Big picture
When a new partner joins, the old partners give up part of their future profits. In return, the new partner usually brings two things: capital (money or assets for the business) and premium for goodwill (payment for a share of the reputation the old partners built).
Admission is a reconstitution, so the three questions from the goodwill chapter come back: who gets the goodwill, who gets the reserves, and who gets the revaluation profit. The answer for reserves and revaluation is always the old partners in the old ratio, because those gains arose before the new partner joined.
A new partner gets two rights: the right to a share in the assets of the firm and the right to a share of future profits.
Learning goals
Calculate the new profit-sharing ratio in every form the question can take.
Calculate the sacrificing ratio of the old partners.
Record premium for goodwill brought in cash, withdrawn, partly brought, not brought, or paid privately.
Calculate and record hidden goodwill, and write off existing goodwill.
Prepare the Revaluation Account and distribute reserves on admission.
Adjust capitals: find the new partner's capital from the old partners', or adjust old partners' capitals to match the new partner's.
Prepare partners' capital accounts and the new balance sheet.
Core ideas
1. Calculating the new ratio
There are four common forms. Work them over a common denominator.
(a) Only the new partner's share is given. The old partners continue to share the remainder in their old ratio, and their sacrificing ratio equals their old ratio.
Example. A and B share 3:2. C is admitted for 1/5. The remaining 4/5 is shared 3:2: A gets 4/5 × 3/5 = 12/25, B gets 4/5 × 2/5 = 8/25, C gets 5/25. New ratio 12:8:5; sacrificing ratio 3:2.
(b) The new partner takes stated fractions from each old partner.
Example. A and B share 3:2. C gets 1/5, taking 1/10 from A and 1/10 from B. A = 3/5 − 1/10 = 5/10; B = 2/5 − 1/10 = 3/10; C = 2/10. New ratio 5:3:2; sacrificing ratio 1:1.
(c) Old partners surrender a fraction of their own shares.
Example. A and B share 3:2. A surrenders 1/3 of his share and B surrenders 1/4 of hers in favour of C.
A gives 3/5 x 1/3 = 1/5 = 2/10 A keeps 3/5 - 1/5 = 4/10
B gives 2/5 x 1/4 = 1/10 B keeps 2/5 - 1/10 = 3/10
C gets 2/10 + 1/10 = 3/10
New ratio 4:3:3 Sacrificing ratio 2:1(d) The new ratio of all partners is given directly. Find the sacrifice of each old partner as old share − new share. If A and B share 3:2 and the new ratio of A, B and C is 2:2:1, then A sacrifices 3/5 − 2/5 = 1/5 and B sacrifices 2/5 − 2/5 = 0. Only A sacrifices, so all of C's premium goes to A.
Note. Never assume the sacrificing ratio is the old ratio. That is true only in case (a). In every other case calculate old − new for each partner.
2. Premium for goodwill brought in cash
The new partner pays the old partners for the share of goodwill they give up. Premium = Firm's goodwill × New partner's share. It is shared by the old partners in the sacrificing ratio.
Example. A and B share 3:2. C is admitted for 1/5 (new ratio 12:8:5, sacrifice 3:2). The firm's goodwill is ₹1,50,000. C brings ₹2,00,000 as capital and his share of goodwill in cash.
C's premium = 1,50,000 × 1/5 = ₹30,000; A gets 18,000 and B gets 12,000.
Entry | Debit | Credit | ₹ |
|---|---|---|---|
Capital and premium brought | Bank A/c | C's Capital A/c 2,00,000 and Premium for Goodwill A/c 30,000 | 2,30,000 |
Premium shared in sacrificing ratio | Premium for Goodwill A/c | A's Capital A/c 18,000 and B's Capital A/c 12,000 | 30,000 |
If old partners withdraw the premium | A's Capital A/c 18,000 and B's Capital A/c 12,000 | Bank A/c | 30,000 |
Premium paid privately to the old partners, outside the business: no entry in the firm's books.
Existing goodwill in the books belongs to the old partners. Write it off first in the old ratio: Old Partners' Capital A/cs Dr, To Goodwill A/c.
3. Premium not brought, or partly brought
Not brought in cash. The new partner's account is debited and the sacrificing partners are credited:
C's Capital (or Current) A/c Dr ₹30,000, To A's Capital A/c ₹18,000, To B's Capital A/c ₹12,000.
Partly brought. Suppose C brings only ₹12,000 of the ₹30,000 premium. The ₹12,000 goes through the Premium for Goodwill Account, and the shortfall of ₹18,000 is debited to C's Capital or Current Account. A and B together are still credited ₹30,000 in 3:2.
Entry | Debit | Credit |
|---|---|---|
Cash brought | Bank A/c 12,000 | Premium for Goodwill A/c 12,000 |
Distribution | Premium for Goodwill A/c 12,000 and C's Current A/c 18,000 | A's Capital A/c 18,000 and B's Capital A/c 12,000 |
Goodwill brought in kind. If the new partner brings an asset (say machinery worth ₹50,000) towards capital: Machinery A/c Dr, To C's Capital A/c.
4. Hidden goodwill
Sometimes the goodwill is not stated. Instead the question says the new partner brings a certain capital for a certain share. The capital the firm "should" have, judged by the new partner's contribution, is compared with the capital it actually has.
Implied total capital = New partner's capital x reciprocal of share
Actual total capital = Old partners' capitals after all adjustments
+ New partner's capital
Hidden goodwill = Implied total capital - Actual total capitalExample. After adjusting reserves and revaluation, A's capital is ₹3,00,000 and B's ₹2,00,000. C brings ₹2,00,000 for a 1/4 share.
Implied total capital = 2,00,000 x 4 = 8,00,000
Actual total capital = 3,00,000 + 2,00,000 + 2,00,000 = 7,00,000
Hidden goodwill of the firm = 1,00,000
C's share of goodwill = 1,00,000 x 1/4 = 25,000C has brought only capital, so his share of goodwill (₹25,000) is debited to his Capital or Current Account and credited to A and B in the sacrificing ratio.
Note. Always use old partners' capitals after distributing reserves, revaluation profit and accumulated profits or losses. Using unadjusted figures is the most common error in hidden goodwill. If the implied capital is less than the actual capital, the difference is not goodwill; it is treated as a capital reserve.
5. Revaluation and reserves on admission
These follow the same rules as on a change in ratio:
Revaluation Account: decreases in assets, increases in liabilities and unrecorded liabilities go on the debit side; increases in assets, decreases in liabilities and unrecorded assets on the credit side. The profit or loss is shared by the old partners in the old ratio. The new partner has no share in it.
Reserves and accumulated profits (General Reserve, credit balance of Profit and Loss, the unused part of Workmen Compensation Reserve and Investment Fluctuation Fund) go to the old partners in the old ratio.
Accumulated losses (debit balance of Profit and Loss, deferred advertisement expenditure) are written off against the old partners in the old ratio.
6. Adjusting capitals
(a) New partner's capital based on the old partners' capitals. Take the old partners' capitals after all adjustments (goodwill, reserves, revaluation), find the total capital of the new firm, and take the new partner's share.
Example. After all adjustments, A has ₹3,60,000 and B ₹2,40,000, a total of ₹6,00,000. C is admitted for 1/5, so the old partners together hold 4/5.
Total capital of new firm = 6,00,000 × 5/4 = ₹7,50,000. C's capital = 7,50,000 × 1/5 = ₹1,50,000.
(b) Old partners' capitals adjusted on the basis of the new partner's capital. Use the new partner's capital to find the total, then give each partner capital in the new ratio. Any surplus is paid out (or credited to a current account) and any deficit is brought in.
Example. New ratio A:B:C = 12:8:5. C brings ₹1,00,000 for his 5/25 share, so total capital = 1,00,000 × 25/5 = ₹5,00,000.
Partner | Required capital | Adjusted capital | Action |
|---|---|---|---|
A (12/25) | 2,40,000 | 2,70,000 | Surplus ₹30,000 withdrawn or credited to Current A/c |
B (8/25) | 1,60,000 | 1,50,000 | Deficit ₹10,000 brought in or debited to Current A/c |
C (5/25) | 1,00,000 | 1,00,000 | None |
Entries: A's Capital A/c Dr ₹30,000, To Bank (or A's Current) A/c; Bank (or B's Current) A/c Dr ₹10,000, To B's Capital A/c.
7. A complete admission problem
A and B share profits 3:2. Their balance sheet on 31 March 2025:
Liabilities | ₹ | Assets | ₹ |
|---|---|---|---|
Creditors | 60,000 | Cash | 30,000 |
General Reserve | 40,000 | Debtors | 80,000 |
A's Capital | 2,00,000 | Stock | 90,000 |
B's Capital | 1,50,000 | Machinery | 1,00,000 |
Building | 1,50,000 | ||
Total | 4,50,000 | Total | 4,50,000 |
C is admitted for 1/5 share on these terms: C brings ₹1,20,000 as capital and his share of goodwill in cash, the firm's goodwill being ₹1,00,000; building is appreciated by 10%; stock is reduced by ₹6,000; a provision for doubtful debts is made at 5% of debtors; outstanding wages of ₹1,000 are recorded. The new ratio is 12:8:5, so the sacrificing ratio is 3:2.
Revaluation Account
Particulars | ₹ | Particulars | ₹ |
|---|---|---|---|
Stock | 6,000 | Building | 15,000 |
Provision for doubtful debts | 4,000 | ||
Outstanding wages | 1,000 | ||
Profit: A (3/5) | 2,400 | ||
Profit: B (2/5) | 1,600 | ||
Total | 15,000 | Total | 15,000 |
Partners' Capital Accounts
Dr Particulars | A | B | C | Cr Particulars | A | B | C |
|---|---|---|---|---|---|---|---|
Balance c/d | 2,38,400 | 1,75,600 | 1,20,000 | Balance b/d | 2,00,000 | 1,50,000 | – |
Revaluation profit | 2,400 | 1,600 | – | ||||
General Reserve | 24,000 | 16,000 | – | ||||
Premium for Goodwill | 12,000 | 8,000 | – | ||||
Bank | – | – | 1,20,000 | ||||
Total | 2,38,400 | 1,75,600 | 1,20,000 | Total | 2,38,400 | 1,75,600 | 1,20,000 |
Premium = 1,00,000 × 1/5 = ₹20,000, shared 3:2. Cash = 30,000 + 1,20,000 + 20,000 = ₹1,70,000.
Balance Sheet of A, B and C
Liabilities | ₹ | Assets | ₹ |
|---|---|---|---|
Creditors | 60,000 | Cash | 1,70,000 |
Outstanding wages | 1,000 | Debtors 80,000 less provision 4,000 | 76,000 |
A's Capital | 2,38,400 | Stock | 84,000 |
B's Capital | 1,75,600 | Machinery | 1,00,000 |
C's Capital | 1,20,000 | Building | 1,65,000 |
Total | 5,95,000 | Total | 5,95,000 |
The General Reserve no longer appears, because it has been distributed.
A reliable problem-solving routine
Work out the new ratio and the sacrificing ratio (old − new for each old partner).
Write off any existing goodwill among old partners in the old ratio.
Prepare the Revaluation Account; share the result in the old ratio.
Distribute reserves and accumulated profits or losses in the old ratio.
Record the new partner's capital and premium: cash, partly, not brought, or hidden goodwill. Share premium in the sacrificing ratio.
Adjust capitals if the question asks, in the new ratio.
Close the capital accounts and prepare the new balance sheet. Check that it balances.
Connections that matter
Goodwill and change in profit sharing supplies the valuation methods, the Revaluation Account and the treatment of reserves, WCR and IFF used here.
Retirement and death is admission in reverse: the outgoing partner is paid for goodwill by the gaining partners.
Partnership fundamentals gives the fixed and fluctuating capital formats; with fixed capitals, adjustments go to current accounts.
Common mistakes
Sharing the premium in the old ratio. Premium goes in the sacrificing ratio; it equals the old ratio only when the new partner's share comes proportionately from all old partners.
Giving the new partner a share of revaluation profit or reserves. They belong only to the old partners.
Using unadjusted capitals for hidden goodwill or for the new partner's capital.
Recording premium paid privately. It does not pass through the firm.
Forgetting to take only the new partner's share of the firm's goodwill as premium.
Leaving the distributed General Reserve on the new balance sheet.
Revision checklist
I can find the new ratio and sacrificing ratio in all four forms.
I can record premium brought in cash, withdrawn, partly brought, not brought or paid privately.
I can calculate hidden goodwill from capitals.
I can prepare the Revaluation Account and distribute reserves to old partners.
I can calculate the new partner's capital, or adjust old partners' capitals to the new ratio.
I can prepare capital accounts and a balancing new balance sheet.