Step 1: Understanding the Question:

The question asks us to calculate the Normal Rate of Return (NRR) based on the given Capital Employed and Normal Profits. The Super Profits information is extra and not required for this calculation.


Step 2: Key Formula or Approach:

The Normal Rate of Return is calculated using the formula that relates Normal Profit, Capital Employed, and the rate itself. The formula is:
\[ Normal Profit = Capital Employed \times \frac{Normal Rate of Return}{100} \]
Rearranging this to find the Normal Rate of Return, we get:
\[ Normal Rate of Return = \frac{Normal Profit}{Capital Employed} \times 100 \]

Step 3: Detailed Explanation:

We are given the following values:

- Capital Employed = Rs 4,00,000

- Normal Profits = Rs 60,000

Now, we substitute these values into the formula:
\[ Normal Rate of Return = \frac{60,000}{4,00,000} \times 100 \]
Simplifying the fraction:
\[ Normal Rate of Return = \frac{6}{40} \times 100 = 0.15 \times 100 \] \[ Normal Rate of Return = 15% \]

Step 4: Final Answer:

The normal rate of return is 15%.
\[ \boxed{15%} \] Quick Tip: Formula to remember:
\[ Normal Profit = Capital \times Normal Rate \] Super Profit = Actual Profit − Normal Profit.
Identify the necessary information and ignore any extra data, like the super profit in this case, which is not needed to find the NRR.

Step 1: Understanding the Question:

The question asks for the maximum possible discount that can be offered on the reissue of forfeited shares. This maximum discount is limited by the amount already received on these shares (excluding any premium).


Step 2: Key Formula or Approach:

The maximum discount on reissue is equal to the amount credited to the Share Forfeiture Account. The Share Forfeiture Account is credited with the amount received from the original shareholder towards the share capital (face value).

Maximum Discount per share = Amount forfeited per share (excluding premium).


Step 3: Detailed Explanation:

1. Determine the amount called up per share:

Face Value = Rs 10, Premium = Rs 2. Total Issue Price = Rs 12.

Unpaid Amount = Second and final call of Rs 4 (including premium).

The call amount includes a premium of Rs2. So, the capital portion of the call is Rs4 - Rs2 = Rs2.

Since the final call was made, the full face value of Rs10 was called up.

2. Calculate the amount paid per share:

Total amount called up per share = Face Value + Premium = Rs10 + Rs2 = Rs12.

Amount unpaid per share = Rs4.

Amount paid per share = Total Called-up - Amount Unpaid = Rs12 - Rs4 = Rs8.

3. Calculate the amount forfeited (credited to Share Forfeiture A/c):

The amount paid (Rs8) includes the premium of Rs2. Since the premium has been received, it is credited to the Securities Premium Account and is not part of the forfeited amount available for discount.

Amount forfeited towards capital = Amount paid - Premium received = Rs8 - Rs2 = Rs6.

Therefore, the amount credited to the Share Forfeiture Account is Rs6 per share.


Step 4: Final Answer:

The maximum amount of discount that can be allowed on reissue is the amount forfeited per share on account of capital, which is Rs6 per share.
\[ \boxed{Rs 6 per share} \] Quick Tip: For reissue of forfeited shares:
Max discount on reissue = Amount credited to Share Forfeiture Account.
The amount credited to Share Forfeiture A/c is the amount received towards the face value (capital) of the share only. Any premium received is not available for discount.
This is a common company accounts MCQ.

Step 1: Understanding the Question:

The question asks to determine the total goodwill of the firm. We are given the retiring partner's capital balance and the final settlement amount paid to her. The difference between these two amounts represents the retiring partner's share of goodwill.


Step 2: Key Formula or Approach:

1. Calculate the retiring partner's share of goodwill by finding the difference between the final settlement amount and her capital balance.

Retiring Partner's Share of Goodwill = Amount Paid - Capital Balance.

2. Calculate the total goodwill of the firm using the retiring partner's share and her profit-sharing ratio.

Total Goodwill = Retiring Partner's Share of Goodwill \(\div\) Retiring Partner's Profit Share.


Step 3: Detailed Explanation:

First, we find the amount paid to Madhuri for her share of goodwill.

Amount Paid in full settlement = Rs 2,25,000.

Madhuri's Capital Balance = Rs 1,80,000.

Madhuri's Share of Goodwill = Rs 2,25,000 - Rs 1,80,000 = Rs 45,000.

This excess payment of Rs 45,000 is for her share in the firm's goodwill.


Next, we calculate the total goodwill of the firm.

The partners' profit-sharing ratio was Lalita : Shivani : Madhuri = 3:2:1.

Madhuri's share in profits = \(\frac{1}{3+2+1} = \frac{1}{6}\).

Since Madhuri's \(\frac{1}{6}\) share of goodwill is Rs 45,000, the total goodwill (the full \(\frac{6}{6}\) share) is:
\[ Total Goodwill = Madhuri's Share \times \frac{1}{Her Ratio} = 45,000 \times \frac{6}{1} = 2,70,000 \]

Step 4: Final Answer:

The goodwill of the firm on Madhuri's retirement was Rs 2,70,000.
\[ \boxed{Rs 2,70,000} \] Quick Tip: Retirement formula:
\[ Goodwill share = Amount paid - Capital balance \] Then, multiply this share by the reciprocal of the retiring partner's profit ratio to find the total goodwill of the firm.

Step 1: Understanding the Question:

We need to calculate the new profit-sharing ratio of all three partners after Mohan is admitted. We are given the old ratio and the terms on which the new partner acquires his share from the old partners.


Step 2: Key Formula or Approach:

The formula to find the new share of an old partner is:

New Share = Old Share - Sacrificed Share.

First, we need to calculate the share sacrificed by each old partner.


Step 3: Detailed Explanation:

1. Old Shares:

Chaman and Vatika's ratio = 4:5.

Chaman's old share = \(\frac{4}{9}\).

Vatika's old share = \(\frac{5}{9}\).

2. Share Sacrificed by Old Partners:

Mohan's share = \(\frac{1}{5}\).

He acquires this share equally from Chaman and Vatika.

Sacrifice by each partner = \(\frac{1}{2}\) of Mohan's share = \(\frac{1}{2} \times \frac{1}{5} = \frac{1}{10}\).

3. Calculate New Shares:

Chaman's New Share = Old Share - Sacrificed Share

\[ = \frac{4}{9} - \frac{1}{10} = \frac{4 \times 10 - 1 \times 9}{90} = \frac{40 - 9}{90} = \frac{31}{90} \]
Vatika's New Share = Old Share - Sacrificed Share

\[ = \frac{5}{9} - \frac{1}{10} = \frac{5 \times 10 - 1 \times 9}{90} = \frac{50 - 9}{90} = \frac{41}{90} \]
Mohan's Share = \(\frac{1}{5}\). To get a common denominator of 90, we multiply the numerator and denominator by 18:

\[ = \frac{1 \times 18}{5 \times 18} = \frac{18}{90} \]
4. New Profit-Sharing Ratio:

The new ratio of Chaman : Vatika : Mohan is \(\frac{31}{90} : \frac{41}{90} : \frac{18}{90}\), which simplifies to 31 : 41 : 18.


Step 4: Final Answer:

The new profit sharing ratio is 31:41:18.
\[ \boxed{31:41:18} \]
\textit{Note: The calculated answer corresponds to option (B), not (C) as listed in the original provided code.
Quick Tip: Admission steps:
Convert the old ratio into fractions.
Calculate the exact fraction of profit sacrificed by each old partner.
Subtract the sacrificed share from each old partner's share.
Express all new shares with a common denominator to find the final ratio.

Step 1: Understanding the Question:

The question asks for the correct accounting entry for an amount recovered from a bad debt at the time of the dissolution of a partnership firm.


Step 2: Key Formula or Approach:

During the dissolution of a firm, a Realisation Account is opened to settle all assets and liabilities. All assets are transferred to this account, and all liabilities are paid from it. Any income or expense that occurs during the dissolution process, including the recovery of a previously written-off bad debt (which is an unrecorded asset), is routed through the Realisation Account. Cash received is an inflow, so the Bank account is debited, and the corresponding credit goes to the Realisation Account, as it is a gain.


Step 3: Detailed Explanation:

1. Calculate the amount recovered:

The original debt written off was Rs 25,000.

The amount recovered is 40% of this debt.

Amount Recovered = \( 40% \times 25,000 = \frac{40}{100} \times 25,000 = Rs 10,000 \).

2. Determine the accounting treatment:

Since the firm is being dissolved, all transactions related to the realization of assets and settlement of liabilities are recorded in the Realisation Account.

The recovery of a bad debt is considered a gain or an income from an unrecorded asset.

In dissolution, all such gains are credited to the Realisation Account. The journal entry would be:

Bank A/c Dr. Rs 10,000

To Realisation A/c Cr. Rs 10,000

Therefore, Rs 10,000 will be credited to the Realisation Account.


Step 4: Final Answer:

The correct accounting treatment is to credit the Realisation Account with Rs 10,000.
\[ \boxed{Rs 10,000 will be credited to Realisation Account} \] Quick Tip: Dissolution rule:
Any money received from an unrecorded asset (like recovery of bad debts) is a gain and is credited to the Realisation Account.
Any payment of an unrecorded liability is a loss and is debited to the Realisation Account.
All gains and losses on the disposal of assets and settlement of liabilities during dissolution are consolidated in the Realisation Account.

Step 1: Understanding the Question:

The question asks us to determine the amount of interest on capital to be allocated to each partner when the total available profit is less than the total interest payable.


Step 2: Key Formula or Approach:

Interest on capital is an appropriation of profit, not a charge against profit (unless specified otherwise). This means it can only be paid out of available profits. If the total interest due exceeds the available profit, the profit is distributed among the partners in the ratio of their interest on capital claims, not their profit-sharing ratio.


Step 3: Detailed Explanation:

1. Calculate the full interest on capital for each partner:

Interest Rate = 6% p.a.

Nidhi's Interest = 6% of Rs 3,00,000 = \(0.06 \times 3,00,000 = Rs 18,000\).

Kunal's Interest = 6% of Rs 2,00,000 = \(0.06 \times 2,00,000 = Rs 12,000\).

2. Calculate the total interest payable:

Total Interest = Rs 18,000 + Rs 12,000 = Rs 30,000.

3. Compare total interest with available profit:

The available profit for the year is Rs 15,000.

Since Profit (Rs 15,000) \(<\) Total Interest (Rs 30,000), the profit is insufficient.

4. Allocate the profit proportionately:

The available profit of Rs 15,000 will be distributed in the ratio of the interest claims.

Ratio of interest claims = Nidhi's Interest : Kunal's Interest = 18,000 : 12,000.

Simplifying the ratio by dividing by 6,000 gives 3 : 2.

Now, distribute the profit of Rs 15,000 in the ratio 3:2.

Interest allowed to Nidhi = \(15,000 \times \frac{3}{3+2} = 15,000 \times \frac{3}{5} = Rs 9,000\).

Interest allowed to Kunal = \(15,000 \times \frac{2}{3+2} = 15,000 \times \frac{2}{5} = Rs 6,000\).


Step 4: Final Answer:

The interest on capital will be Nidhi Rs 9,000 and Kunal Rs 6,000.
\[ \boxed{Nidhi Rs 9,000 ; Kunal Rs 6,000} \] Quick Tip: If profit is less than the total interest on capital:
The available profit is distributed as interest.
The distribution ratio is the ratio of the partners' interest claims, NOT their profit-sharing ratio.
The total amount distributed cannot exceed the available profit.

Step 1: Understanding the Question:

The question asks to calculate the gaining ratio of the continuing partners (Dharam and Karam) after a partner (Raman) retires. We are given both the old and the new profit-sharing ratios.


Step 2: Key Formula or Approach:

The gaining ratio is the proportion in which the continuing partners acquire the share of the retiring partner. When both the old and new profit-sharing ratios are given, the gaining ratio is calculated using the following formula for each continuing partner:

Gain = New Share - Old Share.


Step 3: Detailed Explanation:

1. List the Old Shares:

Old Ratio (Dharam : Karam : Raman) = 7 : 8 : 5. Total = 20.

Dharam's Old Share = \(\frac{7}{20}\).

Karam's Old Share = \(\frac{8}{20}\).

2. List the New Shares:

New Ratio (Dharam : Karam) = 11 : 9. Total = 20.

Dharam's New Share = \(\frac{11}{20}\).

Karam's New Share = \(\frac{9}{20}\).

3. Calculate the Gain for each partner:

Dharam's Gain = New Share - Old Share = \(\frac{11}{20} - \frac{7}{20} = \frac{4}{20}\).

Karam's Gain = New Share - Old Share = \(\frac{9}{20} - \frac{8}{20} = \frac{1}{20}\).

4. Determine the Gaining Ratio:

The gaining ratio is the ratio of the gains of the continuing partners.

Gaining Ratio (Dharam : Karam) = \(\frac{4}{20} : \frac{1}{20}\) = 4 : 1.


Step 4: Final Answer:

The gaining ratio of Dharam and Karam is 4:1.
\[ \boxed{4:1} \] Quick Tip: Gaining ratio formula:
\[ Gain = New share - Old share \] This formula is always used when the new profit-sharing ratio of the continuing partners is specified. If the new ratio is not given, it is assumed they gain in their old profit-sharing ratio.

Step 1: Understanding the Question:

We need to find the new profit-sharing ratio between the surviving partners, Deen and Hari, after Raju's death. The question specifies how they acquire the deceased partner's share.


Step 2: Key Formula or Approach:

The new share of a continuing partner is calculated by adding their gain to their old share.

New Share = Old Share + Gained Share.

First, we determine the share gained by each continuing partner from the deceased partner's share.


Step 3: Detailed Explanation:

1. Old Shares:

Old Ratio (Deen : Raju : Hari) = 7 : 6 : 7. Total = 20.

Deen's Old Share = \(\frac{7}{20}\).

Raju's Share = \(\frac{6}{20}\).

Hari's Old Share = \(\frac{7}{20}\).

2. Share Gained by Continuing Partners:

Raju's share (\(\frac{6}{20}\)) is taken over equally by Deen and Hari.

Share gained by each = \(\frac{1}{2}\) of Raju's share = \(\frac{1}{2} \times \frac{6}{20} = \frac{3}{20}\).

3. Calculate New Shares:

Deen's New Share = Old Share + Gained Share

\[ = \frac{7}{20} + \frac{3}{20} = \frac{10}{20} \]
Hari's New Share = Old Share + Gained Share

\[ = \frac{7}{20} + \frac{3}{20} = \frac{10}{20} \]
4. New Profit-Sharing Ratio:

The new ratio of Deen : Hari is \(\frac{10}{20} : \frac{10}{20}\).

Simplifying this, we get 10 : 10, which is 1 : 1.


Step 4: Final Answer:

The new profit sharing ratio between Deen and Hari will be 1:1.
\[ \boxed{1:1} \] Quick Tip: When a partner's share is taken over by the remaining partners in a specific way (e.g., equally, or in a given ratio):
First, calculate the exact fraction of the outgoing partner's share that each remaining partner gets. This is their 'gain'.
Add this gain to each remaining partner's old share to find their new share.
Finally, express the new shares as a simplified ratio.

Step 1: Understanding the Question:

The question asks for the total amount of cash received (and thus debited to the Bank Account) when the first and final call was made. This amount will be the total call money due, less any amount that was not paid (Calls-in-Arrears). Money received in advance on allotment (from Usha) is not part of the cash inflow at the time of the call.


Step 2: Key Formula or Approach:

Amount received on Call = (Total Shares \(\times\) Call money per share) - Calls-in-Arrears.

Calls-in-Arrears = Number of defaulting shares \(\times\) Call money per share.


Step 3: Detailed Explanation:

1. Calculate the First and Final Call amount per share:

Face Value per share = Rs 10.

Amount on Application = Rs 3.

Amount on Allotment = Rs 2.

Balance on First and Final Call = Rs 10 - (Rs 3 + Rs 2) = Rs 10 - Rs 5 = Rs 5 per share.

2. Calculate the total amount due on the First and Final Call:

Total issued shares = 50,000.

Total amount due = 50,000 shares \(\times\) Rs 5/share = Rs 2,50,000.

3. Calculate the amount of Calls-in-Arrears:

Raj, with 300 shares, did not pay the call money.

Calls-in-Arrears = 300 shares \(\times\) Rs 5/share = Rs 1,500.

4. Calculate the actual amount received in the Bank:

The amount received is the total amount due minus the amount not paid.

Amount received = Total Due - Calls-in-Arrears = Rs 2,50,000 - Rs 1,500 = Rs 2,48,500.

(Note: The amount Usha paid in advance on allotment was received during allotment, not during the call collection period. Therefore, it does not affect the bank transaction for the call.)


Step 4: Final Answer:

The amount to be debited to the Bank Account for the first and final call will be Rs 2,48,500.
\[ \boxed{Rs 2,48,500} \] Quick Tip: When calculating cash received on a specific call:
Start with the total amount due from all shareholders for that call.
Subtract the amount not paid by defaulting shareholders (Calls-in-Arrears).
Do NOT add any amount received in advance (Calls-in-Advance) from a previous stage, as that cash was already received.

Step 1: Understanding the Question:

This is an Assertion-Reason question. We need to evaluate the correctness of both statements individually and then determine if the Reason provides a correct explanation for the Assertion.


Step 2: Key Formula or Approach:

1. Analyze Assertion (A) for its factual correctness based on the principles of partnership.

2. Analyze Reason (R) for its factual correctness.

3. Determine if there is a causal link, where (R) logically leads to or explains (A).


Step 3: Detailed Explanation:

Analysis of Assertion (A): "Partnership Agreement becomes the basis of relationship among the partners."

A Partnership Agreement (or Partnership Deed) is a document that outlines the terms and conditions of the partnership. It specifies the rights, duties, liabilities, profit-sharing ratios, capital contributions, etc., of each partner. Therefore, it legally and practically defines the relationship between the partners. This statement is correct.


Analysis of Reason (R): "Partnership is the result of an agreement between two or more persons to do business and share its profits and losses."

This statement is the legal definition of a partnership as per the Indian Partnership Act, 1932. The very existence of a partnership stems from an agreement (which can be oral or written). This statement is also correct.


Connecting Reason (R) and Assertion (A):

The Reason (R) states that a partnership is fundamentally born from an agreement. Because the partnership itself is the result of an agreement, it logically follows that this agreement (the Partnership Agreement) would form the foundation or basis of the relationship among the partners. The reason directly explains why the assertion is true.


Step 4: Final Answer:

Both Assertion (A) and Reason (R) are correct, and Reason (R) provides the correct explanation for Assertion (A).
\[ \boxed{Both A and R are correct and R explains A} \] Quick Tip: In assertion-reason questions, follow a two-step check:
\textbf{Validity Check:} Is A true? Is R true? If either is false, the answer is simple (C or D).
\textbf{Explanation Check:} If both are true, ask "Is A true because R is true?". If yes, the answer is (A). If no, the answer is (B).

Step 1: Understanding the Question:

The question asks for the amount and the nature of the entry (debit or credit) in the 'Share Forfeiture Account' when shares are forfeited.


Step 2: Key Formula or Approach:

When shares are forfeited, the Share Forfeiture Account is always credited. The amount credited is the total amount received from the shareholder towards the share capital (face value) of the shares. Any premium amount already received is credited to the Securities Premium Account and is not part of the forfeited amount.

Amount to be Credited = (Amount paid per share towards capital) \(\times\) (Number of forfeited shares).


Step 3: Detailed Explanation:

1. Determine the amount paid towards share capital per share:

Total amount paid per share = Rs 6 (this includes the premium).

Premium per share = Rs 1.

The question states that the premium was included in the amount paid. Since the premium has been received, we must exclude it when calculating the amount to be credited to the Share Forfeiture Account.

Amount paid towards capital = Total amount paid - Premium received = Rs 6 - Rs 1 = Rs 5 per share.

2. Calculate the total amount to be credited to the Share Forfeiture Account:

Number of forfeited shares = 600.

Total amount = Rs 5 per share \(\times\) 600 shares = Rs 3,000.

3. Determine the nature of the entry:

The amount received from the defaulting shareholder represents a capital gain to the company upon forfeiture. Therefore, the Share Forfeiture Account is credited.


Step 4: Final Answer:

The 'Share Forfeiture Account' will be credited by Rs 3,000.
\[ \boxed{Credited, Rs 3,000} \] Quick Tip: For Share Forfeiture A/c entries:
It is always a \textbf{credit} entry.
The amount is what has been received on the \textbf{face value (capital)} only.
If the securities premium has been received, ignore it for this calculation. If the premium was called but not received, it is debited (cancelled) in the forfeiture entry.

Step 1: Understanding the Question:

The question asks for the total 'Loss on Issue of Debentures'. This loss is a combination of two components: the discount given at the time of issue and the premium that will be paid at the time of redemption.


Step 2: Key Formula or Approach:

The total loss on the issue of debentures is calculated by adding the discount on issue to the premium on redemption.

Loss on Issue of Debentures = Discount on Issue + Premium on Redemption.


Step 3: Detailed Explanation:

1. Calculate the Discount on Issue:

Face value of debentures issued = Rs 10,00,000.

Discount rate = 10%.

Discount on Issue = 10% of Rs 10,00,000 = \(0.10 \times 10,00,000 = Rs 1,00,000\).

2. Identify the Premium on Redemption:

The question states that "premium on redemption of debentures account was credited by Rs 1,00,000". This is a future liability recognized at the time of issue.

Premium on Redemption = Rs 1,00,000.

3. Calculate the Total Loss on Issue:

Total Loss = Discount on Issue + Premium on Redemption

Total Loss = Rs 1,00,000 + Rs 1,00,000 = Rs 2,00,000.


Step 4: Final Answer:

The amount of loss on the issue of debentures was Rs 2,00,000.
\[ \boxed{Rs 2,00,000} \] Quick Tip: The 'Loss on Issue of Debentures' account aggregates two distinct losses that are recognized at the time of issue:
\textbf{Discount on issue:} An immediate loss representing the cash deficit on issue.
\textbf{Premium on redemption:} A future loss (a liability) that is prudently recognized at the time of issue itself.
Always add both components to find the total loss.

Step 1: Understanding the Question:

The question asks to calculate the total interest payable on debentures for a full financial year.


Step 2: Key Formula or Approach:

Debenture interest is always calculated on the face value (or nominal value) of the debentures, not on the issue price (which might be at a discount or premium).

Total Interest = Total Face Value of Debentures \(\times\) Interest Rate.


Step 3: Detailed Explanation:

1. Calculate the Total Face Value of the Debentures:

Number of debentures issued = 6,000.

Face value per debenture = Rs 100.

Total Face Value = 6,000 debentures \(\times\) Rs 100/debenture = Rs 6,00,000.

2. Calculate the Annual Interest:

The interest rate is given as 10% (from the name "10% debentures").

Annual Interest = Total Face Value \(\times\) Interest Rate

Annual Interest = Rs 6,00,000 \(\times\) 10% = \(6,00,000 \times \frac{10}{100} = Rs 60,000\).

3. Check the Time Period:

The debentures were issued on 1st April 2024, and interest is calculated for the year ended 31st March 2025. This is a full year, so the full annual interest is due. The discount of 8% on issue is irrelevant for calculating the interest payable.


Step 4: Final Answer:

The total amount of interest due on the debentures for the year is Rs 60,000.
\[ \boxed{Rs 60,000} \] Quick Tip: Key rule for debenture interest calculation:
Always use the \textbf{face value} of the debentures, not the issue price or market price.
The coupon rate (e.g., the '10%' in '10% Debentures') is the annual interest rate.
Pay attention to the date of issue to calculate interest for the correct time period.

Step 1: Understanding the Question:

The question asks for the amount of profit that will be transferred to the Profit and Loss Appropriation Account. This is the net profit after all 'charges against profit' have been deducted. Interest on a partner's loan is a charge against profit.


Step 2: Key Formula or Approach:

1. Calculate the interest on the partner's loan. As per the Indian Partnership Act, 1932, if the partnership deed is silent on the interest rate, a rate of 6% p.a. is applied.

2. Deduct this interest from the net profit before interest to find the profit available for appropriation.

Profit for Appropriation = Net Profit - Interest on Partner's Loan.


Step 3: Detailed Explanation:

1. Calculate the Interest on Tej's Loan:

Loan Amount = Rs 50,000.

Date of Loan = 1st April 2024. The period is for the full year until 31st March 2025.

The interest rate is not given in the problem, so we use the statutory rate of 6% p.a.

Interest on Loan = Rs 50,000 \(\times\) 6% \(\times\) 1 year = \(50,000 \times \frac{6}{100} = Rs 3,000\).

2. Calculate the Profit to be Transferred:

Interest on a partner's loan is a charge against profit, meaning it must be deducted in the Profit and Loss Account itself, before arriving at the net profit to be appropriated among partners.

Profit before interest = Rs 3,75,000.

Profit after interest (to be transferred to P\&L Appropriation A/c) = Rs 3,75,000 - Rs 3,000 = Rs 3,72,000.


Step 4: Final Answer:

The amount of profit transferred to the Profit and Loss Appropriation Account will be Rs 3,72,000.
\[ \boxed{Rs 3,72,000} \] Quick Tip: Remember the distinction between 'Charge against Profit' and 'Appropriation of Profit':
\textbf{Charge (e.g., Rent to a partner, Interest on partner's loan):} Must be paid regardless of profit or loss. It is debited to the P\&L Account.
\textbf{Appropriation (e.g., Salary to a partner, Interest on capital):} Paid only if there are profits. It is debited to the P\&L Appropriation Account.
Default interest rate on a partner's loan is 6% p.a. if not specified.

Step 1: Understanding the Question:

The question asks to calculate the opening capital (capital at the beginning of the year) of a partner, Vasu. We are given his closing capital and all the transactions that affected his capital account during the year (additional capital, drawings, and share of profit).


Step 2: Key Formula or Approach:

We need to work backward from the closing capital to find the opening capital. The standard capital account formula is:

Closing Capital = Opening Capital + Additional Capital + Share of Profit - Drawings.

To find the Opening Capital, we rearrange this formula:

Opening Capital = Closing Capital - Additional Capital - Share of Profit + Drawings.


Step 3: Detailed Explanation:

1. Calculate Vasu's share of profit:

Total firm profit = Rs 1,40,000.

Profit sharing ratio (Ashok : Vasu) = 4 : 3.

Vasu's share of profit = \( Total Profit \times \frac{3}{4+3} = 1,40,000 \times \frac{3}{7} = Rs 60,000 \).

2. List all the components for Vasu's capital account:

Closing Capital = Rs 3,75,000.

Additional Capital = Rs 1,50,000.

Drawings = Rs 40,000.

Share of Profit = Rs 60,000.

3. Apply the rearranged formula to find the Opening Capital:

Opening Capital = Closing Capital - Additional Capital - Share of Profit + Drawings.

Opening Capital = Rs 3,75,000 - Rs 1,50,000 - Rs 60,000 + Rs 40,000.

Let's do the calculations step-by-step:

= (Rs 3,75,000 + Rs 40,000) - (Rs 1,50,000 + Rs 60,000)

= Rs 4,15,000 - Rs 2,10,000

= Rs 2,05,000.


Step 4: Final Answer:

Vasu's capital in the beginning of the year was Rs 2,05,000.
\[ \boxed{Rs 2,05,000} \] Quick Tip: To find the opening capital, you need to reverse all the transactions that occurred during the year. Remember the mnemonic:
\[ Opening = Closing - Additions + Subtractions \] Here, 'Additions' are profit share and additional capital, and 'Subtractions' are drawings. So you subtract the additions and add back the subtractions from the closing capital.

Step 1: Understanding the Question:

The question asks us to calculate the 'proportionate capital' that the new partner, Hitesh, must bring in. This means his capital should be proportional to his profit share in the new firm. The calculation will be based on the combined, adjusted capital of the existing partners.


Step 2: Key Formula or Approach:

The process to find the proportionate capital is as follows:

1. Calculate the total adjusted capital of the old partners (Soni and Kush).

2. Determine the combined share of profit of the old partners in the new firm.

3. Use the combined capital and combined share of the old partners to calculate the total capital of the newly constituted firm.

4. Calculate the new partner's capital contribution based on his profit-sharing ratio.
\[ Total Firm Capital = \frac{Combined Adjusted Capital of Old Partners}{Combined Share of Old Partners} \] \[ New Partner's Capital = Total Firm Capital \times New Partner's Profit Share \]

Step 3: Detailed Explanation:

1. Find the combined adjusted capital of the old partners:

The capital balances of Soni and Kush after all adjustments are given.

Combined Capital = Soni's Capital + Kush's Capital

\[ = Rs 7,00,000 + Rs 13,00,000 = Rs 20,00,000 \]
2. Find the combined share of the old partners:

The new partner, Hitesh, is admitted for a \(\frac{1}{5}\) share of the profits.

The remaining share, which belongs to the old partners Soni and Kush, is:

\[ Combined Share = 1 - Hitesh's Share = 1 - \frac{1}{5} = \frac{4}{5} \]
3. Calculate the total capital of the new firm:

The combined capital of Soni and Kush (Rs 20,00,000) represents the \(\frac{4}{5}\) share of the total capital of the new firm.

\[ Total Firm Capital = Rs 20,00,000 \div \frac{4}{5} = Rs 20,00,000 \times \frac{5}{4} = Rs 25,00,000 \]
4. Calculate Hitesh's proportionate capital:

Hitesh needs to bring in capital equal to his \(\frac{1}{5}\) share of the total firm capital.

\[ Hitesh's Capital = Total Firm Capital \times Hitesh's Share = Rs 25,00,000 \times \frac{1}{5} = Rs 5,00,000 \]

Step 4: Final Answer:

The amount of proportionate capital brought in by Hitesh was Rs 5,00,000.
\[ \boxed{Rs 5,00,000} \] Quick Tip: To find the new partner's proportionate capital:
1. Combine the \textbf{adjusted} capitals of the old partners.
2. Find the remaining profit share for the old partners.
3. Calculate the total firm's capital by taking the reciprocal of the old partners' share and multiplying it by their combined capital.
4. Multiply the total firm's capital by the new partner's profit share.