Step-by-step Derivation:

Step 1: Assume the total share of the firm is 1.

Let the total profit be 1.

Step 2: Determine the remaining share after giving the new partner's share.

Sumit's share = $ \frac{1}{5} $

Remaining share for Anil and Vishal = $ 1 - \frac{1}{5} = \frac{4}{5} $

Step 3: Distribute the remaining share among the old partners in their old profit-sharing ratio.

Anil’s new share = $ \frac{3}{5} \text{ of the remaining share} = \frac{3}{5} \times \frac{4}{5} = \frac{12}{25} $

Vishal’s new share = $ \frac{2}{5} \text{ of the remaining share} = \frac{2}{5} \times \frac{4}{5} = \frac{8}{25} $

Step 4: Combine the shares of all partners to form the new ratio.

Sumit's share = $ \frac{1}{5} $. To make the denominator common, multiply by $ \frac{5}{5} \implies \frac{1}{5} \times \frac{5}{5} = \frac{5}{25} $

New Ratio (Anil : Vishal : Sumit) = $ \frac{12}{25} : \frac{8}{25} : \frac{5}{25} $

Thus, the new profit sharing ratio is 12:8:5.

Step-by-step Derivation:

Step 1: Calculate each old partner's new share by subtracting the sacrificed share from their old share.

Anshu’s old share = $ \frac{3}{5} $

Share surrendered by Anshu = $ \frac{2}{10} $

Anshu’s new share = $ \text{Old Share} - \text{Share Surrendered} = \frac{3}{5} - \frac{2}{10} = \frac{6-2}{10} = \frac{4}{10} $

Nitu’s old share = $ \frac{2}{5} $

Share surrendered by Nitu = $ \frac{1}{10} $

Nitu’s new share = $ \text{Old Share} - \text{Share Surrendered} = \frac{2}{5} - \frac{1}{10} = \frac{4-1}{10} = \frac{3}{10} $

Step 2: Combine the shares of all partners to form the new ratio.

Jyoti's share is given as $ \frac{3}{10} $ (which is the sum of shares surrendered by Anshu and Nitu: $ \frac{2}{10} + \frac{1}{10} = \frac{3}{10} $).

New Ratio (Anshu : Nitu : Jyoti) = $ \frac{4}{10} : \frac{3}{10} : \frac{3}{10} $

Thus, the new profit sharing ratio is 4:3:3.

Step-by-step Derivation:

Step 1: Calculate the actual share sacrificed by each old partner.

Ram’s old share = $ \frac{3}{5} $

Share sacrificed by Ram = $ \frac{1}{4} \text{ of } \frac{3}{5} = \frac{1}{4} \times \frac{3}{5} = \frac{3}{20} $

Shyam’s old share = $ \frac{2}{5} $

Share sacrificed by Shyam = $ \frac{1}{3} \text{ of } \frac{2}{5} = \frac{1}{3} \times \frac{2}{5} = \frac{2}{15} $

Step 2: Calculate the new share for each old partner.

Ram’s new share = $ \text{Old Share} - \text{Share Sacrificed} = \frac{3}{5} - \frac{3}{20} = \frac{12-3}{20} = \frac{9}{20} $

Shyam’s new share = $ \text{Old Share} - \text{Share Sacrificed} = \frac{2}{5} - \frac{2}{15} = \frac{6-2}{15} = \frac{4}{15} $

Step 3: Calculate the new partner's share by summing the shares sacrificed by the old partners.

Ghanshyam’s share = $ \frac{3}{20} + \frac{2}{15} = \frac{9+8}{60} = \frac{17}{60} $

Step 4: Combine all shares into a new ratio with a common denominator.

The common denominator for 20, 15, and 60 is 60.

Ram's share = $ \frac{9}{20} = \frac{27}{60} $

Shyam's share = $ \frac{4}{15} = \frac{16}{60} $

Ghanshyam's share = $ \frac{17}{60} $

New Ratio (Ram : Shyam : Ghanshyam) = $ \frac{27}{60} : \frac{16}{60} : \frac{17}{60} $

Thus, the new profit sharing ratio is 27:16:17.

Step-by-step Calculation:

Step 1: Identify the Old and New Shares for each old partner.

Rohit:

Old Share = $ \frac{5}{5+3} = \frac{5}{8} $

New Share = $ \frac{4}{4+2+1} = \frac{4}{7} $

Mohit:

Old Share = $ \frac{3}{8} $

New Share = $ \frac{2}{7} $

Step 2: Calculate the sacrifice for each old partner.

Rohit’s Sacrifice = Old Share - New Share = $ \frac{5}{8} - \frac{4}{7} = \frac{5 \times 7 - 4 \times 8}{56} = \frac{35 - 32}{56} = \frac{3}{56} $

Mohit’s Sacrifice = Old Share - New Share = $ \frac{3}{8} - \frac{2}{7} = \frac{3 \times 7 - 2 \times 8}{56} = \frac{21 - 16}{56} = \frac{5}{56} $

Step 3: Formulate the Sacrificing Ratio.

Sacrificing Ratio (Rohit : Mohit) = $ \frac{3}{56} : \frac{5}{56} $

Thus, the sacrificing ratio is 3:5.

Step-by-step Calculation:

Step 1: Calculate the Sacrifice or Gain for Ramesh.

Old Share = $ \frac{4}{7} $; New Share = $ \frac{2}{6} $

Ramesh's Sacrifice = $ \frac{4}{7} - \frac{2}{6} = \frac{24 - 14}{42} = \frac{10}{42} $. Since the result is positive, Ramesh has made a sacrifice.

Step 2: Calculate the Sacrifice or Gain for Suresh.

Old Share = $ \frac{3}{7} $; New Share = $ \frac{3}{6} = \frac{1}{2} $

Suresh's Sacrifice/Gain = $ \frac{3}{7} - \frac{3}{6} = \frac{18 - 21}{42} = -\frac{3}{42} $. Since the result is negative, Suresh has made a gain.

Step 3: Analyse the result.

Ramesh has sacrificed a $ \frac{10}{42} $ share.

Suresh has gained a $ \frac{3}{42} $ share.

The new partner, Mohan, has gained his share of $ \frac{1}{6} $ or $ \frac{7}{42} $.

We can verify that Total Sacrifice = Total Gain ($ \frac{10}{42} = \frac{3}{42} + \frac{7}{42} $).

In this specific case, Ramesh is the only sacrificing partner. Suresh, being a gaining partner, will also have to compensate Ramesh for his gain. The treatment of goodwill would involve debiting both Suresh's and Mohan's capital accounts and crediting Ramesh's capital account.

Total Profit = $\text{₹} \ (4,00,000 + 3,98,000 + 4,50,000 + 4,45,000 + 5,00,000) = \text{₹} \ 21,93,000$

Average Profit = $ \frac{\text{₹} \ 21,93,000}{5} = \text{₹} \ 4,38,600 $

Goodwill = Average Profit × No. of years' purchase = $\text{₹} \ 4,38,600 \times 4 = \textbf{$\text{₹} \ 17,54,400$}$

Step 1: Calculate Average Profit

Average Profit = $ \frac{\text{₹} \ (40,000+50,000+55,000+70,000+85,000)}{5} = \text{₹} \ 60,000 $

Step 2: Calculate Normal Profit

Normal Profit = $ \text{₹} \ 5,00,000 \times \frac{10}{100} = \text{₹} \ 50,000 $

Step 3: Calculate Super Profit

Super Profit = Average Profit - Normal Profit = $\text{₹} \ 60,000 - \text{₹} \ 50,000 = \text{₹} \ 10,000$

Step 4: Calculate Goodwill

Goodwill = Super Profit × No. of years' purchase = $\text{₹} \ 10,000 \times 3 = \textbf{$\text{₹} \ 30,000$}$

(a) Capitalisation of Average Profits Method

Capitalised Value of the Firm = $ \text{₹} \ 1,00,000 \times \frac{100}{10} = \text{₹} \ 10,00,000 $

Goodwill = Capitalised Value - Capital Employed = $\text{₹} \ 10,00,000 - \text{₹} \ 8,20,000 = \textbf{$\text{₹} \ 1,80,000$}$

(b) Capitalisation of Super Profits Method

Average Profit = $\text{₹} \ 1,00,000$

Normal Profit = Capital Employed × Normal Rate = $\text{₹} \ 8,20,000 \times \frac{10}{100} = \text{₹} \ 82,000$

Super Profit = Average Profit - Normal Profit = $\text{₹} \ 1,00,000 - \text{₹} \ 82,000 = \text{₹} \ 18,000$

Goodwill = $ \text{Super Profit} \times \frac{100}{\text{Normal Rate of Return}} = \text{₹} \ 18,000 \times \frac{100}{10} = \textbf{$\text{₹} \ 1,80,000$}$

Working Note: Calculation of Sacrificing Ratio

Sacrificing Ratio = Old Ratio - New Ratio

• A's Sacrifice = $ \frac{3}{5} - \frac{2}{4} = \frac{12-10}{20} = \frac{2}{20} $
• B's Sacrifice = $ \frac{2}{5} - \frac{1}{4} = \frac{8-5}{20} = \frac{3}{20} $

The Sacrificing Ratio of A:B is 2:3.

Journal Entries

Working Notes:

1. Mohan's Share of Goodwill: $ \text{₹} \ 80,000 \times \frac{1}{4} = \text{₹} \ 20,000 $

2. Sacrificing Ratio: Old Ratio (Ram:Shyam) = 1:1. New ratio is not given, so it is assumed old partners sacrifice in their old ratio. Thus, Sacrificing Ratio = 1:1.

Journal Entry

Journal Entries

Working Note: Calculation of Hidden Goodwill

Sem's share of Goodwill = $\text{₹} \ 1,00,000 \times \frac{1}{4} = \text{₹} \ 25,000$. This will be adjusted through his current account.

Journal Entry

Books of Rajinder, Surinder and Narender

Journal

Books of A, B and C

Journal

Journal Entries

Revaluation Account

Dr.Cr.

Revaluation Account

Dr.Cr.

Partners’ Capital Accounts

Dr.Cr.

Balance Sheet of A, B and C as on April 01, 2017

1. Calculation of New Profit Sharing Ratio:

Let total share = 1. C's Share = $1/4$. Remaining Share = $1 - 1/4 = 3/4$.

A's New Share = $ \frac{3}{4} \times \frac{2}{3} = \frac{6}{12} = \frac{2}{4} $

B's New Share = $ \frac{3}{4} \times \frac{1}{3} = \frac{3}{12} = \frac{1}{4} $

The new profit sharing ratio (A:B:C) is 2:1:1.

2. Calculation of Required Capitals (Based on C's Capital):

C brings $\text{₹} \ 20,000$ for a 1/4 share. Therefore, the total capital of the new firm should be $ \text{₹} \ 20,000 \times \frac{4}{1} = \text{₹} \ 80,000 $.

A's Required Capital = $ \text{₹} \ 80,000 \times \frac{2}{4} = \text{₹} \ 40,000 $.

B's Required Capital = $ \text{₹} \ 80,000 \times \frac{1}{4} = \text{₹} \ 20,000 $.

C's Required Capital = $ \text{₹} \ 80,000 \times \frac{1}{4} = \text{₹} \ 20,000$ (which he brings).

3. Calculation of Surplus or Deficit:

Conclusion: A has an excess capital of $\text{₹} \ 5,000$ and will withdraw this amount. B has a deficit of $\text{₹} \ 5,000$ and will bring in this amount.

Journal Entries for Capital Adjustment

1. Calculation of New Profit Sharing Ratio:

Assuming X and Y continue to share the remaining profit in their old ratio (assumed equal, 1:1).

Z's Share = $1/5$. Remaining Share = $1 - 1/5 = 4/5$.

X's New Share = $ \frac{4}{5} \times \frac{1}{2} = \frac{2}{5} $

Y's New Share = $ \frac{4}{5} \times \frac{1}{2} = \frac{2}{5} $

The new profit sharing ratio (X:Y:Z) is 2:2:1.

2. Calculation of Required Capitals (Based on Agreed Total Capital):

Agreed Total Capital = $\text{₹} \ 4,00,000$.

X's Required Capital = $ \text{₹} \ 4,00,000 \times \frac{2}{5} = \text{₹} \ 1,60,000 $.

Y's Required Capital = $ \text{₹} \ 4,00,000 \times \frac{2}{5} = \text{₹} \ 1,60,000 $.

Z's Required Capital = $ \text{₹} \ 4,00,000 \times \frac{1}{5} = \text{₹} \ 80,000$ (This is the amount Z will bring).

3. Calculation of Surplus or Deficit for X and Y:

Conclusion: X has to withdraw $\text{₹} \ 35,000$ and Y has to withdraw $\text{₹} \ 5,000$. Z has to bring in $\text{₹} \ 80,000$.

(a) Journal Entries when settlement is in Cash

(b) Journal Entries when settlement is via Current Accounts

Working Note: Calculation of Sacrifice and Gain

Here, Manju is the gaining partner and Anju is the sacrificing partner. Manju will compensate Anju for the 1/10th share of goodwill she has gained.

Amount of Compensation = Total Goodwill × Gaining Share = $\text{₹} \ 30,000 \times \frac{1}{10} = \text{₹} \ 3,000$.

Adjustment Journal Entry

Journal

These accumulated profits and losses were earned before the change in ratio and thus belong to the partners in their old ratio of 5:3:2.

Journal Entries

Journal

Working Note 1: Calculation of Sacrifice and Gain

A is the gaining partner and C is the sacrificing partner. A will compensate C for the 2/9th share of goodwill.

Amount of Compensation = $\text{₹} \ 90,000 \times \frac{2}{9} = \text{₹} \ 20,000$.

Revaluation Account

Dr.Cr.

Journal Entries

Journal

The correct option is (a).

Reasoning and Calculation:

When the new partner's share is given, but the problem does not specify how the new partner acquires this share from the old partners, it is assumed that the old partners will share the remaining profit in their old profit-sharing ratio.

Step 1: Calculate the remaining share of profit for old partners.

Let the total share of the firm be 1.

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

Remaining Share = $1 \ - \ \frac{1}{4} = \frac{3}{4}$

Step 2: Distribute the remaining share between A and B in their old ratio (3:1).

A's New Share = $\frac{3}{4}$ of the remaining share = $\frac{3}{4} \ \times \ \frac{3}{4} = \frac{9}{16}$

B's New Share = $\frac{1}{4}$ of the remaining share = $\frac{1}{4} \ \times \ \frac{3}{4} = \frac{3}{16}$

Step 3: Determine the new profit sharing ratio.

C's Share = $\frac{1}{4}$. To get a common denominator, we multiply by $\frac{4}{4}$, so C's share is $\frac{4}{16}$.

The new profit sharing ratio of A : B : C is $\frac{9}{16} : \frac{3}{16} : \frac{4}{16}$.

This corresponds to option (a).

The correct option is (a).

Reasoning and Calculation:

In this case, the shares sacrificed by the old partners (X and Y) in favour of the new partner (Z) are explicitly given. The new profit sharing ratio is calculated by deducting the sacrificed share from the old partner's old share.

Old Ratio of X and Y = 3:2, so X = $\frac{3}{5}$ and Y = $\frac{2}{5}$.

Step 1: Calculate X's new share.

X's New Share = X's Old Share - Share Sacrificed by X

X's New Share = $\frac{3}{5} \ - \ \frac{3}{20} = \frac{12 \ - \ 3}{20} = \frac{9}{20}$

Step 2: Calculate Y's new share.

Y's New Share = Y's Old Share - Share Sacrificed by Y

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

Step 3: Determine the new profit sharing ratio.

Z's Share = $\frac{1}{5}$, which is equal to $\frac{4}{20}$.

The new profit sharing ratio of X : Y : Z is $\frac{9}{20} : \frac{7}{20} : \frac{4}{20}$.

This gives the ratio 9 : 7 : 4, which corresponds to option (a).

The correct option is (b).

Reasoning and Calculation:

When a new partner is admitted for a certain share and the problem does not specify how the old partners contribute to this new share, it is assumed that the old partners sacrifice their share of profits in their old profit-sharing ratio.

In this case, the old profit-sharing ratio of A and B is 3:1. Therefore, their sacrificing ratio will also be 3:1.

Verification by Calculation:

Step 1: Calculate the new profit sharing ratio.

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 = $\frac{1}{4} \ \times \ \frac{3}{4} = \frac{3}{16}$

Step 2: Calculate the sacrificed share for each partner.

Sacrifice = Old Ratio - New Ratio

A's Sacrifice = $\frac{3}{4} \ - \ \frac{9}{16} = \frac{12 \ - \ 9}{16} = \frac{3}{16}$

B's Sacrifice = $\frac{1}{4} \ - \ \frac{3}{16} = \frac{4 \ - \ 3}{16} = \frac{1}{16}$

Step 3: Determine the sacrificing ratio.

Sacrificing Ratio of A : B = $\frac{3}{16} : \frac{1}{16}$

This simplifies to 3 : 1, which is the same as their old profit-sharing ratio and corresponds to option (b).

The correct option is (c) old partner’s capital account.

Reasoning:

General Reserve represents accumulated profits that were earned by the firm before the admission of the new partner. Therefore, it belongs exclusively to the old partners. At the time of admission, it is distributed among the old partners in their old profit-sharing ratio by crediting their capital (or current) accounts.

The correct option is (b) Rs. 5,000 each.

Reasoning and Calculation:

The amount of goodwill brought by the new partner is distributed among the old partners in their sacrificing ratio. First, we need to determine the share sacrificed by each old partner.

Step 1: Determine the share sacrificed by each partner.

Ashish's total share = $\frac{1}{4}$

Share sacrificed by Asha = $\frac{1}{8}$ (given)

Share sacrificed by Nisha = Total Share - Share from Asha = $\frac{1}{4} \ - \ \frac{1}{8} = \frac{2 \ - \ 1}{8} = \frac{1}{8}$

So, the sacrificing ratio of Asha : Nisha is $\frac{1}{8} : \frac{1}{8}$, which is 1 : 1.

Step 2: Calculate Ashish's share of goodwill.

Total Goodwill of the firm = $\textsf{₹ } \ 40,000$

Ashish's share of Goodwill = $\textsf{₹ } \ 40,000 \ \times \ \frac{1}{4} = \textsf{₹ } \ 10,000$

Step 3: Distribute Ashish's share of goodwill between Asha and Nisha in their sacrificing ratio (1:1).

Amount credited to Asha's Capital A/c = $\textsf{₹ } \ 10,000 \ \times \ \frac{1}{2} = \textsf{₹ } \ 5,000$

Amount credited to Nisha's Capital A/c = $\textsf{₹ } \ 10,000 \ \times \ \frac{1}{2} = \textsf{₹ } \ 5,000$

The correct option is (c) old partnership is reconstituted.

Reasoning:

The admission of a new partner changes the existing agreement among the partners. This leads to the termination of the old partnership agreement and the formation of a new one. This process is known as the reconstitution of the partnership. The firm itself (the business) continues to exist, but the relationship among the partners is altered. Dissolution of the firm means the business is permanently closed down, which is not the case here.

The correct option is (b) Assets account.

Reasoning:

When the value of an asset increases, the journal entry to record this change is:

Asset A/c ............... Dr.

    To Revaluation A/c (or Profit and Loss Adjustment A/c)

Therefore, the increase is debited to the specific Assets account to reflect its new, higher value in the books. The corresponding credit for the gain is made to the Revaluation Account (also known as the Profit and Loss Adjustment Account).

The correct option is (a) old partners in old profit sharing ratio.

Reasoning:

Undistributed profits (like General Reserve, Profit and Loss A/c credit balance) were accumulated from the earnings of the firm before the new partner was admitted. Therefore, these profits belong exclusively to the partners who were present during that period. They must be distributed among the old partners in their old profit-sharing ratio.

This problem requires the calculation of goodwill using the Average Profit Method. The steps are as follows:

Step 1: Calculate the Total Profit of the last three years

Total Profit = Profit of Year 1 + Profit of Year 2 + Profit of Year 3

Total Profit = $\textsf{₹ } \ 5,00,000 \ + \ \textsf{₹ } \ 4,00,000 \ + \ \textsf{₹ } \ 6,00,000 = \textsf{₹ } \ 15,00,000$

Step 2: Calculate the Average Profit

The formula for Average Profit is:

$\text{Average Profit} = \frac{\text{Total Profit}}{\text{Number of Years}}$

Average Profit = $\frac{\textsf{₹ } \ 15,00,000}{3} = \textsf{₹ } \ 5,00,000$

Step 3: Calculate the Goodwill

The formula for Goodwill is:

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

Goodwill = $\textsf{₹ } \ 5,00,000 \ \times \ 4 = \textsf{₹ } \ 20,00,000$

The value of the firm's goodwill is $\textsf{₹ } \ 20,00,000$.

This problem requires the calculation of goodwill using the Super Profit Method. The calculation involves the following steps:

Step 1: Calculate the Average Profit of the last four years

Total Profit = $\textsf{₹ } \ 16,000 + \textsf{₹ } \ 20,000 + \textsf{₹ } \ 24,000 + \textsf{₹ } \ 32,000 = \textsf{₹ } \ 92,000$

Average Profit = $\frac{\textsf{₹ } \ 92,000}{4} = \textsf{₹ } \ 23,000$

Step 2: Calculate the Normal Profit

Normal Profit represents the expected return on the capital invested in the business.

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

Normal Profit = $\textsf{₹ } \ 1,00,000 \ \times \ \frac{18}{100} = \textsf{₹ } \ 18,000$

Step 3: Calculate the Super Profit

Super Profit is the excess of average profit over the normal profit.

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

Super Profit = $\textsf{₹ } \ 23,000 \ - \ \textsf{₹ } \ 18,000 = \textsf{₹ } \ 5,000$

Step 4: Calculate the Goodwill

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

Goodwill = $\textsf{₹ } \ 5,000 \ \times \ 3 = \textsf{₹ } \ 15,000$

The value of the firm's goodwill is $\textsf{₹ } \ 15,000$.

Using the data and calculations from the previous question:

Average Profit = $\textsf{₹ } \ 23,000$

Super Profit = $\textsf{₹ } \ 5,000$

Capital Investment = $\textsf{₹ } \ 1,00,000$

Normal Rate of Return = $18\%$

1. Goodwill by Capitalisation of Super Profits Method

Under this method, goodwill is calculated by determining the amount of capital needed to earn the super profit at the normal rate of return.

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

Goodwill = $\textsf{₹ } \ 5,000 \ \times \ \frac{100}{18} = \textsf{₹ } \ 27,777.78$

So, Goodwill is approximately $\textsf{₹ } \ 27,778$.

2. Goodwill by Capitalisation of Average Profits Method

This method involves two steps:

(i) Calculate the Capitalised Value of the Firm: This is the total capital that should be invested to earn the average profit at the normal rate of return.

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

Capitalised Value = $\textsf{₹ } \ 23,000 \ \times \ \frac{100}{18} = \textsf{₹ } \ 1,27,777.78 \approx \textsf{₹ } \ 1,27,778$

(ii) Calculate Goodwill:

$\text{Goodwill} = \text{Capitalised Value of the Firm} \ - \ \text{Actual Capital Investment}$

Goodwill = $\textsf{₹ } \ 1,27,778 \ - \ \textsf{₹ } \ 1,00,000 = \textsf{₹ } \ 27,778$

Conclusion and Verification

No, the amount of goodwill will not be different. As verified by the numerical calculations above, both methods yield the same result:

• Goodwill by Capitalisation of Super Profits = $\textsf{₹ } \ 27,778$

• Goodwill by Capitalisation of Average Profits = $\textsf{₹ } \ 27,778$

Working Note:

The sacrificing ratio needs to be determined to distribute the premium for goodwill. Since it's not specified how Kachroo acquires his share, it is assumed that the old partners sacrifice in their old profit-sharing ratio.

Old Ratio (Giri : Shanta) = 1:1

Therefore, Sacrificing Ratio (Giri : Shanta) = 1:1.

(a) When no goodwill appears in the books of the firm.

The amount of goodwill brought by Kachroo ($\textsf{₹ } \ 20,000$) will be distributed between Giri and Shanta in their sacrificing ratio (1:1).

Journal Entries

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

As per Accounting Standard 26, existing goodwill must be written off at the time of reconstitution of the firm. It will be written off against the old partners in their old profit-sharing ratio (1:1).

Journal Entries

Working Notes:

1. Calculation of Opening Cash Balance (before admission)

We can find the opening cash balance by preparing the Balance Sheet of the old firm.

Balance Sheet (Old Firm)

2. Revaluation Account

To record the loss on revaluation of assets.

Revaluation Account

Dr.Cr.

3. Partners' Capital Accounts

To calculate the adjusted capitals of all partners.

Partners’ Capital Accounts

Dr.Cr.

4. Ascertainment of Cash in Hand (Closing Balance)

Balance Sheet of the New Firm as at ...

Note: There is a discrepancy of $\textsf{₹ } \ 100$ in the Balance Sheet, which indicates a possible error in the figures provided in the question.

Working Notes:

1. Calculation of Sacrificing Ratio:

Since the question does not specify how Ina acquires her share, it is assumed that the old partners, Benu and Sunil, sacrifice in their old profit-sharing ratio of 3:2. Thus, the Sacrificing Ratio is 3:2.

2. Distribution of Goodwill, General Reserve, and P&L A/c:

• Goodwill ($\textsf{₹ } \ 1,00,000$): Benu gets $\textsf{₹ } \ 60,000$ (3/5), Sunil gets $\textsf{₹ } \ 40,000$ (2/5).

• General Reserve ($\textsf{₹ } \ 1,20,000$): Benu gets $\textsf{₹ } \ 72,000$ (3/5), Sunil gets $\textsf{₹ } \ 48,000$ (2/5).

• Profit & Loss A/c ($\textsf{₹ } \ 60,000$): Benu gets $\textsf{₹ } \ 36,000$ (3/5), Sunil gets $\textsf{₹ } \ 24,000$ (2/5).

Journal Entries

1. Calculation of New Profit Sharing Ratio

Gaurav's Share = $\frac{1}{5}$

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

This remaining share will be divided between Ashoo and Rahul in their old ratio of 5:3.

Ashoo's New Share = $\frac{4}{5} \times \frac{5}{8} = \frac{20}{40} = \frac{5}{10}$

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

Gaurav's Share = $\frac{1}{5} = \frac{2}{10}$

New Profit Sharing Ratio (Ashoo : Rahul : Gaurav) = 5 : 3 : 2

2. Calculation of Capital to be brought in by Gaurav

The adjusted capitals of the old partners represent the capital for their combined share in the new firm.

Combined Capital of Ashoo and Rahul = $\textsf{₹ } \ 45,000 + \textsf{₹ } \ 35,000 = \textsf{₹ } \ 80,000$

Combined Share of Ashoo and Rahul = $\frac{4}{5}$

Total Capital of the New Firm (based on old partners' capital) = $\textsf{₹ } \ 80,000 \times \frac{5}{4} = \textsf{₹ } \ 1,00,000$

Gaurav's Proportionate Capital = Total Capital of New Firm $\times$ Gaurav's Share

Gaurav's Capital = $\textsf{₹ } \ 1,00,000 \times \frac{1}{5} = \textbf{\textsf{₹ } \ 20,000}$

3. Journal Entries

The sacrificing ratio will be the same as the old ratio, 5:3.

Journal Entries

The admission of a new partner leads to the reconstitution of the partnership firm. The following matters need to be adjusted at this time:

1. Ascertainment of New Profit Sharing Ratio and Sacrificing Ratio: The profit-sharing ratio changes, so a new ratio for all partners must be calculated. The sacrificing ratio (the proportion in which old partners give up their share) is also determined.

2. Accounting Treatment of Goodwill: Goodwill of the firm is valued, and the new partner compensates the sacrificing partners for acquiring a share in future profits. This is done by bringing in a 'premium for goodwill'.

3. Revaluation of Assets and Reassessment of Liabilities: Assets and liabilities are revalued to their current market values. The resulting profit or loss is distributed among the old partners in their old profit-sharing ratio.

4. Distribution of Accumulated Profits, Reserves, and Losses: Any existing reserves, undistributed profits, or losses appearing in the old balance sheet are distributed among the old partners in their old profit-sharing ratio.

5. Adjustment of Partners' Capitals: The capital contribution of the new partner is recorded. Sometimes, the capitals of the old partners are also adjusted to be in proportion to their new profit-sharing ratio.

It is necessary to ascertain the new profit-sharing ratio for old partners, as well as the new partner, for the following reasons:

• Reduction in Share: When a new partner is admitted, they acquire their share of future profits from the old partners. Consequently, the share of the old partners gets reduced. The new profit-sharing ratio reflects this new, reduced share for each of the old partners.

• Basis for Future Profits: The new profit-sharing ratio becomes the basis for distributing all future profits and losses of the reconstituted firm among all partners (including the new one).

• Basis for Future Adjustments: This new ratio is also used for making future adjustments, such as the treatment of goodwill at the time of retirement or death of a partner from the reconstituted firm.

In essence, the admission of a partner terminates the old partnership agreement and creates a new one with a new set of relationships, which must be defined by the new profit-sharing ratio.

Meaning of Sacrificing Ratio

The Sacrificing Ratio is the ratio in which the old partners agree to surrender or 'sacrifice' a portion of their share of profits in favour of a new partner. It is calculated as the difference between an old partner's old profit share and their new profit share.

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

Purpose of Calculation

The primary reason for calculating the sacrificing ratio is for the treatment of goodwill. When a new partner is admitted, they are required to bring in an amount, known as the 'Premium for Goodwill', to compensate the old partners. This compensation is for the loss of future profits that the old partners will incur due to the admission of the new partner.

The sacrificing ratio determines the proportion in which this premium for goodwill is distributed among the old partners. The partner who sacrifices a larger share of their profit is entitled to a larger share of the goodwill compensation.

The sacrificing ratio is used whenever there is a reconstitution of a partnership firm that results in a change in the profit-sharing ratio of existing partners. The main occasions are:

1. Admission of a New Partner:

This is the most common occasion. The premium for goodwill brought in by the new partner is distributed among the old partners in their sacrificing ratio to compensate them for the share of profit they have surrendered.

2. Change in Profit Sharing Ratio among Existing Partners:

When existing partners decide to change their mutual profit-sharing ratio, some partners may gain a share while others sacrifice a share. In such cases, the gaining partner(s) must compensate the sacrificing partner(s) by paying a proportionate amount of the firm's goodwill. The sacrificing ratio is used to determine who receives this compensation.

As per Accounting Standard 26 (AS-26) on Intangible Assets, goodwill should only be recorded in the books when consideration in money or money's worth has been paid for it. Self-generated goodwill should not be shown as an asset.

Therefore, if any goodwill already exists in the books at the time of admission of a new partner, it must be written off immediately. This is done before recording the goodwill brought in by the new partner.

The existing goodwill is written off by debiting the capital accounts of the old partners in their old profit-sharing ratio and crediting the Goodwill Account. The journal entry would be:

Journal Entry

After this, the goodwill brought in by the new partner is treated separately in the usual manner.

There is a need for the revaluation of assets and reassessment of liabilities on the admission of a partner for the following key reasons:

• To Record True and Fair Value: Over time, the values of assets and liabilities shown in the Balance Sheet (book values) may differ significantly from their current market values. Revaluation is done to bring them to their true and fair values at the date of admission.

• To Give Credit to Old Partners: Any increase in the value of assets or decrease in the value of liabilities represents an unrealised profit. This profit was earned due to the efforts of the old partners before the new partner's admission. Therefore, this profit rightly belongs to the old partners and must be credited to their capital accounts in their old profit-sharing ratio.

• To Protect the New Partner: Conversely, any decrease in asset values or increase in liabilities is a loss that occurred before admission. The old partners must bear this loss. Revaluation ensures that the new partner does not suffer from a reduction in the value of assets that occurred prior to their joining.

• To Present a Fair Financial Position: Revaluation ensures that the Balance Sheet of the reconstituted firm shows a true and fair view of its financial position on the date the new partner is admitted.

In essence, revaluation is an exercise in fairness, ensuring that past profits or losses arising from changes in asset and liability values are correctly attributed to the old partners before the new profit-sharing arrangement begins.

Yes, it is highly advisable that assets and liabilities are revalued at the time of admission of a new partner. It is a crucial step to ensure fairness among the old and new partners.

Reasons for Revaluation

The primary reasons for revaluing assets and reassessing liabilities are as follows:

1. To Reflect True and Fair Value: The values of assets and liabilities recorded in the books (book value) may have changed over time due to market fluctuations, usage, or other factors. Revaluation brings these values to their current, more realistic market price, ensuring the Balance Sheet of the new firm presents a true and fair view.

2. To Credit Old Partners for Appreciation: If the value of an asset has increased, this appreciation is an unrealised profit earned through the efforts of the old partners before the new partner's admission. It is only fair that this gain is credited to the old partners' capital accounts in their old profit-sharing ratio.

3. To Protect the New Partner from Past Losses: Conversely, if an asset's value has decreased or a liability has increased, it represents a loss that occurred before the new partner joined. This loss must be borne by the old partners. Revaluation ensures that the new partner does not suffer financially for a loss that they did not contribute to.

4. To Ensure No Undue Advantage/Disadvantage: By revaluing, the firm ensures that neither the incoming partner gets an undue share in previously unrecorded gains, nor do the old partners pass on unrecorded losses to the new partner.

Accounting Treatment

The accounting treatment for revaluation is carried out by preparing a temporary nominal account called the Revaluation Account (or Profit and Loss Adjustment Account).

1. Recording Changes in Value:

• An increase in the value of an asset or a decrease in the value of a liability is a gain. It is credited to the Revaluation Account.

• A decrease in the value of an asset or an increase in the value of a liability is a loss. It is debited to the Revaluation Account.

• Any unrecorded asset is credited, and any unrecorded liability is debited to the Revaluation Account.

2. Ascertaining Profit or Loss on Revaluation:

After recording all changes, the Revaluation Account is balanced.

• If the credit side is greater than the debit side, the balancing figure is a Revaluation Profit.

• If the debit side is greater than the credit side, the balancing figure is a Revaluation Loss.

3. Distribution of Profit or Loss:

The resulting profit or loss on revaluation is transferred to the old partners' capital (or current) accounts in their old profit-sharing ratio. The new partner has no share in this profit or loss.

4. Balance Sheet Presentation:

In the new Balance Sheet prepared after the admission, all assets and liabilities are shown at their new, revalued figures.

Meaning of Goodwill

Goodwill is an intangible asset that represents the good name, reputation, and business connections of a firm. It is the value of the firm's ability to earn profits over and above the normal profit that would be earned by a similar business. This superior earning capacity arises from various favourable attributes that a business has built up over time, which helps in attracting and retaining customers.

In simple terms, it is the monetary value of a firm's reputation. It cannot be seen or touched but has a realisable value when the business is sold.

Factors Affecting Goodwill

The value of a firm's goodwill is influenced by numerous factors that contribute to its profit-earning capacity. Some of the key factors are:

1. Efficient Management: A firm with experienced, capable, and efficient management will have higher productivity and profitability, leading to higher goodwill.

2. Quality of Products/Services: If a firm consistently provides high-quality products and services, it builds a strong customer base and a good reputation, which enhances its goodwill.

3. Favourable Location: A business located in a prime or easily accessible area will attract more customers and, therefore, will have a higher value of goodwill.

4. Longevity of the Business: An older, well-established business is generally better known to customers and has a stronger reputation than a new one. This longevity contributes to a higher goodwill value.

5. Nature of Business: Businesses that deal in products with stable and high demand, or those that have a monopoly or limited competition, tend to have higher and more stable profits, resulting in greater goodwill.

6. Possession of Licenses, Patents, Trademarks: If a firm holds valuable patents, trademarks, or import licenses, it may have a competitive advantage over others, which increases the value of its goodwill.

7. Good Customer Relations: Excellent after-sales service and strong relationships with customers lead to repeat business and loyalty, which is a significant component of goodwill.

8. Low Risk: A business with lower inherent risks will be valued more highly, thus having greater goodwill.

Goodwill is valued to determine the compensation payable by a new partner to the old partners for acquiring a share in the firm's future profits. The following are the main methods of valuing goodwill:

1. Average Profit Method

Under this method, goodwill is calculated based on the average profits of the past few years. It assumes that a new business will not be able to earn profits in its initial years, so the new partner must compensate for the profits they will earn from day one.

The formula is:

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

To calculate the average profit, the past profits are adjusted for any abnormal gains or losses.

2. Super Profit Method

This method values goodwill based on the 'super profit', which is the excess of a firm's average profit over the normal profit (the return expected on the capital employed).

The steps are as follows:

1. Calculate Average Profit: Find the average profit of the past few years after adjustments.

2. Calculate Normal Profit: $\text{Normal Profit} = \text{Capital Employed} \ \times \ \text{Normal Rate of Return}$

3. Calculate Super Profit: $\text{Super Profit} = \text{Average Profit} \ - \ \text{Normal Profit}$

4. Calculate Goodwill: $\text{Goodwill} = \text{Super Profit} \ \times \ \text{Number of Years' Purchase}$

3. Capitalisation Method

This method values goodwill by capitalising the profits of the firm. It has two approaches:

(a) Capitalisation of Average Profit:

This approach determines the total value of the business based on its average profits and then deducts the actual capital employed to find the value of goodwill.

1. Calculate the Capitalised Value of the Firm: $\text{Capitalised Value} = \text{Average Profit} \ \times \ \frac{100}{\text{Normal Rate of Return}}$

2. Calculate Goodwill: $\text{Goodwill} = \text{Capitalised Value of Firm} \ - \ \text{Capital Employed}$

(b) Capitalisation of Super Profit:

This approach directly capitalises the super profit to find the value of goodwill.

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

When it is agreed that the capitals of all partners should be proportionate to their new profit-sharing ratio, adjustments are made to the partners' capital accounts. The process involves calculating the required capital for each partner and then adjusting any surplus or deficit by either cash withdrawal or contribution.

The total capital of the new firm can be determined in one of two ways:

Case 1: Based on the New Partner's Capital

The total capital of the firm is calculated based on the capital brought in by the new partner for their share.

Steps:

1. Calculate the Total Capital of the New Firm = New Partner's Capital $\times$ Reciprocal of their Profit Share.

2. Calculate the Required Capital for each partner by multiplying the total capital by their respective new profit share.

3. Compare the Required Capital with the Adjusted Existing Capital of each old partner (after all adjustments for goodwill, revaluation, reserves, etc.).

4. If the Existing Capital is more than the Required Capital, the partner has a surplus and will withdraw the excess cash. If the Existing Capital is less, the partner has a deficit and will bring in the required cash.

Illustration:

A and B are partners. Their adjusted capitals are A: $\textsf{₹ } \ 60,000$ and B: $\textsf{₹ } \ 40,000$. They admit C for a 1/4th share. C brings in $\textsf{₹ } \ 30,000$ as capital. Their new profit ratio is 2:1:1.

Total Capital of the firm = $\textsf{₹ } \ 30,000 \times \frac{4}{1} = \textsf{₹ } \ 1,20,000$.

A's Required Capital = $\textsf{₹ } \ 1,20,000 \times \frac{2}{4} = \textsf{₹ } \ 60,000$. (Existing = Required, No adjustment)

B's Required Capital = $\textsf{₹ } \ 1,20,000 \times \frac{1}{4} = \textsf{₹ } \ 30,000$. (Existing $\textsf{₹ } \ 40,000$ > Required $\textsf{₹ } \ 30,000$. B will withdraw $\textsf{₹ } \ 10,000$).

C's Required Capital = $\textsf{₹ } \ 1,20,000 \times \frac{1}{4} = \textsf{₹ } \ 30,000$. (He brings this amount).

Adjustment Entry for B: B's Capital A/c Dr. 10,000 To Cash/Bank A/c 10,000.

Case 2: Based on the Old Partners' Adjusted Capitals

The new partner is asked to bring in proportionate capital based on the combined capital of the old partners.

Steps:

1. Calculate the Combined Adjusted Capital of the old partners.

2. Determine the Combined Share of the old partners in the new firm.

3. Calculate the Total Capital of the New Firm = Combined Adjusted Capital $\times$ Reciprocal of their Combined Share.

4. Calculate the New Partner's Capital = Total Capital $\times$ New Partner's Share.

Illustration:

Using the same figures, A's and B's combined adjusted capital is $\textsf{₹ } \ 1,00,000$. Their combined share is 3/4.

Total Capital of the firm = $\textsf{₹ } \ 1,00,000 \times \frac{4}{3} = \textsf{₹ } \ 1,33,333$.

C's Capital to be brought in = $\textsf{₹ } \ 1,33,333 \times \frac{1}{4} = \textsf{₹ } \ 33,333$.

Adjustment Entry for C: Cash/Bank A/c Dr. 33,333 To C's Capital A/c 33,333.

When a new partner is admitted, they must compensate the sacrificing partners for the share of future profits they are acquiring. This compensation is called 'Premium for Goodwill'. If the new partner is not in a position to bring their share of goodwill in cash, the adjustment is made through their Capital Account (or preferably, their Current Account).

According to Accounting Standard 26 (AS-26), the Goodwill account cannot be raised in the books unless consideration in money or money's worth has been paid for it. Therefore, the modern and accepted practice is not to raise the Goodwill account but to pass an adjusting journal entry.

Accounting Treatment:

The treatment involves debiting the new partner's account and crediting the old partners' accounts in their sacrificing ratio.

1. Calculate the New Partner's Share of Goodwill: First, the total goodwill of the firm is valued, and then the new partner's share is calculated based on their profit-sharing ratio.

2. Pass the Adjustment Journal Entry: The new partner's Capital or Current Account is debited with their share of goodwill, and the sacrificing partners' Capital or Current Accounts are credited in their sacrificing ratio.

The journal entry is as follows:

Journal Entry

Note: Using the new partner's Current Account is often preferred for this adjustment. This ensures that their capital contribution remains intact and is not reduced by the goodwill adjustment. The debit balance in the current account is then shown on the asset side of the Balance Sheet until it is written off.

At the time of admission of a new partner, the treatment of goodwill depends on whether the new partner brings their share of goodwill in cash and what the old partners decide to do with that amount. The primary methods are as follows:

Method 1: Premium for Goodwill is Paid Privately

If the new partner pays their share of goodwill directly to the old partners outside the business (privately), no journal entry is recorded in the books of the firm, as it is a transaction between the partners in their personal capacity.

Method 2: Premium for Goodwill is Brought in Cash and Retained in the Business

This is the most common method. The accounting treatment involves two steps:

1. Entry for bringing in goodwill:

   Cash/Bank A/c Dr.

   To Premium for Goodwill A/c

2. Entry for distributing goodwill to sacrificing partners:

   Premium for Goodwill A/c Dr.

   To Sacrificing Partners' Capital A/cs (in sacrificing ratio)

Method 3: Premium for Goodwill is Brought in Cash and Withdrawn by Old Partners

The first two entries from Method 2 are passed. An additional entry is then passed for the withdrawal of the goodwill amount by the sacrificing partners.

1. Entry for withdrawal of goodwill:

   Sacrificing Partners' Capital A/cs Dr.

   To Cash/Bank A/c

Method 4: New Partner is Unable to Bring Goodwill in Cash

When the new partner does not bring their share of goodwill in cash, the adjustment is made through their capital or current account, as per AS-26.

1. Entry for goodwill adjustment:

   New Partner's Current A/c (or Capital A/c) Dr.

   To Sacrificing Partners' Capital A/cs (in sacrificing ratio)

Method 5: Dealing with Existing Goodwill

If goodwill already appears in the books of the old firm, it must first be written off by debiting the old partners' capital accounts in their old profit-sharing ratio.

1. Entry for writing off existing goodwill:

   Old Partners' Capital A/cs Dr. (in old ratio)

   To Goodwill A/c

After this, the goodwill brought by the new partner is treated as per the methods described above.

Accumulated profits, losses, and reserves are the results of past operations of the firm. Since they were earned or incurred before the admission of a new partner, they belong exclusively to the old partners and must be distributed among them. The new partner has no right to or liability for these past items.

The treatment involves transferring these items to the old partners' capital (or current) accounts in their old profit-sharing ratio.

Treatment of Accumulated Profits and Reserves

Items like General Reserve, Reserve Fund, Profit and Loss Account (Credit Balance), Workmen Compensation Reserve (excess over claim), and Investment Fluctuation Reserve (excess over loss in value) represent undistributed profits.

To distribute them, these accounts are debited (to close them), and the old partners' capital accounts are credited.

Journal Entry

Treatment of Accumulated Losses

Items like Profit and Loss Account (Debit Balance) and Deferred Revenue Expenditure (e.g., Advertisement Suspense Account) represent accumulated losses.

To write them off, the old partners' capital accounts are debited, and these loss accounts are credited.

Journal Entry

After revaluation of assets and reassessment of liabilities has been completed at the time of a partner's admission, the assets and liabilities appear at their new, revalued figures in the Balance Sheet of the reconstituted firm. The book values are adjusted to reflect their current market values.

Illustration with an Imaginary Balance Sheet

Let's assume the following Balance Sheet of A and B before the admission of C:

Balance Sheet (Before Admission)

Adjustments on C's Admission:

• Stock is to be appreciated by 20%.

• Machinery is to be depreciated by 10%.

• Creditors are found to be overvalued by $\textsf{₹ } \ 5,000$.

Revaluation Changes:

• Stock (New Value) = $\textsf{₹ } \ 50,000 + (20\% \text{ of } 50,000) = \textsf{₹ } \ 60,000$ (Increase of $\textsf{₹ } \ 10,000$)

• Machinery (New Value) = $\textsf{₹ } \ 1,10,000 - (10\% \text{ of } 1,10,000) = \textsf{₹ } \ 99,000$ (Decrease of $\textsf{₹ } \ 11,000$)

• Creditors (New Value) = $\textsf{₹ } \ 30,000 - \textsf{₹ } \ 5,000 = \textsf{₹ } \ 25,000$ (Decrease of $\textsf{₹ } \ 5,000$)

The Revaluation Profit will be $\textsf{₹ } \ 10,000 (Stock) + \textsf{₹ } \ 5,000 (Creditors) - \textsf{₹ } \ 11,000 (Machinery) = \textsf{₹ } \ 4,000$. This profit will be added to the capitals of A and B.

The Balance Sheet of the new firm will show the assets and liabilities at these new figures.

Balance Sheet (After Admission) - Extract

In this case, the new partner C's share is given, but the ratio in which the old partners (A and B) are sacrificing their share is not mentioned. Therefore, it is assumed that A and B will sacrifice their share in their old profit-sharing ratio, which is 3:2.

Step-by-step calculation:

1. Let the total profit of the firm be 1.

2. C's share in the profit is given as $\frac{1}{6}$.

3. Calculate the remaining share of profit for the old partners A and B:

$ \text{Remaining Share} = 1 - \text{C's Share} = 1 - \frac{1}{6} = \frac{5}{6} $

4. This remaining share of $\frac{5}{6}$ will be distributed between A and B in their old profit-sharing ratio (3:2).

$ \text{A's New Share} = \frac{5}{6} \times \frac{3}{5} = \frac{15}{30} = \frac{1}{2} $

$ \text{B's New Share} = \frac{5}{6} \times \frac{2}{5} = \frac{10}{30} = \frac{1}{3} $

5. Combine the new shares of all partners to find the new ratio:

$ \text{New Ratio (A : B : C)} = \frac{1}{2} : \frac{1}{3} : \frac{1}{6} $

To express this as a simple ratio, we find the common denominator (which is 6):

$ = \frac{3}{6} : \frac{2}{6} : \frac{1}{6} $

Thus, the new profit sharing ratio of A, B, and C is 3 : 2 : 1.

This scenario is similar to the previous one. The new partner D's share is given, but the sacrifice made by the old partners (A, B, and C) is not specified. We assume that the old partners sacrifice their share in their existing profit-sharing ratio (3:2:1).

Step-by-step calculation:

1. The old profit sharing ratio of A:B:C is 3:2:1 or $\frac{3}{6} : \frac{2}{6} : \frac{1}{6}$.

2. D is admitted for 10% share, which is equal to $\frac{10}{100} = \frac{1}{10}$.

3. Let the total profit of the firm be 1. The remaining share for A, B, and C is:

$ \text{Remaining Share} = 1 - \text{D's Share} = 1 - \frac{1}{10} = \frac{9}{10} $

4. This remaining share of $\frac{9}{10}$ will be shared by A, B, and C in their old ratio (3:2:1).

$ \text{A's New Share} = \frac{9}{10} \times \frac{3}{6} = \frac{27}{60} $

$ \text{B's New Share} = \frac{9}{10} \times \frac{2}{6} = \frac{18}{60} $

$ \text{C's New Share} = \frac{9}{10} \times \frac{1}{6} = \frac{9}{60} $

5. D's share is $\frac{1}{10}$, which can be written as $\frac{6}{60}$ to have a common denominator.

6. The new profit sharing ratio of A : B : C : D is:

$ = \frac{27}{60} : \frac{18}{60} : \frac{9}{60} : \frac{6}{60} $

We can simplify this by removing the common denominator and dividing all parts by their common factor, 3.

$ = 27 : 18 : 9 : 6 \implies 9 : 6 : 3 : 2 $

Thus, the new profit sharing ratio of A, B, C, and D is 9 : 6 : 3 : 2.

In this case, it is clearly stated that the new partner, Z, acquires his share equally from the old partners, X and Y. This means the sacrificing ratio of X and Y is 1:1.

Step-by-step calculation:

1. Old profit sharing ratio of X:Y is 5:3 or $\frac{5}{8} : \frac{3}{8}$.

2. Z is admitted for a $\frac{1}{10}$ share.

3. Z acquires this share equally from X and Y. So, the share sacrificed by each old partner is:

$ \text{Sacrifice by X} = \frac{1}{10} \times \frac{1}{2} = \frac{1}{20} $

$ \text{Sacrifice by Y} = \frac{1}{10} \times \frac{1}{2} = \frac{1}{20} $

4. Calculate the new share for X and Y by deducting their sacrifice from their old share.

$ \text{X's New Share} = \text{Old Share} - \text{Sacrificed Share} = \frac{5}{8} - \frac{1}{20} = \frac{25 - 2}{40} = \frac{23}{40} $

$ \text{Y's New Share} = \frac{3}{8} - \frac{1}{20} = \frac{15 - 2}{40} = \frac{13}{40} $

5. Z's share is $\frac{1}{10}$, which can be written as $\frac{4}{40}$ to have a common denominator.

6. The new profit sharing ratio of X : Y : Z is:

$ = \frac{23}{40} : \frac{13}{40} : \frac{4}{40} $

Thus, the new profit sharing ratio of X, Y, and Z is 23 : 13 : 4.

Here, the new partner D acquires his entire share from only one of the old partners, A. Therefore, only A's share will be reduced, while the shares of B and C will remain unchanged relative to each other.

Step-by-step calculation:

1. Old profit sharing ratio of A:B:C is 2:2:1 or $\frac{2}{5} : \frac{2}{5} : \frac{1}{5}$.

2. D is admitted for a $\frac{1}{8}$ share.

3. This entire share is acquired from A. So, the share sacrificed by A is $\frac{1}{8}$. B and C sacrifice nothing.

4. Calculate the new share for A. The shares of B and C remain the same.

$ \text{A's New Share} = \text{Old Share} - \text{Sacrificed Share} = \frac{2}{5} - \frac{1}{8} = \frac{16 - 5}{40} = \frac{11}{40} $

$ \text{B's New Share (Unchanged)} = \frac{2}{5} $

$ \text{C's New Share (Unchanged)} = \frac{1}{5} $

5. D's share is $\frac{1}{8}$.

6. To find the new ratio, we need a common denominator, which is 40.

$ \text{A} = \frac{11}{40} $

$ \text{B} = \frac{2}{5} = \frac{16}{40} $

$ \text{C} = \frac{1}{5} = \frac{8}{40} $

$ \text{D} = \frac{1}{8} = \frac{5}{40} $

Thus, the new profit sharing ratio of A, B, C, and D is 11 : 16 : 8 : 5.

In this problem, the new partner R's share is given, and the specific ratio in which he acquires this share from the old partners (P and Q) is also provided. We will first calculate the actual share sacrificed by P and Q and then deduct it from their old shares.

Step-by-step calculation:

1. Old profit sharing ratio of P:Q is 2:1 or $\frac{2}{3} : \frac{1}{3}$.

2. R is admitted for a $\frac{1}{5}$ share.

3. R acquires this share from P and Q in the ratio of 1:2. So, we calculate the sacrifice of each partner:

$ \text{Share sacrificed by P} = \frac{1}{5} \times \frac{1}{3} = \frac{1}{15} $

$ \text{Share sacrificed by Q} = \frac{1}{5} \times \frac{2}{3} = \frac{2}{15} $

4. Calculate the new share for P and Q by subtracting the sacrificed share from their old share.

$ \text{P's New Share} = \frac{2}{3} - \frac{1}{15} = \frac{10 - 1}{15} = \frac{9}{15} $

$ \text{Q's New Share} = \frac{1}{3} - \frac{2}{15} = \frac{5 - 2}{15} = \frac{3}{15} $

5. R's share is $\frac{1}{5}$, which is equal to $\frac{3}{15}$.

6. The new profit sharing ratio of P : Q : R is:

$ = \frac{9}{15} : \frac{3}{15} : \frac{3}{15} $

This can be simplified by dividing all parts by 3.

$ = 3 : 1 : 1 $

Thus, the new profit sharing ratio of P, Q, and R is 3 : 1 : 1.

This scenario specifies the ratio in which the new partner acquires his share from all the old partners. We will calculate the individual sacrifice of A, B, and C and then determine their new shares.

Step-by-step calculation:

1. Old profit sharing ratio of A:B:C is 3:2:2 or $\frac{3}{7} : \frac{2}{7} : \frac{2}{7}$.

2. D is admitted for a $\frac{1}{5}$ share.

3. D acquires this share from A, B, and C in the ratio of 2:2:1. The total of this ratio is $2+2+1=5$.

$ \text{Share sacrificed by A} = \frac{1}{5} \times \frac{2}{5} = \frac{2}{25} $

$ \text{Share sacrificed by B} = \frac{1}{5} \times \frac{2}{5} = \frac{2}{25} $

$ \text{Share sacrificed by C} = \frac{1}{5} \times \frac{1}{5} = \frac{1}{25} $

4. Calculate the new shares for A, B, and C.

$ \text{A's New Share} = \frac{3}{7} - \frac{2}{25} = \frac{75 - 14}{175} = \frac{61}{175} $

$ \text{B's New Share} = \frac{2}{7} - \frac{2}{25} = \frac{50 - 14}{175} = \frac{36}{175} $

$ \text{C's New Share} = \frac{2}{7} - \frac{1}{25} = \frac{50 - 7}{175} = \frac{43}{175} $

5. D's share is $\frac{1}{5}$, which is equal to $\frac{35}{175}$.

6. The new profit sharing ratio of A : B : C : D is:

$ = \frac{61}{175} : \frac{36}{175} : \frac{43}{175} : \frac{35}{175} $

Thus, the new profit sharing ratio of A, B, C, and D is 61 : 36 : 43 : 35.

In this problem, the exact fraction of profit sacrificed by each of the old partners (A and B) is given directly. We simply need to subtract these sacrificed shares from their respective old shares to find their new shares.

Step-by-step calculation:

1. Old profit sharing ratio of A:B is 3:2 or $\frac{3}{5} : \frac{2}{5}$.

2. Share sacrificed by A = $\frac{2}{7}$.

3. Share sacrificed by B = $\frac{1}{7}$.

4. The new partner C's share is the sum of the sacrifices made by A and B.

$ \text{C's Share} = \frac{2}{7} + \frac{1}{7} = \frac{3}{7} $ (This matches the information given in the question).

5. Calculate the new share for A and B.

$ \text{A's New Share} = \text{Old Share} - \text{Sacrificed Share} = \frac{3}{5} - \frac{2}{7} = \frac{21 - 10}{35} = \frac{11}{35} $

$ \text{B's New Share} = \frac{2}{5} - \frac{1}{7} = \frac{14 - 5}{35} = \frac{9}{35} $

6. C's share is $\frac{3}{7}$, which is equal to $\frac{15}{35}$ to have a common denominator.

7. The new profit sharing ratio of A : B : C is:

$ = \frac{11}{35} : \frac{9}{35} : \frac{15}{35} $

Thus, the new profit sharing ratio of A, B, and C is 11 : 9 : 15.

In this problem, the exact fraction of profit sacrificed by each of the old partners (A, B and C) is given directly. We can calculate the new shares of the old partners by subtracting their sacrificed shares from their old shares.

Step-by-step calculation:

1. Old profit sharing ratio of A:B:C is 3:3:2 or $\frac{3}{8} : \frac{3}{8} : \frac{2}{8}$.

2. The shares sacrificed by the old partners are:

- A sacrifices: $\frac{2}{7}$

- B sacrifices: $\frac{1}{7}$

- C sacrifices: $\frac{1}{7}$

3. The new partner D's share is the sum of the sacrifices made by A, B, and C.

$ \text{D's Share} = \frac{2}{7} + \frac{1}{7} + \frac{1}{7} = \frac{4}{7} $ (This matches the information given).

4. Calculate the new share for A, B, and C.

$ \text{A's New Share} = \text{Old Share} - \text{Sacrificed Share} = \frac{3}{8} - \frac{2}{7} = \frac{21 - 16}{56} = \frac{5}{56} $

$ \text{B's New Share} = \frac{3}{8} - \frac{1}{7} = \frac{21 - 8}{56} = \frac{13}{56} $

$ \text{C's New Share} = \frac{2}{8} - \frac{1}{7} = \frac{14 - 8}{56} = \frac{6}{56} $

5. D's share is $\frac{4}{7}$, which is equal to $\frac{32}{56}$ to have a common denominator.

6. The new profit sharing ratio of A : B : C : D is:

$ = \frac{5}{56} : \frac{13}{56} : \frac{6}{56} : \frac{32}{56} $

Thus, the new profit sharing ratio of A, B, C, and D is 5 : 13 : 6 : 32.

In this scenario, the old partners are surrendering a certain fraction 'of' their own share. We first need to calculate the actual share sacrificed by each partner and then find the new partner's total share by adding these sacrifices.

Step-by-step calculation:

1. Old profit sharing ratio of Radha:Rukmani is 3:2 or $\frac{3}{5} : \frac{2}{5}$.

2. Calculate the share sacrificed by each partner:

$ \text{Share sacrificed by Radha} = \frac{1}{3} \text{ of her share} = \frac{1}{3} \times \frac{3}{5} = \frac{3}{15} = \frac{1}{5} $

$ \text{Share sacrificed by Rukmani} = \frac{1}{4} \text{ of her share} = \frac{1}{4} \times \frac{2}{5} = \frac{2}{20} = \frac{1}{10} $

3. Calculate the new share for Radha and Rukmani.

$ \text{Radha's New Share} = \text{Old Share} - \text{Sacrificed Share} = \frac{3}{5} - \frac{1}{5} = \frac{2}{5} $

$ \text{Rukmani's New Share} = \frac{2}{5} - \frac{1}{10} = \frac{4 - 1}{10} = \frac{3}{10} $

4. Gopi's new share is the sum of shares sacrificed by Radha and Rukmani.

$ \text{Gopi's Share} = \frac{1}{5} + \frac{1}{10} = \frac{2 + 1}{10} = \frac{3}{10} $

5. The new profit sharing ratio of Radha : Rukmani : Gopi is:

$ = \frac{2}{5} : \frac{3}{10} : \frac{3}{10} $

To express this with a common denominator of 10:

$ = \frac{4}{10} : \frac{3}{10} : \frac{3}{10} $

Thus, the new profit sharing ratio is 4 : 3 : 3.

Similar to the previous problem, the old partners are surrendering a fraction 'of' their own shares. We will calculate the sacrificed share for each, determine their new shares, and find the new partner's share by summing the sacrifices.

Step-by-step calculation:

1. Old ratio of Singh:Gupta:Khan is 3:2:3 or $\frac{3}{8} : \frac{2}{8} : \frac{3}{8}$.

2. Calculate the share sacrificed by each old partner:

$ \text{Sacrificed by Singh} = \frac{1}{3} \times \frac{3}{8} = \frac{1}{8} $

$ \text{Sacrificed by Gupta} = \frac{1}{4} \times \frac{2}{8} = \frac{2}{32} = \frac{1}{16} $

$ \text{Sacrificed by Khan} = \frac{1}{5} \times \frac{3}{8} = \frac{3}{40} $

3. Calculate the new shares of the old partners:

$ \text{Singh's New Share} = \frac{3}{8} - \frac{1}{8} = \frac{2}{8} = \frac{1}{4} $

$ \text{Gupta's New Share} = \frac{2}{8} - \frac{1}{16} = \frac{4 - 1}{16} = \frac{3}{16} $

$ \text{Khan's New Share} = \frac{3}{8} - \frac{3}{40} = \frac{15 - 3}{40} = \frac{12}{40} = \frac{3}{10} $

4. Jain's share is the sum of all sacrifices:

$ \text{Jain's Share} = \frac{1}{8} + \frac{1}{16} + \frac{3}{40} = \frac{10 + 5 + 6}{80} = \frac{21}{80} $

5. The new profit sharing ratio of Singh : Gupta : Khan : Jain is:

$ = \frac{1}{4} : \frac{3}{16} : \frac{3}{10} : \frac{21}{80} $

To find the simple ratio, we use a common denominator of 80:

$ = \frac{20}{80} : \frac{15}{80} : \frac{24}{80} : \frac{21}{80} $

Thus, the new profit sharing ratio is 20 : 15 : 24 : 21.

The sacrificing ratio is the ratio in which the old partners have agreed to sacrifice their share of profits in favour of the new partner. It is calculated by finding the difference between the old profit share and the new profit share for each of the old partners.

Formula: Sacrificing Ratio = Old Ratio - New Ratio

Step-by-step calculation:

1. Old Ratio (Sandeep : Navdeep) = $5:3$ or $\frac{5}{8} : \frac{3}{8}$.

2. New Ratio (Sandeep : Navdeep : C) = $4:2:1$ or $\frac{4}{7} : \frac{2}{7} : \frac{1}{7}$.

3. Calculate the sacrifice made by each old partner:

$ \text{Sandeep's Sacrifice} = \frac{5}{8} - \frac{4}{7} = \frac{35 - 32}{56} = \frac{3}{56} $

$ \text{Navdeep's Sacrifice} = \frac{3}{8} - \frac{2}{7} = \frac{21 - 16}{56} = \frac{5}{56} $

4. The sacrificing ratio is the ratio of the sacrifices made by Sandeep and Navdeep.

$ \text{Sacrificing Ratio} = \frac{3}{56} : \frac{5}{56} = 3:5 $

Thus, the sacrificing ratio of Sandeep and Navdeep is 3 : 5.

This problem has two parts. First, we need to calculate the new profit sharing ratio of all three partners. Then, we can find the sacrificing ratio by comparing the old and new ratios of the original partners.

Part 1: Calculation of New Profit Sharing Ratio

1. Let the total profit be 1.

2. Ravi's share is $\frac{1}{8}$.

3. Remaining share for Rao and Swami = $1 - \frac{1}{8} = \frac{7}{8}$.

4. This remaining share of $\frac{7}{8}$ will be divided between Rao and Swami in their new agreed ratio of 4:3.

$ \text{Rao's New Share} = \frac{7}{8} \times \frac{4}{7} = \frac{28}{56} = \frac{1}{2} $

$ \text{Swami's New Share} = \frac{7}{8} \times \frac{3}{7} = \frac{21}{56} = \frac{3}{8} $

5. The new profit sharing ratio of Rao : Swami : Ravi is:

$ = \frac{1}{2} : \frac{3}{8} : \frac{1}{8} $

With a common denominator of 8, this becomes $\frac{4}{8} : \frac{3}{8} : \frac{1}{8}$.

Thus, the new profit sharing ratio is 4 : 3 : 1.

Part 2: Calculation of Sacrificing Ratio

Sacrificing Ratio = Old Ratio - New Ratio

1. Old Ratio (Rao : Swami) = $3:2$ or $\frac{3}{5} : \frac{2}{5}$.

2. New Ratio (Rao : Swami : Ravi) = $4:3:1$ or $\frac{4}{8} : \frac{3}{8} : \frac{1}{8}$.

3. Calculate the sacrifice for each old partner:

$ \text{Rao's Sacrifice} = \frac{3}{5} - \frac{4}{8} = \frac{24 - 20}{40} = \frac{4}{40} $

$ \text{Swami's Sacrifice} = \frac{2}{5} - \frac{3}{8} = \frac{16 - 15}{40} = \frac{1}{40} $

4. The sacrificing ratio of Rao and Swami is $\frac{4}{40} : \frac{1}{40}$.

Thus, the sacrificing ratio is 4 : 1.

This question requires the valuation of goodwill using the Average Profit Method. The steps are to calculate the average profit of the given years and then multiply it by the specified number of years' purchase.

Step 1: Calculate the Total Profit of the last five years

$ \text{Total Profit} = \textsf{₹ } 40,000 + \textsf{₹ } 50,000 + \textsf{₹ } 60,000 + \textsf{₹ } 50,000 + \textsf{₹ } 60,000 = \textsf{₹ } 2,60,000 $

Step 2: Calculate the Average Profit

$ \text{Average Profit} = \frac{\text{Total Profit}}{\text{Number of Years}} = \frac{\textsf{₹ } 2,60,000}{5} = \textsf{₹ } 52,000 $

Step 3: Calculate the Value of Goodwill

The number of years' purchase is given as four.

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

$ = \textsf{₹ } 52,000 \times 4 = \textsf{₹ } 2,08,000 $

Thus, the value of goodwill is ₹ 2,08,000.

This requires the valuation of goodwill using the Super Profit Method. Super profit is the excess of the firm's actual average profit over the normal profit that is expected to be earned in a similar business.

Step 1: Calculate Normal Profit

Normal profit is the return expected on the capital employed, based on the normal rate of return.

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

$ = \textsf{₹ } 2,00,000 \times \frac{15}{100} = \textsf{₹ } 30,000 $

Step 2: Calculate Super Profit

Super profit is the difference between the actual profit earned and the normal profit.

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

$ = \textsf{₹ } 48,000 - \textsf{₹ } 30,000 = \textsf{₹ } 18,000 $

Step 3: Calculate the Value of Goodwill

The number of years' purchase is given as three.

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

$ = \textsf{₹ } 18,000 \times 3 = \textsf{₹ } 54,000 $

Thus, the value of goodwill is ₹ 54,000.

This valuation of goodwill is based on the Super Profit Method. We need to follow three steps: calculate average profit, calculate normal profit, find the super profit, and then calculate goodwill.

Step 1: Calculate Average Profit

Total Profits of last 5 years = $\textsf{₹ } 40,000 + \textsf{₹ } 50,000 + \textsf{₹ } 55,000 + \textsf{₹ } 70,000 + \textsf{₹ } 85,000 = \textsf{₹ } 3,00,000$

$ \text{Average Profit} = \frac{\text{Total Profit}}{\text{Number of Years}} = \frac{\textsf{₹ } 3,00,000}{5} = \textsf{₹ } 60,000 $

Step 2: Calculate Normal Profit

Normal Profit is the expected return on the capital employed.

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

$ = \textsf{₹ } 5,00,000 \times \frac{10}{100} = \textsf{₹ } 50,000 $

Step 3: Calculate Super Profit

Super Profit is the excess of average profit over normal profit.

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

$ = \textsf{₹ } 60,000 - \textsf{₹ } 50,000 = \textsf{₹ } 10,000 $

Step 4: Calculate the Value of Goodwill

Goodwill is calculated as 3 years' purchase of the super profit.

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

$ = \textsf{₹ } 10,000 \times 3 = \textsf{₹ } 30,000 $

Thus, the value of goodwill is ₹ 30,000.

The Capitalisation Method can be applied in two ways: (a) Capitalisation of Average Profit and (b) Capitalisation of Super Profit. Here, we will use the Capitalisation of Average Profit method as it is more direct with the given information.

Step 1: Calculate the Capitalised Value of the Business

This represents the total capital required to earn the given profit at the normal rate of return.

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

$ = \textsf{₹ } 1,50,000 \times \frac{100}{20} = \textsf{₹ } 7,50,000 $

Step 2: Calculate the Capital Employed (Net Assets)

Capital Employed is the total capital contributed by the partners.

$ \text{Capital Employed} = \text{Rajan's Capital} + \text{Rajani's Capital} $

$ = \textsf{₹ } 3,00,000 + \textsf{₹ } 2,00,000 = \textsf{₹ } 5,00,000 $

Step 3: Calculate the Value of Goodwill

Goodwill is the difference between the capitalised value of the business and the actual capital employed.

$ \text{Goodwill} = \text{Capitalised Value} - \text{Capital Employed} $

$ = \textsf{₹ } 7,50,000 - \textsf{₹ } 5,00,000 = \textsf{₹ } 2,50,000 $

Thus, the value of goodwill is ₹ 2,50,000.

This problem also requires the use of the Capitalisation of Average Profit Method for valuing goodwill. The steps remain the same: find the capitalised value of the business, determine the capital employed (net assets), and then find the difference.

Step 1: Calculate the Capitalised Value of the Business

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

$ = \textsf{₹ } 1,00,000 \times \frac{100}{10} = \textsf{₹ } 10,00,000 $

Step 2: Calculate the Capital Employed (Net Assets)

Capital Employed is the difference between total assets and external liabilities.

$ \text{Capital Employed} = \text{Total Assets} - \text{External Liabilities} $

$ = \textsf{₹ } 10,00,000 - \textsf{₹ } 1,80,000 = \textsf{₹ } 8,20,000 $

Step 3: Calculate the Value of Goodwill

$ \text{Goodwill} = \text{Capitalised Value of Business} - \text{Capital Employed} $

$ = \textsf{₹ } 10,00,000 - \textsf{₹ } 8,20,000 = \textsf{₹ } 1,80,000 $

Thus, the value of goodwill is ₹ 1,80,000.

First, we need to find the sacrificing ratio of the old partners, Verma and Sharma. Since the new partner's share is given without specifying how he acquires it, we assume the old partners sacrifice in their old profit-sharing ratio, which is 5:3. Hence, the Sacrificing Ratio is 5:3.

The goodwill premium brought by Ghosh ($\textsf{₹ }$ 4,000) will be distributed between Verma and Sharma in this sacrificing ratio.

• Verma's share of goodwill = $\textsf{₹ } 4,000 \times \frac{5}{8} = \textsf{₹ } 2,500$
• Sharma's share of goodwill = $\textsf{₹ } 4,000 \times \frac{3}{8} = \textsf{₹ } 1,500$

a) When the amount of goodwill is retained in the business.

b) When the amount of goodwill is fully withdrawn.

(The first two entries are the same as in part a)

c) When 50% of the amount of goodwill is withdrawn.

(The first two entries are the same as in part a)

d) When goodwill is paid privately.

When the new partner pays the goodwill premium to the old partners privately (outside the business), no entry is recorded in the books of the firm for the goodwill amount. Only the entry for capital brought in will be passed.

Step 1: Calculate the Sacrificing Ratio

Sacrificing Ratio = Old Ratio - New Ratio

$ \text{A's Sacrifice} = \frac{3}{5} - \frac{2}{4} = \frac{12 - 10}{20} = \frac{2}{20} $

$ \text{B's Sacrifice} = \frac{2}{5} - \frac{1}{4} = \frac{8 - 5}{20} = \frac{3}{20} $

The sacrificing ratio of A : B is 2 : 3.

Step 2: Calculate C's Share of Goodwill

C's Share of Goodwill = Total Firm's Goodwill $\times$ C's Profit Share

$ = \textsf{₹ } 20,000 \times \frac{1}{4} = \textsf{₹ } 5,000 $

This amount will be distributed between A and B in their sacrificing ratio (2:3).

• A's share of goodwill = $\textsf{₹ } 5,000 \times \frac{2}{5} = \textsf{₹ } 2,000$
• B's share of goodwill = $\textsf{₹ } 5,000 \times \frac{3}{5} = \textsf{₹ } 3,000$

Journal Entries

Step 1: Write off Existing Goodwill

As per Accounting Standard 26, existing goodwill must be written off in the old partners' capital accounts in their old profit-sharing ratio (3:2).

Step 2: Calculate Sacrificing Ratio

$ \text{Arti's Sacrifice} = \frac{3}{5} - \frac{2}{4} = \frac{12 - 10}{20} = \frac{2}{20} $

$ \text{Bharti's Sacrifice} = \frac{2}{5} - \frac{1}{4} = \frac{8 - 5}{20} = \frac{3}{20} $

Sacrificing Ratio is 2 : 3.

Step 3: Distribute Premium for Goodwill

Sarthi's premium of $\textsf{₹ }$ 10,000 will be credited to Arti and Bharti in their sacrificing ratio (2:3).

• Arti's share = $\textsf{₹ } 10,000 \times \frac{2}{5} = \textsf{₹ } 4,000$
• Bharti's share = $\textsf{₹ } 10,000 \times \frac{3}{5} = \textsf{₹ } 6,000$

Journal Entries

Step 1: Write off Existing Goodwill

The existing goodwill of $\textsf{₹ }$ 40,000 will be written off by debiting the old partners' capital accounts in their old profit-sharing ratio (4:3).

Step 2: Determine the Sacrificing Ratio

Since no information is given about how Z acquires his share, we assume the old partners sacrifice in their old ratio. Thus, the sacrificing ratio is 4 : 3.

Step 3: Distribute Premium for Goodwill

Z's premium of $\textsf{₹ }$ 7,000 will be credited to X and Y in the sacrificing ratio (4:3).

• X's share = $\textsf{₹ } 7,000 \times \frac{4}{7} = \textsf{₹ } 4,000$
• Y's share = $\textsf{₹ } 7,000 \times \frac{3}{7} = \textsf{₹ } 3,000$

Journal Entries

This case involves the partial bringing of goodwill in cash. The amount brought in ($\textsf{₹ }$ 10,000) will be treated through the "Premium for Goodwill Account," and the unpaid amount ($\textsf{₹ }$ 5,000) will be adjusted by debiting the new partner's current account.

Step 1: Calculate the Sacrificing Ratio

Sacrificing Ratio = Old Ratio - New Ratio

$ \text{Aditya's Sacrifice} = \frac{3}{5} - \frac{2}{4} = \frac{12 - 10}{20} = \frac{2}{20} $

$ \text{Balan's Sacrifice} = \frac{2}{5} - \frac{1}{4} = \frac{8 - 5}{20} = \frac{3}{20} $

The sacrificing ratio of Aditya : Balan is 2 : 3.

Step 2: Distribute the Goodwill

Total goodwill of Christopher ($\textsf{₹ }$ 15,000) will be credited to Aditya and Balan in the sacrificing ratio (2:3).

• Aditya's share = $\textsf{₹ } 15,000 \times \frac{2}{5} = \textsf{₹ } 6,000$
• Balan's share = $\textsf{₹ } 15,000 \times \frac{3}{5} = \textsf{₹ } 9,000$

Journal Entries

When a new partner is unable to bring their share of goodwill in cash, the adjustment is made by debiting the new partner's Current Account and crediting the old partners' Capital Accounts in their sacrificing ratio.

Step 1: Calculate Kanwar's Share of Goodwill

Kanwar's Share of Goodwill = Total Firm's Goodwill $\times$ Kanwar's Profit Share

$ = \textsf{₹ } 80,000 \times \frac{1}{4} = \textsf{₹ } 20,000 $

Step 2: Determine the Sacrificing Ratio

Since the new partner's share is given without specifics on how he acquires it, the old partners (Amar and Samar) are assumed to sacrifice in their old profit-sharing ratio. Therefore, the sacrificing ratio is 3 : 1.

Step 3: Distribute Goodwill among Sacrificing Partners

• Amar's share = $\textsf{₹ } 20,000 \times \frac{3}{4} = \textsf{₹ } 15,000$
• Samar's share = $\textsf{₹ } 20,000 \times \frac{1}{4} = \textsf{₹ } 5,000$

Journal Entry

Preliminary Calculations (Common for all cases):

1. Value of Firm's Goodwill:

Average Profit = $\frac{\textsf{₹ }(50,000 + 60,000 + 90,000 + 70,000)}{4} = \frac{\textsf{₹ } 2,70,000}{4} = \textsf{₹ } 67,500$

Goodwill = Average Profit $\times$ 3 Years' Purchase = $\textsf{₹ } 67,500 \times 3 = \textsf{₹ } 2,02,500$

2. Ram Lal's Share of Goodwill:

Share = $\textsf{₹ } 2,02,500 \times \frac{1}{4} = \textsf{₹ } 50,625$

3. Sacrificing Ratio:

Assumed to be the old ratio, i.e., 3 : 2 for Mohan Lal and Sohan Lal.

a) When Goodwill already appears in the books at Rs. 2,02,500.

b) When Goodwill appears in the books at Rs. 2,500.

c) When Goodwill appears in the books at Rs. 2,05,000.

Since Hari is unable to bring goodwill in cash and the partners decide not to show goodwill in the books, we will pass a single adjustment entry by debiting the new partner's current account and crediting the sacrificing partners' capital accounts.

Step 1: Calculate Sacrificing Ratio

Old Ratio (Rajesh:Mukesh) = 1:1 or $\frac{1}{2}:\frac{1}{2}$

New Ratio (Rajesh:Mukesh:Hari) = 4:3:2 or $\frac{4}{9}:\frac{3}{9}:\frac{2}{9}$

$ \text{Rajesh's Sacrifice} = \frac{1}{2} - \frac{4}{9} = \frac{9 - 8}{18} = \frac{1}{18} $

$ \text{Mukesh's Sacrifice} = \frac{1}{2} - \frac{3}{9} = \frac{9 - 6}{18} = \frac{3}{18} $

Sacrificing Ratio is 1 : 3.

Step 2: Calculate Hari's Share of Goodwill

Hari's Share = Firm's Goodwill $\times$ Hari's Profit Share = $\textsf{₹ } 36,000 \times \frac{2}{9} = \textsf{₹ } 8,000$

Step 3: Distribute Goodwill among Sacrificing Partners

• Rajesh gets = $\textsf{₹ } 8,000 \times \frac{1}{4} = \textsf{₹ } 2,000$
• Mukesh gets = $\textsf{₹ } 8,000 \times \frac{3}{4} = \textsf{₹ } 6,000$

Journal Entry

The treatment requires passing a single adjustment entry through the partners' capital or current accounts, debiting the gaining partner and crediting the sacrificing partners.

Step 1: Calculate Sacrificing Ratio

Old Ratio (Amar:Akbar) = 1:1 or $\frac{1}{2}:\frac{1}{2}$

New Ratio (Amar:Akbar:Anthony) = 4:3:2 or $\frac{4}{9}:\frac{3}{9}:\frac{2}{9}$

$ \text{Amar's Sacrifice} = \frac{1}{2} - \frac{4}{9} = \frac{9 - 8}{18} = \frac{1}{18} $

$ \text{Akbar's Sacrifice} = \frac{1}{2} - \frac{3}{9} = \frac{9 - 6}{18} = \frac{3}{18} $

Sacrificing Ratio is 1 : 3.

Step 2: Distribute Anthony's Share of Goodwill

Anthony's share of goodwill is $\textsf{₹ }$ 45,000. This will be credited to Amar and Akbar in their sacrificing ratio (1:3).

• Amar's Share = $\textsf{₹ } 45,000 \times \frac{1}{4} = \textsf{₹ } 11,250$
• Akbar's Share = $\textsf{₹ } 45,000 \times \frac{3}{4} = \textsf{₹ } 33,750$

Journal Entry

1. Journal Entries

2. Revaluation Account

Revaluation Account

Dr.Cr.

3. Partners’ Capital Accounts

Partners’ Capital Accounts

Dr.Cr.

4. Balance Sheet after Admission

Balance Sheet as at March 31, 2016

At the time of admission of a new partner, any existing reserves, accumulated profits, or losses appearing in the books of the firm are distributed to the old partners in their old profit-sharing ratio. This is done because these items belong to the partners who were present before the new partner's admission.

The Old Profit Sharing Ratio of Leela and Meeta is 5:3.

Distribution of General Reserve ($\textsf{₹ }$ 16,000):

• Leela's Share = $\textsf{₹ } 16,000 \times \frac{5}{8} = \textsf{₹ } 10,000$
• Meeta's Share = $\textsf{₹ } 16,000 \times \frac{3}{8} = \textsf{₹ } 6,000$

Distribution of Profit and Loss A/c ($\textsf{₹ }$ 24,000):

• Leela's Share = $\textsf{₹ } 24,000 \times \frac{5}{8} = \textsf{₹ } 15,000$
• Meeta's Share = $\textsf{₹ } 24,000 \times \frac{3}{8} = \textsf{₹ } 9,000$

Journal Entries

A debit balance in the Profit and Loss Account represents an accumulated loss. At the time of a new partner's admission, any existing accumulated profits or losses must be distributed to the old partners in their old profit-sharing ratio. This is because the loss belongs to the period before the new partner joined the firm.

The loss of $\textsf{₹ }$ 40,000 will be debited to the capital accounts of Amit and Viney in their old ratio of 3:1.

Distribution of Loss:

• Amit's Share = $\textsf{₹ } 40,000 \times \frac{3}{4} = \textsf{₹ } 30,000$ (Debit)
• Viney's Share = $\textsf{₹ } 40,000 \times \frac{1}{4} = \textsf{₹ } 10,000$ (Debit)

Journal Entry

1. Journal Entries

2. New Balance Sheet

Balance Sheet as at April 01, 2017

This problem involves the Adjustment of Old Partners' Capitals on the basis of the new partner's capital.

Step 1: Calculate New Profit Sharing Ratio

Remaining Share = $1 - \frac{1}{4} = \frac{3}{4}$.

A's New Share = $\frac{3}{4} \times \frac{3}{4} = \frac{9}{16}$. B's New Share = $\frac{3}{4} \times \frac{1}{4} = \frac{3}{16}$. C's Share = $\frac{1}{4} = \frac{4}{16}$.

New Ratio is 9 : 3 : 4.

Step 2: Calculate Total Capital of the New Firm

Total Capital = C's Capital $\times$ Reciprocal of C's Share = $\textsf{₹ } 20,000 \times \frac{4}{1} = \textsf{₹ } 80,000$.

Step 3: Calculate New Capitals of A and B

A's New Capital = $\textsf{₹ } 80,000 \times \frac{9}{16} = \textsf{₹ } 45,000$.

B's New Capital = $\textsf{₹ } 80,000 \times \frac{3}{16} = \textsf{₹ } 15,000$.

Step 4: Determine Cash to be Brought in or Withdrawn

Journal Entries

Step 1: Calculate New Profit Sharing Ratio

Pinky's New Share = $\frac{3}{6} - \frac{1}{8} = \frac{12-3}{24} = \frac{9}{24}$

Qumar's New Share = $\frac{2}{6} - \frac{1}{16} = \frac{16-3}{48} = \frac{13}{48}$

Roopa's New Share = $\frac{1}{6} - \frac{1}{16} = \frac{8-3}{48} = \frac{5}{48}$

Seema's Share = $\frac{1}{4} = \frac{12}{48}$

New Ratio = $\frac{18}{48}:\frac{13}{48}:\frac{5}{48}:\frac{12}{48} \implies$ 18 : 13 : 5 : 12.

Step 2: Calculate New Capitals of All Partners

Total Capital = $\textsf{₹ }$ 2,40,000

• Pinky's Capital = $2,40,000 \times \frac{18}{48} = \textsf{₹ } 90,000$
• Qumar's Capital = $2,40,000 \times \frac{13}{48} = \textsf{₹ } 65,000$
• Roopa's Capital = $2,40,000 \times \frac{5}{48} = \textsf{₹ } 25,000$
• Seema's Capital = $2,40,000 \times \frac{12}{48} = \textsf{₹ } 60,000$

Step 3: Determine Cash Adjustment

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Revaluation Account

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Cash Account

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Balance Sheet as at ...

Revaluation Account

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Partners’ Capital Accounts

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Balance Sheet as at March 31, 2016

Journal Entries

Balance Sheet as at March 31, 2017