Always start with revaluation, then goodwill, then reserves, then capital adjustment. Each step feeds into the next.
In numerical problems, first write down the old ratio, new ratio, and sacrificing ratio. Then proceed stepwise. Most mistakes happen when students jump to capital accounts without revaluing assets first.
Final takeaway: Admission of a partner is not just about bringing in cash. It’s about fairly resetting the score so that the new partner starts on equal footing with the old ones, without taking away what the old partners earned before she arrived. Every adjustment — revaluation, goodwill, reserves, capital — serves that single idea.
When a partner retires, the continuing partners acquire the retiring partner's share of profits. The ratio in which the continuing partners acquire this share is known as the gaining ratio.
In this case, B retires, and his share is taken over by A and C equally.
-
Calculate B's share:
The old profit-sharing ratio of A, B, and C is 4:3:2.
Total shares = 4+3+2=9.
B's share = 3/9.
-
Calculate the share gained by A:
A takes 1/2 of B's share.
Share gained by A = (1/2)×(3/9)=3/18.
-
Calculate the share gained by C:
C takes 1/2 of B's share.
Share gained by C = (1/2)×(3/9)=3/18.
-
Determine the Gaining Ratio:
The gaining ratio is the ratio of the shares gained by A and C.
Gaining Ratio (A : C) = 3/18:3/18=1:1.
The gaining ratio of A and C is 1 : 1.
The gaining ratio of A and C upon B's retirement is 1 : 1.
When a partner retires from a firm, their share of profits is typically acquired by the remaining partners. This acquisition leads to an increase in the profit share of the continuing partners. The ratio in which the continuing partners acquire the retiring partner's share is known as the Gaining Ratio. It represents the proportion in which the remaining partners gain a share of profits from the outgoing partner.
The Gaining Ratio is crucial for several adjustments in partnership accounts, such as distributing goodwill among the remaining partners, as goodwill is often compensated to the retiring partner by the gaining partners in their gaining ratio.
To calculate the gaining ratio, we need to determine how much share each continuing partner acquires from the retiring partner.
Here's the treatment:
- Identify the old profit-sharing ratio of all partners.
- Identify the share of the retiring partner.
- Determine how the retiring partner's share is taken over by the continuing partners. This information is usually explicitly stated in the question.
- Calculate the gain for each continuing partner by applying the agreed-upon proportion to the retiring partner's share.
- Express these individual gains as a ratio to find the Gaining Ratio.
Let's apply this to the given problem.
Solution
Working Notes:
-
Old Profit Sharing Ratio:
A : B : C = 4 : 3 : 2
Total shares = 4+3+2=9
Individual shares:
A's share = 4/9
B's share = 3/9
C's share = 2/9
-
Retiring Partner's Share:
B retires, so B's share = 3/9
-
Acquisition of B's Share:
B's share is taken over by A and C equally.
"Equally" means in the ratio of 1 : 1.
-
Calculation of Gain for A:
A's gain = (1/2) of B's share
A's gain = (1/2) × (3/9)
A's gain = 3/18
-
Calculation of Gain for C:
C's gain = (1/2) of B's share
C's gain = (1/2) × (3/9)
C's gain = 3/18
-
Gaining Ratio:
Gaining Ratio = A's gain : C's gain
Gaining Ratio = 3/18 : 3/18
To simplify the ratio, we can multiply both sides by 18:
Gaining Ratio = 3 : 3
Further simplifying by dividing by 3:
Gaining Ratio = 1 : 1
The gaining ratio of A and C upon B's retirement is 1 : 1.
Showing the 12 most recent of 122 on this concept.
- CBSE 2026Set 67/3/11 markMCQQ.Dharam and Karan were partners in a firm sharing profits and losses in the ratio of 7 : 3. On 1st April, 2025, they admitted Vinod as a new partner in the firm. Dharam surrendered 1/3rd of his share in favour of Vinod and Karan surrendered 1/4th of his share in favour of Vinod. The new profit sharing ratio will be : (A) 7 : 3 : 1 (B) 56 : 27 : 10 (C) 27 : 56 : 10 (D) 56 : 27 : 37
›Reveal solutionSolution
The new profit-sharing ratio after Vinod's admission is 56 : 27 : 37 (Option D). Dharam and Karan each sacrifice a portion of their original 7:3 ratio to give Vinod his share.
Concept First: Why We Calculate Sacrifice and New Ratio
When a new partner is admitted, the old partners surrender (sacrifice) a part of their own profit share to the newcomer. The new ratio is simply the old partners' remaining shares plus the new partner's acquired share. The key rule: the sacrificing ratio is the proportion in which the old partners give up their share; the new ratio is what remains after the sacrifice.
Here, Dharam and Karan do not sacrifice equally — Dharam gives up 1/3rd of his share, and Karan gives up 1/4th of his share. So we must first find each old partner's original share, then deduct the surrendered portion, and finally add Vinod's share.
Watch outA common mistake is to treat the surrendered fractions (1/3 and 1/4) as fractions of the total profit. They are fractions of each partner's own share, not of the whole. Always read "surrendered 1/3rd of his share" as 1/3 × (that partner's old ratio).
Step-by-Step Solution
Step 1: Write the old ratio.
Dharam : Karan = 7 : 3.
Total parts = 7 + 3 = 10.
So Dharam's old share = 7/10, Karan's old share = 3/10.
Step 2: Calculate the surrendered shares.
- Dharam surrenders 1/3 of his share = 1/3 × 7/10 = 7/30.
- Karan surrenders 1/4 of his share = 1/4 × 3/10 = 3/40.
Step 3: Calculate the new shares of old partners.
- Dharam's new share = Old share – Surrendered = 7/10 – 7/30. Convert to common denominator 30: 21/30 – 7/30 = 14/30 = 7/15.
- Karan's new share = 3/10 – 3/40. Convert to common denominator 40: 12/40 – 3/40 = 9/40.
Step 4: Calculate Vinod's share.
Vinod gets the total surrendered amount:
= Dharam's surrender + Karan's surrender = 7/30 + 3/40.
LCM of 30 and 40 is 120: 28/120 + 9/120 = 37/120.
Step 5: Express all shares with a common denominator to find the ratio.
- Dharam: 7/15 = 56/120 (multiply numerator and denominator by 8).
- Karan: 9/40 = 27/120 (multiply by 3).
- Vinod: 37/120.
So the new ratio = 56 : 27 : 37 (check: 56+27+37=120, matching the common denominator). Comparing with the given options — (A) 7:3:1, (B) 56:27:10, (C) 27:56:10, (D) 56:27:37 — this matches option (D).
Therefore, the correct answer is (D) 56 : 27 : 37.
TipA quick check: the actual fractions 56/120, 27/120, and 37/120 sum to 120/120 = 1, confirming the whole profit is accounted for. The ratio parts (56, 27, 37) are simply these fractions scaled up by the common denominator 120 — they don't need to sum to the old ratio's total (10), since ratios are relative, not absolute.
Working Notes (for verification)
Partner Old Share Surrendered Fraction Surrendered Amount New Share (fraction) New Ratio Part Dharam 7/10 1/3 of his share 7/30 7/10 – 7/30 = 14/30 = 7/15 = 56/120 56 Karan 3/10 1/4 of his share 3/40 3/10 – 3/40 = 9/40 = 27/120 27 Vinod — — 7/30 + 3/40 = 37/120 37/120 37 Total 1 56/120 + 27/120 + 37/120 = 120/120 = 1 120 ✓Final answerThe new profit-sharing ratio is 56 : 27 : 37, which corresponds to option (D).
- CBSE 2026Set 67/3/11 markMCQQ.Assertion (A) : In case of admission of a new partner in the partnership firm, there is a need to ascertain the new profit sharing ratio among all the partners. Reason (R) : On admission of a new partner, the profit sharing ratio among the old partners will change, keeping in view their respective contribution to the profit sharing ratio of the incoming partner. Choose the correct option from the following : (A) Both Assertion (A) and Reason (R) are correct and Reason (R) is the correct explanation of Assertion (A). (B) Both Assertion (A) and Reason (R) are correct, but Reason (R) is not the correct explanation of Assertion (A). (C) Assertion (A) is correct, but Reason (R) is incorrect. (D) Assertion (A) is incorrect, but Reason (R) is correct.
›Reveal solutionSolution
Both the assertion and the reason are correct, and the reason correctly explains why a new profit-sharing ratio is necessary upon the admission of a new partner.
When a new partner is admitted into a partnership firm, it signifies a fundamental change in the existing partnership agreement. A partnership is defined by the agreement among its partners, particularly concerning how profits and losses are shared.
Let's break down the assertion and the reason:
Assertion (A): In case of admission of a new partner in the partnership firm, there is a need to ascertain the new profit sharing ratio among all the partners.
This assertion is correct.
The moment a new partner joins, they become entitled to a share of the firm's future profits. Since the total profit pie remains 100%, and this pie must now be shared among more individuals (the old partners plus the new partner), the existing profit-sharing arrangement becomes obsolete. A new agreement, and consequently a new profit-sharing ratio, must be established to define how profits will be distributed among all partners, including the newly admitted one. Without a new ratio, there would be no clear basis for distributing profits.
Reason (R): On admission of a new partner, the profit sharing ratio among the old partners will change, keeping in view their respective contribution to the profit sharing ratio of the incoming partner.
This reason is also correct.
When a new partner is admitted, they acquire their share of profits from the existing partners. The old partners must sacrifice a portion of their individual shares to accommodate the new partner. This act of sacrifice directly alters their individual profit shares and, consequently, their profit-sharing ratio among themselves and in relation to the new partner. The phrase "keeping in view their respective contribution to the profit sharing ratio of the incoming partner" refers to the sacrificing ratio, which dictates how the old partners give up their share to the new partner. This change in the old partners' individual shares is a direct consequence of the new partner's admission.
Connecting Assertion (A) and Reason (R):
The reason (R) provides the underlying explanation for the assertion (A). The need to ascertain a new profit-sharing ratio (A) arises precisely because the admission of a new partner necessitates a change in the profit-sharing arrangement among the old partners (R) to accommodate the incoming partner's share. If the old partners' shares didn't change, or if a new partner didn't take a share, there would be no need for a new ratio. Therefore, the change in the old partners' ratio to accommodate the new partner is the direct cause for the requirement of a new overall profit-sharing ratio for the entire firm.
✓Final answerBoth Assertion (A) and Reason (R) are correct, and Reason (R) is the correct explanation of Assertion (A). Therefore, option (A) is the correct choice.
- CBSE 2026Set 67/3/11 markMCQQ.Chaman, Raman and Suman were partners in a firm sharing profits and losses in the ratio of 5 : 3 : 2. With effect from 1st April, 2025, they decided to share the future profits in the ratio of 2 : 3 : 5. For this purpose, it was agreed that the goodwill of the firm be valued at ₹ 1,00,000. The treatment of goodwill without opening goodwill account will be : (A) Debit Chaman's Capital A/c by ₹ 30,000 and Credit Suman's Capital A/c by ₹ 30,000 (B) Debit Suman's Capital A/c by ₹ 30,000 and Credit Chaman's Capital A/c by ₹ 30,000 (C) Debit Chaman's Capital A/c and Suman's Capital A/c by ₹ 15,000 each and credit Raman's Capital A/c by ₹ 30,000 (D) Debit Raman's Capital A/c by ₹ 30,000 and Credit Chaman's Capital A/c and Suman's Capital A/c by ₹ 15,000 each
›Reveal solutionSolution
Suman, the gaining partner, will compensate Chaman, the sacrificing partner, by debiting Suman's Capital Account and crediting Chaman's Capital Account with ₹ 30,000 for their respective shares of goodwill.
When partners decide to change their profit-sharing ratio, it means some partners will gain a larger share of future profits, while others will sacrifice a portion of their existing share. This change has an implication for the firm's goodwill. Goodwill represents the firm's reputation and its ability to earn super profits. If a partner gains a share in future profits, they are effectively gaining a share in these future super profits, which are attributable to the firm's existing goodwill, without having contributed to earning that goodwill in the past.
To ensure fairness, the gaining partner(s) must compensate the sacrificing partner(s) for their respective shares of the firm's goodwill. This compensation is typically done by adjusting the partners' capital accounts directly, without opening a separate Goodwill Account in the books. The capital account of the gaining partner is debited (as they are effectively paying for the share of goodwill they are acquiring), and the capital account of the sacrificing partner is credited (as they are receiving compensation for the share of goodwill they are giving up). This treatment ensures that the financial impact of the change in profit-sharing ratio, particularly concerning goodwill, is reflected in the partners' capital balances.
Working Notes
WN 1: Calculation of Sacrificing and Gaining Ratios
The sacrificing or gaining ratio for each partner is calculated by subtracting their new profit share from their old profit share.
- A positive result indicates a sacrifice.
- A negative result indicates a gain.
Old Ratio (Chaman : Raman : Suman) = 5:3:2 (Total 10 parts)
New Ratio (Chaman : Raman : Suman) = 2:3:5 (Total 10 parts)
-
Chaman's Share:
Old Share = 5/10
New Share = 2/10
Change = 5/10−2/10=3/10 (Sacrifice)
-
Raman's Share:
Old Share = 3/10
New Share = 3/10
Change = 3/10−3/10=0 (Neither sacrifice nor gain)
-
Suman's Share:
Old Share = 2/10
New Share = 5/10
Change = 2/10−5/10=−3/10 (Gain)
WN 2: Calculation of Goodwill Adjustment
The firm's goodwill is valued at ₹ 1,00,000. The adjustment for goodwill is made based on the sacrificing or gaining share of each partner.
-
Chaman's Share of Goodwill (Sacrifice):
₹ 1,00,000×3/10=₹30,000
-
Suman's Share of Goodwill (Gain):
₹ 1,00,000×3/10=₹30,000
Watch outAlways remember that the gaining partner's capital account is debited, and the sacrificing partner's capital account is credited. A common mistake is to reverse this entry, which would incorrectly increase the gaining partner's capital and decrease the sacrificing partner's capital.
Journal Entry
Date Particulars L.F. Debit (₹) Credit (₹) April 1, 2025 Suman's Capital A/c 30,000 To Chaman's Capital A/c 30,000 (Being adjustment for goodwill on change in profit-sharing ratio) ✓Final answerThe correct treatment of goodwill without opening a goodwill account is to Debit Suman's Capital A/c by ₹ 30,000 and Credit Chaman's Capital A/c by ₹ 30,000. This corresponds to option (B).
- CBSE 2026Set 67/3/11 markMCQQ.(a) Anup, Bharti and Manoj were partners in a firm sharing profits and losses in the ratio of 11 : 8 : 1. From 1st April, 2025, they decided to share the future profits in the ratio of 2 : 2 : 1. The gain or sacrifice of each partner due to change in profit sharing ratio will be : (A) Anup's gain 3/20, Manoj's sacrifice 3/20 (B) Anup's sacrifice 3/20, Manoj's gain 3/20 (C) Anup's gain 3/20, Manoj's gain 3/20 (D) Anup's sacrifice 3/20, Manoj's sacrifice 3/20(OR)(b) Arun, Varun and Tarun were partners in a firm sharing profits and losses in the ratio of 5 : 3 : 2. On 31st March, 2025, Arun died. Varun and Tarun decided to share future profits equally. The gaining ratio of Varun and Tarun will be : (A) 1 : 1 (B) 3 : 2 (C) 2 : 3 (D) 5 : 2
›Reveal solutionSolution
Part (a): Anup sacrifices 3/20, Manoj gains 3/20 — option (B).
Part (b): Gaining ratio of Varun and Tarun = 2:3 — option (C).
Part (a)
Sacrifice/gain = Old share − New share (positive = sacrifice, negative = gain). Using denominator 20:
- Old: Anup 11/20, Bharti 8/20, Manoj 1/20
- New (2:2:1): Anup 8/20, Bharti 8/20, Manoj 4/20
- Anup: 11/20 − 8/20 = +3/20 → sacrifice 3/20
- Bharti: 0 → no change
- Manoj: 1/20 − 4/20 = −3/20 → gain 3/20
✓Final answerAnup's sacrifice 3/20 and Manoj's gain 3/20 — option (B).
Part (b)
On a partner's death the continuing partners' gaining ratio = New share − Old share.
- Old: Varun 3/10, Tarun 2/10
- New (equal): each 1/2 = 5/10
- Varun's gain = 5/10 − 3/10 = 2/10; Tarun's gain = 5/10 − 2/10 = 3/10
- Gaining ratio = 2 : 3
Watch outTarun gains more because his old share was smaller — the gaining ratio (2:3) is not the equal new ratio.
✓Final answerThe gaining ratio of Varun and Tarun is 2 : 3 — option (C).
- CBSE 2026Set 67/3/11 markMCQQ.Atul and Nisha were partners in a firm sharing profits and losses in the ratio of 4 : 1. Their capitals were ₹ 1,20,000 and ₹ 90,000 respectively. On 1st April, 2025, they admitted Mona as a new partner in the firm for 1/4th share in the future profits. Mona brought ₹ 1,00,000 as her capital. The value of goodwill of the firm was : (A) ₹ 22,500 (B) ₹ 4,00,000 (C) ₹ 90,000 (D) ₹ 1,00,000
›Reveal solutionSolution
Solution: Valuation of Goodwill on Admission of a Partner
The value of goodwill of the firm is ₹90,000 (Option C), calculated by comparing Mona's capital contribution with her share in the reconstituted firm.
Concept: Goodwill Valuation through Capitalisation Method
When a new partner is admitted and brings capital for a specified share, we can infer the firm's total value (including goodwill) by treating her capital as proportionate to her share. The logic is straightforward: if Mona brings ₹1,00,000 for a 1/4th share, then the total capital of the firm should be ₹4,00,000 (since ₹1,00,000 ÷ 1/4 = ₹4,00,000).
The goodwill is the difference between this total capitalised value and the actual tangible capital contributed by all partners.
Treatment
- Calculate Total Capitalised Value of the firm based on the new partner's capital and share.
- Sum the Actual Capital brought in or standing (old partners' capital + new partner's capital).
- Goodwill = Total Capitalised Value − Total Actual Capital.
This method assumes that the new partner's capital contribution correctly values her fractional ownership in the entire firm, tangible assets plus intangible goodwill.
Solution
Working Note 1: Total Capitalised Value of the Firm
Mona is admitted for 1/4th share and brings ₹1,00,000 as capital.
If ₹1,00,000 represents 1/4th of the total firm value, then:
Total Capitalised Value=Mona’s ShareMona’s Capital=1/4₹1,00,000=₹1,00,000×4=₹4,00,000
Working Note 2: Total Actual Capital in the Firm
The actual capital standing in the firm after Mona's admission comprises:
Partner Capital (₹) Atul 1,20,000 Nisha 90,000 Mona 1,00,000 Total Actual Capital 3,10,000 Working Note 3: Value of Goodwill
Goodwill=Total Capitalised Value−Total Actual Capital
Goodwill=₹4,00,000−₹3,10,000=₹90,000
Watch outA common mistake is to assume that the new partner's capital equals goodwill or to add goodwill separately without capitalising the firm first. Goodwill is an implied value derived from the difference between what the firm is worth (capitalised value) and what has been physically contributed (actual capital).
TipWhenever a new partner brings capital for a fractional share, use the formula:
Total Value = New Partner's Capital ÷ New Partner's Share.
Then subtract all partners' actual capital to isolate goodwill.
✓Final answerThe value of goodwill of the firm is ₹90,000. The correct answer is (C) ₹90,000.
- CBSE 2026Set 67/3/11 markMCQQ.Yashoda and Devi were partners in a firm sharing profits and losses in the ratio of 3 : 2. On 31st March, 2025, their balance sheet showed land and building at ₹ 20,00,000 and furniture at ₹ 6,00,000. On that date they admitted Poonam as a new partner for 1/4th share in the future profits of the firm. On Poonam's admission, it was found that land and building is undervalued by 20%. On Poonam's admission, Revaluation Account will be : (A) debited by ₹ 5,00,000 (B) debited by ₹ 25,00,000 (C) credited by ₹ 25,00,000 (D) credited by ₹ 5,00,000
›Reveal solutionSolution
Land and building is undervalued by 20%, so its book value of ₹20,00,000 must be increased by ₹5,00,000. This gain is credited to the Revaluation Account. The correct answer is (D) credited by ₹5,00,000.
When a new partner is admitted, the firm's assets and liabilities are revalued to reflect their current fair values. This ensures the incoming partner does not benefit from hidden reserves or suffer from hidden losses. The Revaluation Account is a nominal account that captures all gains and losses from revaluation. Gains are credited, losses are debited. The net balance is then transferred to the old partners' capital accounts in their profit-sharing ratio.
Here, the only revaluation is the increase in land and building. The book value is ₹20,00,000, and it is undervalued by 20%. "Undervalued by 20%" means the book value is 20% less than the true value — i.e., the book value represents only 80% of the true value. So the true value = book value ÷ (1 – 0.20) = ₹20,00,000 ÷ 0.80 = ₹25,00,000. The increase is ₹25,00,000 – ₹20,00,000 = ₹5,00,000.
This increase is a gain, so it is credited to the Revaluation Account. The journal entry is:
Date Particulars L.F. Debit (₹) Credit (₹) 2025
Mar 31Land and Building A/c Dr. 5,00,000 To Revaluation A/c 5,00,000 (Being increase in value of land and building on revaluation) The Revaluation Account will therefore show a credit of ₹5,00,000. No other revaluation items are given, so the account balance is a credit of ₹5,00,000.
Watch outA common mistake is to compute 20% of ₹20,00,000 as ₹4,00,000. But "undervalued by 20%" means the book value is 80% of the true value, not that the true value is 120% of book value. Always divide by (1 – percentage) when an asset is undervalued.
TipTo avoid confusion: if an asset is undervalued by x%, the increase = (book value × x) / (100 – x). Here, (20,00,000 × 20) / 80 = ₹5,00,000.
Thus, the Revaluation Account is credited by ₹5,00,000.
✓Final answerThe Revaluation Account is credited by ₹5,00,000. The correct option is (D).
- CBSE 2026Set 67/4/11 markMCQQ.P, Q and R were partners in a firm sharing profits and losses in the ratio of 6 : 5 : 4. They admitted S as a new partner for 1/8th share in the profits of the firm. It was agreed that Q would retain his original share. The sacrificing ratio of P and R will be : (A) 6 : 5 (B) 4 : 5 (C) 3 : 2 (D) 5 : 4
›Reveal solutionSolution
The sacrificing ratio of P and R is 3 : 2 (Option C).
Concept: Sacrificing Ratio on Admission of a Partner
When a new partner is admitted, the existing partners sacrifice a portion of their profit share in favour of the incoming partner. The sacrificing ratio measures how much each old partner gives up. It is calculated as:
Sacrificing Ratio=Old Share−New Share
The partner who sacrifices more is entitled to a larger share of goodwill compensation from the new partner. In this problem, Q retains his original share (sacrifices nothing), so only P and R sacrifice. We must first determine the new profit-sharing ratio, then compute individual sacrifices.
Treatment and Solution
Step 1: Determine the old profit-sharing ratio
P, Q and R share profits in the ratio 6:5:4.
Total parts = 6+5+4=15
- P's old share = 156=52
- Q's old share = 155=31
- R's old share = 154
Step 2: S is admitted for 81 share
The remaining share available for P, Q and R together = 1−81=87
Step 3: Q retains his original share
Q's new share = Q's old share = 31
This is the critical constraint. Q does not sacrifice anything.
Step 4: Calculate the combined new share of P and R
Since Q takes 31 out of the 87 available to the old partners:
Combined share of P and R = 87−31
To subtract, find a common denominator (24):
87−31=2421−248=2413
Step 5: P and R will share this 2413 in their old ratio of 6:4 (i.e., 3:2)
P's new share = 53×2413=12039=4013
R's new share = 52×2413=12026=6013
NoteWhen one partner retains his original share, the remaining partners continue to share the balance in their old mutual ratio.
Working Notes
W.N. 1: Sacrifice by P
P’s sacrifice=Old share−New share=52−4013
Convert 52 to denominator 40: 52=4016
P’s sacrifice=4016−4013=403
W.N. 2: Sacrifice by R
R’s sacrifice=154−6013
Convert 154 to denominator 60: 154=6016
R’s sacrifice=6016−6013=603=201
W.N. 3: Sacrificing Ratio
Sacrificing Ratio (P : R)=403:201
To compare, convert to a common denominator (40):
403:402=3:2
Watch outA common mistake is to assume the sacrificing ratio equals the old profit-sharing ratio. Here, P and R's old ratio was 6:4 (or 3:2), which happens to match the sacrificing ratio — but this is coincidental because Q retained his full share. Always compute sacrifice = old − new for each partner.
✓Final answerP sacrifices 403 and R sacrifices 201 (i.e., 402), giving a sacrificing ratio of 3 : 2. The correct answer is (C) 3 : 2.
- CBSE 2026Set 67/4/11 markMCQQ.(a) Ravi, Sohan and Neena were partners in a firm sharing profits and losses in the ratio of 5 : 3 : 2. On 1st April 2025, Sohan retired and his share was taken up by Ravi and Neena in the ratio of 2 : 1. The new profit sharing ratio between Ravi and Neena will be : (A) 3 : 2 (B) 2 : 1 (C) 5 : 4 (D) 7 : 3(OR)(b) Kunal, Raj and Leela were partners in a firm sharing profits and losses in the ratio of 4 : 3 : 2. On 1st April, 2025, Kunal retired. Raj and Leela decided to share profits in the future in the ratio of 5 : 3. The gaining ratio between Raj and Leela will be : (A) 5 : 3 (B) 3 : 2 (C) 21 : 11 (D) 7 : 5
›Reveal solutionSolution
Part (a): New ratio Ravi:Neena = 7:3 -> (D). Part (b): Gaining ratio Raj:Leela = 21:11 -> (C).
Part (a)
Sohan's 3/10 taken 2:1 by Ravi (2/10) and Neena (1/10): Ravi 5/10+2/10 = 7/10, Neena 2/10+1/10 = 3/10 -> 7:3.
✓Final answer(D) 7 : 3
Part (b)
Gaining ratio = New share - Old share. Raj = 5/8 - 3/9 = 21/72; Leela = 3/8 - 2/9 = 11/72 -> 21:11.
✓Final answer(C) 21 : 11
- CBSE 2026Set 67/4/11 markMCQQ.(a) Rohan and Meeta were partners in a firm sharing profits and losses in the ratio of 5 : 4. Their capitals were ₹ 3,00,000 and ₹ 2,00,000 respectively. They admitted Kabir as a new partner for 1/5th share in the profits of the firm. Kabir brought ₹ 1,50,000 as his capital. Kabir's share in the goodwill of the firm was : (A) ₹ 50,000 (B) ₹ 20,000 (C) ₹ 1,00,000 (D) ₹ 2,50,000(OR)(b) Ravi, Nisha and Priya were partners in a firm sharing profits and losses in the ratio of 4 : 3 : 1. Ravi retired and the balance in his Capital Account after making necessary adjustments on account of reserves and revaluation of assets and re-assessment of liabilities was ₹ 2,40,000. Nisha and Priya agreed to pay him ₹ 2,70,000 in full settlement of his claim. The value of goodwill of the firm was : (A) ₹ 30,000 (B) ₹ 90,000 (C) ₹ 60,000 (D) ₹ 1,20,000
›Reveal solutionSolution
Part (a): Kabir's share of goodwill = Rs.20,000 -> (B). Part (b): Value of firm's goodwill = Rs.60,000 -> (C).
Part (a)
Hidden goodwill = capital implied by new partner - actual capital = (1,50,000 x 5) - 6,50,000 = 1,00,000. Kabir's 1/5 share = Rs.20,000.
✓Final answer(B) Rs.20,000
Part (b)
Excess paid over adjusted capital = Ravi's share of goodwill = 2,70,000 - 2,40,000 = 30,000. Ravi's profit share = 4/8 = 1/2, so firm goodwill = 30,000 x 2 = Rs.60,000.
✓Final answer(C) Rs.60,000
- CBSE 2026Set 67/4/11 markMCQQ.Asha, Manan and Niyati were partners in a firm sharing profits and losses in the ratio of 3 : 2 : 1. With effect from 1st April, 2025, they agreed to share profits and losses equally. Due to change in the profit sharing ratio, Asha's gain or sacrifice will be : (A) Sacrifice 1/6 (B) Gain 1/6 (C) Sacrifice 1/12 (D) Gain 1/12
›Reveal solutionSolution
Asha's old profit share was 3/6 and her new share is 1/3. The difference, 1/6, represents her sacrifice due to the change in the profit-sharing ratio.
When partners decide to change their existing profit-sharing ratio, it means that some partners will now get a larger share of future profits, while others will get a smaller share. The partner whose share increases is said to 'gain', and the partner whose share decreases is said to 'sacrifice'. This adjustment is crucial because it often necessitates accounting for accumulated profits, reserves, and revaluation of assets and liabilities to ensure fairness, as the future distribution of these items will be based on the new ratio.
To determine whether a partner gains or sacrifices, we compare their old profit share with their new profit share.
Sacrificing Share=Old Share−New Share
If the result is positive, the partner has sacrificed.
If the result is negative, the partner has gained (a negative sacrifice is a gain).
Alternatively, you can use:
Gaining Share=New Share−Old Share
If the result is positive, the partner has gained.
If the result is negative, the partner has sacrificed (a negative gain is a sacrifice).
Both formulas yield the same absolute value, but the sign convention differs. For consistency, we will use the first formula: Sacrificing Share=Old Share−New Share.
Let's apply this to Asha.
Working Notes
1. Calculation of Asha's Sacrifice or Gain
-
Old Profit Sharing Ratio: Asha : Manan : Niyati = 3 : 2 : 1
- Total parts in old ratio = 3+2+1=6
- Asha's Old Share = 3/6
-
New Profit Sharing Ratio: Asha : Manan : Niyati = Equally, which is 1 : 1 : 1
- Total parts in new ratio = 1+1+1=3
- Asha's New Share = 1/3
-
Calculate Asha's Sacrifice/Gain:
- Sacrificing Share = Old Share - New Share
- Asha's Sacrifice = 3/6−1/3
- To subtract these fractions, we need a common denominator, which is 6.
- Asha's Sacrifice = 3/6−(1×2)/(3×2)
- Asha's Sacrifice = 3/6−2/6
- Asha's Sacrifice = 1/6
Since the result is positive (1/6), Asha has sacrificed 1/6 of her share of profits.
Watch outAlways ensure you use a common denominator when adding or subtracting fractions to avoid calculation errors. A common mistake is to subtract numerators and denominators directly.
✓Final answerAsha's sacrifice due to the change in the profit-sharing ratio is 1/6. Therefore, option (A) Sacrifice 1/6 is the correct answer.
-
- CBSE 2026Set 67/5/11 markMCQQ.There are two statements Assertion (A) and Reason (R) : Assertion (A) : At the time of admission of a new partner in a partnership firm, the newly admitted partner brings an agreed amount of capital either in cash or in kind. Reason (R) : On admission, the new partner gets the right to acquire share in the assets and profits of the partnership firm. Choose the correct option from the following : (A) Both Assertion (A) and Reason (R) are correct and Reason (R) is the correct explanation of Assertion (A). (B) Both Assertion (A) and Reason (R) are correct, but Reason (R) is not the correct explanation of Assertion (A). (C) Assertion (A) is correct, but Reason (R) is incorrect. (D) Assertion (A) is incorrect, but Reason (R) is correct.
›Reveal solutionSolution
Both the Assertion and the Reason are correct, and the Reason correctly explains why the new partner brings capital — because they gain a share in the firm’s assets and profits.
When a new partner is admitted into an existing partnership, the firm’s original agreement is effectively rewritten. The old partners have been running the business with their own capital, skills, and shared risks. Now, a newcomer steps in. Naturally, that newcomer must contribute something of value to the firm — otherwise, why would the existing partners give up a portion of their ownership? This contribution is what the Assertion refers to: the new partner brings an agreed amount of capital, which can be in cash (money) or in kind (assets like machinery, land, or stock).
The Reason states that on admission, the new partner acquires the right to a share in the firm’s assets and profits. This is the very essence of partnership — every partner has a claim on the firm’s net assets and a right to a portion of the profits as per the partnership deed. Without bringing capital, the new partner would be getting something for nothing, which would be unfair to the existing partners who built the business. So the capital brought in is the price of acquiring that share.
NoteThe capital brought by the new partner is not a gift — it becomes part of the firm’s total capital, and the new partner’s capital account is credited with that amount. The existing partners’ capital accounts may also be adjusted through revaluation or goodwill adjustments, but that is a separate accounting treatment.
Now, is the Reason the correct explanation of the Assertion? Yes. The Assertion states what happens (the new partner brings capital), and the Reason explains why it happens (because the new partner gets a share in assets and profits). The two are directly linked: the right to share in assets and profits is the consideration for bringing capital. Without that right, there would be no reason for the new partner to contribute anything.
ImportantThe new partner’s capital contribution is not optional or arbitrary — it is the foundation of their ownership stake. The partnership deed usually specifies the amount, and if the new partner brings less than their share of the firm’s net worth, the difference may be adjusted through goodwill or revaluation.
Therefore, both statements are factually correct as per the principles of partnership accounting, and the Reason logically supports the Assertion.
✓Final answerOption (A) is correct: Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct explanation of Assertion (A).
- CBSE 2026Set 67/5/11 markMCQQ.(a) Guru and Prakash were partners in a firm sharing profits and losses in the ratio of 7 : 3. They admitted Anu as a new partner for 1/4th share in the profits of the firm. On the date of Anu’s admission, the Profit and Loss Account of Guru and Prakash showed a credit balance of ₹ 40,000. The necessary journal entry for its treatment will be : (A) Profit and Loss A/c Dr. — Debit ₹ 40,000 | To Guru’s Capital A/c — Credit ₹ 21,000 | To Prakash’s Capital A/c — Credit ₹ 9,000 | To Anu’s Capital A/c — Credit ₹ 10,000 (B) Profit and Loss A/c Dr. — Debit ₹ 40,000 | To Guru’s Capital A/c — Credit ₹ 28,000 | To Prakash’s Capital A/c — Credit ₹ 12,000 (C) Guru’s Capital A/c Dr. — Debit ₹ 21,000 | Prakash’s Capital A/c Dr. — Debit ₹ 9,000 | Anu’s Capital A/c Dr. — Debit ₹ 10,000 | To Profit and Loss A/c — Credit ₹ 40,000 (D) Guru’s Capital A/c Dr. — Debit ₹ 28,000 | Prakash’s Capital A/c Dr. — Debit ₹ 12,000 | To Profit and Loss A/c — Credit ₹ 40,000(OR)(b) Samta, Mamta and Geeta were partners in a firm sharing profits and losses in the ratio of 11 : 5 : 4. On 31st March, 2025 Samta died. On Samta’s death, the goodwill of the firm was valued at ₹ 1,80,000. The necessary journal entry for the treatment of goodwill on Samta’s death will be : (A) Samta’s Capital A/c Dr. — Debit ₹ 99,000 | To Mamta’s Capital A/c — Credit ₹ 55,000 | To Geeta’s Capital A/c — Credit ₹ 44,000 (B) Mamta’s Capital A/c Dr. — Debit ₹ 1,00,000 | Geeta’s Capital A/c Dr. — Debit ₹ 80,000 | To Samta’s Capital A/c — Credit ₹ 1,80,000 (C) Samta’s Capital A/c Dr. — Debit ₹ 1,80,000 | To Mamta’s Capital A/c — Credit ₹ 1,00,000 | To Geeta’s Capital A/c — Credit ₹ 80,000 (D) Mamta’s Capital A/c Dr. — Debit ₹ 55,000 | Geeta’s Capital A/c Dr. — Debit ₹ 44,000 | To Samta’s Capital A/c — Credit ₹ 99,000
›Reveal solutionSolution
Part (a): P&L credit balance Rs 40,000 goes to old partners Guru:Prakash 7:3 -> option (B) (Guru 28,000, Prakash 12,000).
Part (b): On Samta's death, Mamta and Geeta pay her share of goodwill in gaining ratio 5:4 -> option (D) (Mamta 55,000, Geeta 44,000, Samta 99,000).
Part (a)
Accumulated profit (a credit balance in the Profit and Loss Account) was earned before the new partner joined, so it is distributed to the old partners only, in their old ratio, by debiting the P&L Account and crediting their capital accounts.
- Old ratio Guru : Prakash = 7 : 3; balance = Rs 40,000.
- Guru = 7/10 x 40,000 = Rs 28,000; Prakash = 3/10 x 40,000 = Rs 12,000.
Particulars Debit (Rs) Credit (Rs) Profit and Loss A/c Dr. 40,000 To Guru's Capital A/c 28,000 To Prakash's Capital A/c 12,000 Anu is not credited. This matches option (B).
✓Final answerThe correct journal entry is Option (B).
Part (b)
When a partner dies, the continuing partners gain the deceased partner's share and must compensate her estate for the goodwill in their gaining ratio.
- Old ratio Samta : Mamta : Geeta = 11 : 5 : 4. Samta's share = 11/20.
- Samta's share of goodwill = 11/20 x 1,80,000 = Rs 99,000.
- Mamta and Geeta continue 5 : 4, which is also their gaining ratio.
- Mamta = 5/9 x 99,000 = Rs 55,000; Geeta = 4/9 x 99,000 = Rs 44,000.
Particulars Debit (Rs) Credit (Rs) Mamta's Capital A/c Dr. 55,000 Geeta's Capital A/c Dr. 44,000 To Samta's Capital A/c 99,000 This matches option (D).
✓Final answerThe correct journal entry is Option (D).
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