Reconstitution of a Partnership Firm – Admission of a Partner — NCERT Solutions

Correct Answer: (a) A $\frac{9}{16}$, B $\frac{3}{16}$, C $\frac{4}{16}$

Given:

• Old ratio of A : B = 3 : 1
• C's share = 1/4

Working:

Remaining share for A and B = $1 - \frac{1}{4} = \frac{3}{4}$

A's new share = $\frac{3}{4} \times \frac{3}{4} = \frac{9}{16}$

B's new share = $\frac{1}{4} \times \frac{3}{4} = \frac{3}{16}$

C's share = $\frac{1}{4} = \frac{4}{16}$

New profit sharing ratio = A : B : C = $\frac{9}{16} : \frac{3}{16} : \frac{4}{16}$ = 9 : 3 : 4

This matches option (a).

Correct Answer: (a) 9 : 7 : 4

Given:

• Old ratio X : Y = 3 : 2, i.e., X = 3/5, Y = 2/5
• Z's share = 1/5 (acquired 3/20 from X and 1/20 from Y)

Working:

X's new share = $\frac{3}{5} - \frac{3}{20} = \frac{12}{20} - \frac{3}{20} = \frac{9}{20}$

Y's new share = $\frac{2}{5} - \frac{1}{20} = \frac{8}{20} - \frac{1}{20} = \frac{7}{20}$

Z's share = $\frac{1}{5} = \frac{4}{20}$

New profit sharing ratio = X : Y : Z = $\frac{9}{20} : \frac{7}{20} : \frac{4}{20}$ = 9 : 7 : 4

Correct Answer: (b) 3 : 1

Reasoning:

When no specific agreement is mentioned about the manner in which C acquires his share, it is assumed that A and B sacrifice in their old profit sharing ratio, i.e., 3 : 1.

Verification:

C's share = 1/4. Remaining share = 3/4 distributed in ratio 3:1.

A's sacrifice = $\frac{3}{4} \times \frac{1}{4} = \frac{3}{16}$

B's sacrifice = $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$

Sacrificing ratio = 3 : 1 (same as old ratio).

Correct Answer: (c) old partner's capital account

Reasoning: General reserve represents accumulated profits earned by the firm before the admission of the new partner. The new partner has no claim over such reserves. Therefore, at the time of admission, general reserve is transferred to the old partners' capital accounts in their old profit sharing ratio.

Correct Answer: (b) Rs. 5,000 each

Given:

• Old ratio Asha : Nisha = 2 : 1
• Ashish admitted for 1/4 share
• Asha gifted 1/8 to Ashish; Nisha contributed remaining 1/8
• Goodwill = Rs. 40,000

Working:

Ashish's share = 1/4 = 2/8

Asha's sacrifice = 1/8; Nisha's sacrifice = 1/8

Sacrificing ratio = Asha : Nisha = 1/8 : 1/8 = 1 : 1

Ashish's share of goodwill = $\frac{1}{4} \times 40,000 =$ Rs. 10,000

This Rs. 10,000 is credited to Asha and Nisha in sacrificing ratio 1:1:

• Asha's share = Rs. 5,000
• Nisha's share = Rs. 5,000

Correct Answer: (c) old partnership is reconstituted

Reasoning: On admission of a new partner, the old partnership agreement comes to an end and a new partnership agreement is formed. However, the firm continues its business — it is not dissolved. Hence, the old partnership is reconstituted (not dissolved).

Correct Answer: (b) Assets account

Reasoning: When the value of an asset increases on revaluation, the asset account is debited (to show the increased value) and the Revaluation Account (Profit and Loss Adjustment Account) is credited. So the debit entry goes to the Assets account.

Correct Answer: (a) old partners in old profit sharing ratio

Reasoning: Undistributed profits (e.g., credit balance of Profit & Loss Account) were earned by the firm before the admission of the new partner. The new partner has no right over these profits. Therefore, they are transferred to the old partners' capital accounts in their old profit sharing ratio.

Given:

• Profits: Rs. 5,00,000; Rs. 4,00,000; Rs. 6,00,000
• Years of purchase = 4

Step 1: Calculate Average Profits
$$\text{Average Profit} = \frac{5,00,000 + 4,00,000 + 6,00,000}{3} = \frac{15,00,000}{3} = \text{Rs. }5,00,000$$

Step 2: Calculate Goodwill
$$\text{Goodwill} = \text{Average Profit} \times \text{Years of Purchase}$$
$$= 5,00,000 \times 4 = \textbf{Rs. }\mathbf{20,00,000}$$

Given:

• Profits: Rs. 16,000; Rs. 20,000; Rs. 24,000; Rs. 32,000
• Capital Investment = Rs. 1,00,000
• Normal Rate of Return = 18%
• Years of purchase = 3

Step 1: Average Profit
$$\text{Average Profit} = \frac{16,000 + 20,000 + 24,000 + 32,000}{4} = \frac{92,000}{4} = \text{Rs. }23,000$$

Step 2: Normal Profit
$$\text{Normal Profit} = 1,00,000 \times \frac{18}{100} = \text{Rs. }18,000$$

Step 3: Super Profit
$$\text{Super Profit} = 23,000 - 18,000 = \text{Rs. }5,000$$

Step 4: Goodwill
$$\text{Goodwill} = 5,000 \times 3 = \textbf{Rs. }\mathbf{15,000}$$

Using data from Q2: Average Profit = Rs. 23,000; Normal Profit = Rs. 18,000; Super Profit = Rs. 5,000; Normal Rate = 18%

Method 1: Capitalisation of Super Profits
$$\text{Goodwill} = \frac{\text{Super Profit}}{\text{Normal Rate of Return}} \times 100$$
$$= \frac{5,000}{18} \times 100 = \text{Rs. }27,778 \text{ (approx.)}$$

Method 2: Capitalisation of Average Profits
$$\text{Capitalised Value of Firm} = \frac{\text{Average Profit}}{\text{Normal Rate}} \times 100 = \frac{23,000}{18} \times 100 = \text{Rs. }1,27,778$$

$$\text{Goodwill} = \text{Capitalised Value} - \text{Actual Capital Employed}$$
$$= 1,27,778 - 1,00,000 = \textbf{Rs. }\mathbf{27,778}$$

Conclusion: Both methods give the same result (Rs. 27,778). The amount of goodwill is NOT different under both methods — they are equivalent approaches.

Given:

• Old ratio Giri : Shanta = 1 : 1
• Kachroo's share = 1/5
• Goodwill brought by Kachroo = Rs. 20,000

Sacrificing Ratio (Giri : Shanta = 1 : 1, sacrifice equally)

Goodwill distributed: Giri = Rs. 10,000; Shanta = Rs. 10,000

(a) When no goodwill appears in the books:

(b) When goodwill appears in the books at Rs. 40,000:

First, write off existing goodwill in old ratio (1:1):

Then record Kachroo's goodwill as in part (a):

Given:

• Old partners: Aslam, Jackab, Hari — equal ratio (1:1:1)
• Capitals: Aslam Rs. 1,500; Jackab Rs. 1,750; Hari Rs. 2,000
• Satnam pays Rs. 1,500 for 1/4 goodwill + Rs. 1,800 as capital
• Liabilities = Rs. 3,000
• Assets (excluding cash): Motors Rs. 1,200; Furniture Rs. 400; Stock Rs. 2,650; Debtors Rs. 3,780
• Revalued: Motors Rs. 950; Furniture Rs. 380

Step 1: Find Cash in Hand (before Satnam's admission)

Total Assets = Total Liabilities + Capital
$$= 3,000 + 1,500 + 1,750 + 2,000 = \text{Rs. }8,250$$

Assets excluding cash = 1,200 + 400 + 2,650 + 3,780 = Rs. 8,030

$$\text{Cash in hand} = 8,250 - 8,030 = \text{Rs. }220$$

Step 2: Revaluation Loss

• Motors: 1,200 − 950 = Rs. 250 (loss)
• Furniture: 400 − 380 = Rs. 20 (loss)
• Total Revaluation Loss = Rs. 270

Shared equally: Rs. 90 each (Aslam, Jackab, Hari)

Step 3: Adjusted Capitals (after revaluation)

• Aslam: 1,500 − 90 = Rs. 1,410
• Jackab: 1,750 − 90 = Rs. 1,660
• Hari: 2,000 − 90 = Rs. 1,910

Step 4: Goodwill Treatment

Satnam pays Rs. 1,500 for 1/4 share of goodwill → Total goodwill = Rs. 6,000

Goodwill credited to old partners equally: Rs. 500 each

• Aslam: 1,410 + 500 = Rs. 1,910
• Jackab: 1,660 + 500 = Rs. 2,160
• Hari: 1,910 + 500 = Rs. 2,410
• Satnam's Capital = Rs. 1,800

Step 5: Cash in Hand after admission
$$\text{Cash} = 220 + 1,500 + 1,800 = \text{Rs. }3,520$$

Balance Sheet of the New Firm after Satnam's Admission

Given:

• Old ratio Benu : Sunil = 3 : 2
• Ina admitted for 1/4 share
• Ina brings: Capital Rs. 2,00,000 + Goodwill Rs. 1,00,000
• General Reserve = Rs. 1,20,000; P&L (Cr.) = Rs. 60,000

Sacrificing Ratio = Old ratio = 3 : 2

Goodwill distributed: Benu = $\frac{3}{5} \times 1,00,000$ = Rs. 60,000; Sunil = Rs. 40,000

Journal Entries:

1. Ina's capital and goodwill brought in:
$$\text{Bank A/c Dr.} \quad 3,00,000$$
$$\quad \text{To Ina's Capital A/c} \quad 2,00,000$$
$$\quad \text{To Premium for Goodwill A/c} \quad 1,00,000$$
(Being capital and goodwill premium brought in by Ina)

2. Goodwill distributed to old partners:
$$\text{Premium for Goodwill A/c Dr.} \quad 1,00,000$$
$$\quad \text{To Benu's Capital A/c} \quad 60,000$$
$$\quad \text{To Sunil's Capital A/c} \quad 40,000$$
(Being goodwill premium credited to old partners in sacrificing ratio 3:2)

3. General Reserve transferred to old partners:
$$\text{General Reserve A/c Dr.} \quad 1,20,000$$
$$\quad \text{To Benu's Capital A/c} \quad 72,000$$
$$\quad \text{To Sunil's Capital A/c} \quad 48,000$$
(Being general reserve distributed in old ratio 3:2)

4. Profit & Loss Account transferred to old partners:
$$\text{Profit \& Loss A/c Dr.} \quad 60,000$$
$$\quad \text{To Benu's Capital A/c} \quad 36,000$$
$$\quad \text{To Sunil's Capital A/c} \quad 24,000$$
(Being P&L credit balance distributed in old ratio 3:2)

Given:

• Old ratio Ashoo : Rahul = 5 : 3
• Gaurav's share = 1/5
• Goodwill brought by Gaurav = Rs. 4,000
• Adjusted capitals: Ashoo = Rs. 45,000; Rahul = Rs. 35,000

Step 1: New Profit Sharing Ratio

Remaining share = $1 - \frac{1}{5} = \frac{4}{5}$

Ashoo's new share = $\frac{5}{8} \times \frac{4}{5} = \frac{20}{40} = \frac{1}{2}$

Rahul's new share = $\frac{3}{8} \times \frac{4}{5} = \frac{12}{40} = \frac{3}{10}$

Gaurav's share = $\frac{1}{5} = \frac{4}{20}$

Converting to common denominator (40):

• Ashoo = 20/40; Rahul = 12/40; Gaurav = 8/40

New ratio = 20 : 12 : 8 = 5 : 3 : 2

Step 2: Capital to be brought in by Gaurav

Total capital of new firm (based on old partners' adjusted capitals):

Old partners hold 4/5 of total capital = 45,000 + 35,000 = Rs. 80,000

$$\text{Total Capital} = \frac{80,000}{4} \times 5 = \text{Rs. }1,00,000$$

Gaurav's capital = $\frac{1}{5} \times 1,00,000 = \textbf{Rs. }\mathbf{20,000}$

Step 3: Sacrificing Ratio = Old ratio = 5 : 3

Goodwill: Ashoo = $\frac{5}{8} \times 4,000$ = Rs. 2,500; Rahul = $\frac{3}{8} \times 4,000$ = Rs. 1,500

Journal Entries:

1. Gaurav brings capital and goodwill:
$$\text{Bank A/c Dr.} \quad 24,000$$
$$\quad \text{To Gaurav's Capital A/c} \quad 20,000$$
$$\quad \text{To Premium for Goodwill A/c} \quad 4,000$$

2. Goodwill distributed to old partners:
$$\text{Premium for Goodwill A/c Dr.} \quad 4,000$$
$$\quad \text{To Ashoo's Capital A/c} \quad 2,500$$
$$\quad \text{To Rahul's Capital A/c} \quad 1,500$$

At the time of admission of a new partner, the following matters require adjustments:

1. New Profit Sharing Ratio and Sacrificing Ratio: The new profit sharing ratio of all partners (old and new) must be determined. The sacrificing ratio of old partners must also be calculated.

2. Goodwill: The goodwill of the firm must be valued and the new partner must compensate the old partners for their sacrifice. Adjustments are made through the new partner's capital account or cash brought in.

3. Revaluation of Assets and Liabilities: Assets and liabilities are revalued to reflect their current fair values. Any gain or loss on revaluation is shared among old partners in their old profit sharing ratio.

4. Accumulated Profits and Losses (Reserves): Any undistributed profits, general reserves, or accumulated losses appearing in the balance sheet are transferred to old partners' capital accounts in their old profit sharing ratio.

5. Adjustment of Partners' Capitals: If agreed, the capitals of all partners are adjusted to be proportionate to their new profit sharing ratio.

When a new partner is admitted, he acquires a share in the profits of the firm. This share is contributed (sacrificed) by the old partners. As a result, the old partners' shares in profits change (reduce).

It is necessary to ascertain the new profit sharing ratio for old partners because:

1. Future profit distribution must be done in the correct new ratio.
2. Goodwill adjustment — the sacrificing ratio (derived from old and new shares) determines how much goodwill credit each old partner receives.
3. Capital adjustments — if capitals are to be proportionate to profit sharing ratio, the new ratio is needed.
4. Correct accounting — all future transactions, drawings, and settlements depend on the new ratio.

Without determining the new ratio, it would be impossible to distribute profits correctly among all partners.

Sacrificing Ratio:

Sacrificing ratio is the ratio in which the old partners agree to give up (sacrifice) a part of their share in profits in favour of the new partner. It is calculated as:

$$\text{Sacrificing Ratio} = \text{Old Share} - \text{New Share}$$

Why it is calculated:

1. Goodwill distribution: The premium for goodwill brought in by the new partner is distributed among the old partners in their sacrificing ratio. Each old partner is compensated in proportion to the share they have sacrificed.

2. Fairness: It ensures that each old partner is compensated fairly for the share of profit they have given up to the new partner.

3. Hidden goodwill adjustment: Even when goodwill is not brought in cash, the adjustment entry for goodwill is made using the sacrificing ratio.

Usually, the sacrificing ratio is the same as the old profit sharing ratio, but it can differ based on the agreement between partners.

Sacrificing ratio is used on the following occasions:

1. At the time of admission of a new partner: The premium for goodwill brought in by the new partner is credited to the old partners' capital accounts in their sacrificing ratio.

2. When the new partner cannot bring goodwill in cash: The new partner's capital account is debited and the old partners' capital accounts are credited in the sacrificing ratio.

3. When goodwill already exists in the books: After writing off existing goodwill, the new goodwill premium is distributed in the sacrificing ratio.

4. When there is a change in profit sharing ratio among existing partners: The partner who gains in profit share compensates the partner who sacrifices, and the sacrificing ratio determines the amount of compensation.

Treatment of Existing Goodwill when New Partner Brings Goodwill in Cash:

When goodwill already appears in the books of the firm and the new partner brings his share of goodwill in cash, the following procedure is followed:

Step 1: Write off the existing goodwill by debiting the old partners' capital accounts in their old profit sharing ratio:
$$\text{Old Partners' Capital A/cs Dr. (in old ratio)}$$
$$\quad \text{To Goodwill A/c}$$

Step 2: Record the goodwill brought in by the new partner:
$$\text{Bank/Cash A/c Dr.}$$
$$\quad \text{To Premium for Goodwill A/c}$$

Step 3: Distribute the premium for goodwill among old partners in their sacrificing ratio:
$$\text{Premium for Goodwill A/c Dr.}$$
$$\quad \text{To Old Partners' Capital A/cs (in sacrificing ratio)}$$

This ensures that the goodwill account does not appear in the new firm's balance sheet (as per AS-26), and old partners are compensated for their sacrifice.

Need for Revaluation of Assets and Liabilities on Admission of a Partner:

At the time of admission of a new partner, assets and liabilities are revalued for the following reasons:

1. Fair representation: The book values of assets and liabilities may not reflect their current market values. Revaluation ensures that the balance sheet shows true and fair values.

2. Equity among partners: Any increase or decrease in the value of assets and liabilities that occurred during the period when only the old partners were in the firm should benefit or be borne by the old partners only. The new partner should neither gain nor lose on account of changes that occurred before his admission.

3. Correct capital accounts: The old partners' capital accounts are adjusted for the gain or loss on revaluation before the new partner joins, ensuring that the new partner starts with a fair position.

4. Unrecorded assets/liabilities: Sometimes certain assets or liabilities may be unrecorded. Revaluation helps bring them into the books.

The gain or loss on revaluation is transferred to old partners' capital accounts in their old profit sharing ratio.

Yes, it is advisable to revalue assets and liabilities at the time of admission of a partner.

Reasons:

1. True and fair view: Book values may differ from current market values due to price changes, depreciation, or appreciation. Revaluation ensures the balance sheet reflects true values.

2. Protection of old partners' interests: Any appreciation or depreciation in asset values that occurred before the new partner's admission belongs to the old partners. If not revalued, the new partner would share in gains/losses that are not his.

3. Correct profit/loss sharing: Without revaluation, future profits/losses would be distorted because unrealised gains or losses would be mixed with post-admission profits.

4. Unrecorded items: Revaluation helps identify and record previously unrecorded assets or liabilities.

Accounting Treatment — Revaluation Account (Profit & Loss Adjustment Account):

• If Credit side > Debit side → Gain on Revaluation → Credited to old partners' capital accounts in old ratio.
• If Debit side > Credit side → Loss on Revaluation → Debited to old partners' capital accounts in old ratio.

Journal Entries:

For increase in asset value:
$$\text{Asset A/c Dr.} \quad \text{To Revaluation A/c}$$

For decrease in asset value:
$$\text{Revaluation A/c Dr.} \quad \text{To Asset A/c}$$

For gain on revaluation:
$$\text{Revaluation A/c Dr.} \quad \text{To Old Partners' Capital A/cs (old ratio)}$$

For loss on revaluation:
$$\text{Old Partners' Capital A/cs Dr. (old ratio)} \quad \text{To Revaluation A/c}$$

Meaning of Goodwill:

Goodwill is the value of the reputation, good name, and business connections of a firm that enables it to earn profits in excess of the normal rate of return. It is an intangible asset that arises from the favourable impression a business has created in the minds of its customers, suppliers, and the public over a period of time.

In accounting terms: Goodwill = Capitalised Value of Firm − Net Assets (Capital Employed)

Or: Goodwill = Super Profit × Years of Purchase

Factors Affecting Goodwill:

1. Nature of business: Firms with stable and regular demand (e.g., essential goods) have higher goodwill.

2. Location: A business situated at a prime or convenient location enjoys higher goodwill.

3. Quality of products/services: Superior quality products and after-sales service enhance goodwill.

4. Management efficiency: Competent and experienced management leads to higher profits and goodwill.

5. Favourable contracts: Long-term contracts with suppliers or customers add to goodwill.

6. Capital required: Businesses requiring less capital to earn the same profit have higher goodwill.

7. Trend of profits: A consistent upward trend in profits increases goodwill.

8. Reputation and brand name: A well-known brand or trademark enhances goodwill significantly.

9. Market position: Monopoly or dominant market position increases goodwill.

10. Risk involved: Lower risk businesses command higher goodwill.

Methods of Valuation of Goodwill:

1. Average Profits Method:

Goodwill is calculated as a certain number of years' purchase of the average profits.

$$\text{Average Profit} = \frac{\text{Sum of Profits of past years}}{\text{Number of years}}$$

$$\text{Goodwill} = \text{Average Profit} \times \text{Number of Years' Purchase}$$

Example: If average profit = Rs. 50,000 and years of purchase = 3, then Goodwill = Rs. 1,50,000.

2. Super Profits Method:

Super profit is the excess of actual/average profit over normal profit.

$$\text{Normal Profit} = \text{Capital Employed} \times \frac{\text{Normal Rate of Return}}{100}$$

$$\text{Super Profit} = \text{Average Profit} - \text{Normal Profit}$$

$$\text{Goodwill} = \text{Super Profit} \times \text{Number of Years' Purchase}$$

3. Capitalisation Method:

This has two sub-methods:

(a) Capitalisation of Average Profits:

$$\text{Capitalised Value of Firm} = \frac{\text{Average Profit}}{\text{Normal Rate of Return}} \times 100$$

$$\text{Goodwill} = \text{Capitalised Value} - \text{Net Assets (Capital Employed)}$$

(b) Capitalisation of Super Profits:

$$\text{Goodwill} = \frac{\text{Super Profit}}{\text{Normal Rate of Return}} \times 100$$

Both sub-methods give the same result.

Note: The choice of method depends on the agreement between the partners. Each method may give a different value of goodwill.

Adjustment of Capitals in Proportion to New Profit Sharing Ratio:

When partners agree that their capitals should be proportionate to the new profit sharing ratio, the following steps are followed:

Step 1: Determine the new profit sharing ratio.

Step 2: Use the new partner's capital as the base (or total capital as given) to calculate the required capital of each partner.

$$\text{Required Capital of a Partner} = \text{New Partner's Capital} \times \frac{\text{Partner's share}}{\text{New Partner's share}}$$

OR if total capital is given:
$$\text{Required Capital} = \text{Total Capital} \times \text{Partner's share in new ratio}$$

Step 3: Compare required capital with actual capital (after all adjustments for goodwill, revaluation, reserves).

• If Required > Actual → Partner brings in the shortfall (debit Bank, credit Capital)
• If Required < Actual → Partner withdraws the excess (debit Capital, credit Bank or Current A/c)

Example:

A and B share profits 2:1. C is admitted for 1/4 share. New ratio = 2:1:1. C brings Rs. 20,000 as capital. Adjusted capitals: A = Rs. 45,000; B = Rs. 15,000.

Total capital based on C = $20,000 \times 4 =$ Rs. 80,000

Required: A = $\frac{2}{4} \times 80,000 =$ Rs. 40,000; B = $\frac{1}{4} \times 80,000 =$ Rs. 20,000

• A has Rs. 45,000 but needs Rs. 40,000 → Withdraw Rs. 5,000
• B has Rs. 15,000 but needs Rs. 20,000 → Bring in Rs. 5,000

Journal Entries:
$$\text{A's Capital A/c Dr.} \quad 5,000 \quad \text{To Bank A/c} \quad 5,000$$
$$\text{Bank A/c Dr.} \quad 5,000 \quad \text{To B's Capital A/c} \quad 5,000$$

Treatment of Goodwill when New Partner Cannot Bring it in Cash:

When the new partner is unable to bring his share of goodwill premium in cash, the adjustment is made through capital accounts without any cash transaction. Two methods are used:

Method 1: Through Goodwill Account (Raising and Writing Off)

Step 1: Raise goodwill in the books by crediting old partners in old ratio:
$$\text{Goodwill A/c Dr.}$$
$$\quad \text{To Old Partners' Capital A/cs (old ratio)}$$

Step 2: Write off goodwill by debiting all partners (including new) in new ratio:
$$\text{All Partners' Capital A/cs Dr. (new ratio)}$$
$$\quad \text{To Goodwill A/c}$$

The net effect is that the new partner's capital account is debited for his share of goodwill and old partners are credited in their sacrificing ratio.

Method 2: Direct Adjustment (Without Opening Goodwill Account)

The new partner's capital account is directly debited and old partners' capital accounts are credited in their sacrificing ratio:

$$\text{New Partner's Capital A/c Dr.}$$
$$\quad \text{To Old Partners' Capital A/cs (sacrificing ratio)}$$

This method is simpler and does not create a goodwill account in the books, which is in line with AS-26 (goodwill should not be shown as an asset unless purchased).

Both methods produce the same net effect on the capital accounts of all partners.

Methods for Treatment of Goodwill on Admission of a New Partner:

Case 1: New Partner Brings Goodwill in Cash (Premium Method)

$$\text{Bank A/c Dr.}$$
$$\quad \text{To Premium for Goodwill A/c}$$

$$\text{Premium for Goodwill A/c Dr.}$$
$$\quad \text{To Old Partners' Capital A/cs (sacrificing ratio)}$$

If old partners withdraw the amount: Debit their capital accounts and credit Bank.

Case 2: New Partner Brings Part of Goodwill in Cash

Record cash received, credit old partners for full goodwill in sacrificing ratio, and debit new partner's capital for the balance not brought in cash.

Case 3: New Partner Cannot Bring Goodwill in Cash

Method A — Raising and Writing Off Goodwill:

• Raise goodwill: Credit old partners in old ratio
• Write off goodwill: Debit all partners in new ratio

Method B — Direct Adjustment:
$$\text{New Partner's Capital A/c Dr.}$$
$$\quad \text{To Old Partners' Capital A/cs (sacrificing ratio)}$$

Case 4: Goodwill Already Exists in Books

• First write off existing goodwill by debiting old partners in old ratio
• Then treat new goodwill as per Cases 1, 2, or 3 above

Case 5: Hidden Goodwill

When goodwill is not given, it is inferred:
$$\text{Total Capital (implied)} = \frac{\text{New Partner's Capital}}{\text{New Partner's Share}}$$
$$\text{Goodwill} = \text{Implied Total Capital} - \text{Actual Total Capital}$$

Treatment of Accumulated Profits, Losses and Reserves on Admission:

At the time of admission of a new partner, any accumulated profits, reserves, or losses appearing in the balance sheet must be dealt with as follows:

1. Accumulated Profits / General Reserve / Reserve Fund (Credit Balance):

These belong to the old partners as they were earned before the new partner's admission. They are transferred to old partners' capital accounts in their old profit sharing ratio:

$$\text{General Reserve A/c Dr.}$$
$$\quad \text{To Old Partners' Capital A/cs (old ratio)}$$

$$\text{Profit \& Loss A/c Dr. (if Cr. balance)}$$
$$\quad \text{To Old Partners' Capital A/cs (old ratio)}$$

2. Accumulated Losses (Debit Balance of P&L Account) / Deferred Revenue Expenditure:

These are losses incurred before the new partner's admission and must be borne by old partners only:

$$\text{Old Partners' Capital A/cs Dr. (old ratio)}$$
$$\quad \text{To Profit \& Loss A/c (if Dr. balance)}$$

Reason: The new partner should neither benefit from past profits nor bear past losses. All such items must be cleared before the new partner joins, ensuring a clean start for the reconstituted firm.

Note: The new profit sharing ratio is NOT used for this adjustment — only the old profit sharing ratio is used.

Values of Assets and Liabilities After Revaluation:

After revaluation, assets and liabilities appear at their revised (revalued) figures in the new balance sheet. The old book values are replaced by the new revalued amounts.

Example:

Suppose A and B are partners (old ratio 2:1). C is admitted. The following revaluations are made:

• Land & Building: increased from Rs. 50,000 to Rs. 60,000
• Stock: decreased from Rs. 20,000 to Rs. 18,000
• Provision for Doubtful Debts: created at Rs. 1,000 on Debtors of Rs. 20,000

Revaluation Account:

Balance Sheet (Extract) After Revaluation:

Conclusion: After revaluation, assets appear at their new revalued figures (not original book values), and liabilities are adjusted to reflect their current obligations. The gain/loss on revaluation is distributed among old partners before the new partner joins.

Given:

• Old ratio A : B = 3 : 2
• C's share = 1/6

Working:

Remaining share for A and B = $1 - \frac{1}{6} = \frac{5}{6}$

A's new share = $\frac{3}{5} \times \frac{5}{6} = \frac{15}{30} = \frac{1}{2}$

B's new share = $\frac{2}{5} \times \frac{5}{6} = \frac{10}{30} = \frac{1}{3}$

C's share = $\frac{1}{6} = \frac{5}{30}$

New ratio = $\frac{15}{30} : \frac{10}{30} : \frac{5}{30}$ = 3 : 2 : 1

Given:

• Old ratio A : B : C = 3 : 2 : 1
• D's share = 10% = 1/10

Working:

Remaining share = $1 - \frac{1}{10} = \frac{9}{10}$

A's new share = $\frac{3}{6} \times \frac{9}{10} = \frac{27}{60} = \frac{9}{20}$

B's new share = $\frac{2}{6} \times \frac{9}{10} = \frac{18}{60} = \frac{6}{20}$

C's new share = $\frac{1}{6} \times \frac{9}{10} = \frac{9}{60} = \frac{3}{20}$

D's share = $\frac{1}{10} = \frac{2}{20}$

New ratio = $\frac{9}{20} : \frac{6}{20} : \frac{3}{20} : \frac{2}{20}$ = 9 : 6 : 3 : 2

Given:

• Old ratio X : Y = 5 : 3
• Z's share = 1/10, acquired equally from X and Y
• X's sacrifice = Y's sacrifice = $\frac{1}{10} \times \frac{1}{2} = \frac{1}{20}$

Working:

X's new share = $\frac{5}{8} - \frac{1}{20} = \frac{25}{40} - \frac{2}{40} = \frac{23}{40}$

Y's new share = $\frac{3}{8} - \frac{1}{20} = \frac{15}{40} - \frac{2}{40} = \frac{13}{40}$

Z's share = $\frac{1}{10} = \frac{4}{40}$

New ratio = X : Y : Z = 23 : 13 : 4