Class 12 Accountancy Part-1 Chapter 4 Reconstitution of Partnership : Retirement of a Partner

Key Concept: Sacrifice made by Continuing Partner Also

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that when a continuing partner sacrifices his share of profit on the retirement of a partner, his capital account is credited with the proportionate amount of goodwill. This is true because the sacrificing partner gives up a part of his profit share, and as per accounting treatment, his capital account is credited.
The Reason states that the sacrificing partner's contribution to the firm's goodwill needs to be compensated by the gaining partners. This is also true because the gaining partners acquire the sacrificed share and must compensate the sacrificer.
Furthermore, the Reason correctly explains the Assertion as the compensation mechanism (Reason) justifies why the sacrificing partner's capital account is credited (Assertion).

Key Concept: Adjustment of Capitals

b) \$40,000
[Solution Description]
The total capital of the new firm is \$100,000. The new profit-sharing ratio between Y and Z is $2 : 3$. To find Y's new capital:
$\text{Y's Capital} = \frac{2}{2 + 3} \times 100,000 = \frac{2}{5} \times 100,000 = \$40,000$

Key Concept: Goodwill Adjustment, Revaluation of Assets and Liabilities

c) `52,000
[Solution Description]
First, calculate C's share of goodwill: $60,000 \times \frac{1}{6} = `10,000$. Next, calculate C's share of revaluation profit: $12,000 \times \frac{1}{6} = `2,000$. Add these to C's capital balance: $40,000 + 10,000 + 2,000 = `52,000$.

Key Concept: Journal Entry for Hidden Goodwill

c) \$12,000
[Solution Description]
Step 1: Calculate hidden goodwill = \$90,000 - \$72,000 = \$18,000.
Step 2: Gaining ratio is 2:1 (A:B).
Step 3: A's share = $\frac{2}{3} \times \$18,000 = \$12,000$.
Therefore, A’s Capital A/c will be debited with \$12,000.

Key Concept: Payment of Amount Due to Retiring Partner

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
According to the syllabus, when a partner retires, the amount due to them can be settled in various ways, including lump sum payment or instalments with or without interest as per the partnership deed. This makes Assertion (A) true. The Reason (R) states that the retiring partner’s loan account is a liability for the new firm, which is also true and correctly explains why the amount due can be paid in instalments (to manage the firm's cash flow while recognizing the obligation). Thus, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: Adjustment of Unrecorded Assets

b) Asset \$15,000 + Cash \$50,000
[Solution Description]
The unrecorded asset must first be recorded by debiting the asset account and crediting Revaluation Account. The revaluation profit is distributed among partners in their profit-sharing ratio (1:1:1).
Revised settlement to R:
$\text{Total Adjusted Claim} = 60,000 + (\frac{15,000}{3}) = 65,000$
Settlement: \$15,000 (asset) + \$50,000 (cash) = \$65,000.

Key Concept: Retirement of a Partner

d) Assertion is false, but Reason is true.
[Solution Description]
The assertion states that a partner can retire only with the consent of all other partners. While this is one way a partner can retire as per Section 32(1)(a) of the Indian Partnership Act, 1932, it is not the only way. The reason correctly cites Section 32(1)(a), but the assertion is incomplete because a partner can also retire via an express agreement or by giving written notice in case of a partnership at will (as per Sections 32(1)(b) and 32(1)(c)). Thus, the assertion is false, while the reason is true.

Key Concept: Determination of Amount Payable to a Retiring Partner

d) Assertion is false, but Reason is true.
[Solution Description]
The assertion states that the amount payable to a retiring partner includes only his capital balance, which is false because it also includes his share of goodwill, revaluation profits/losses, and undistributed profits. The reason is partially true but incomplete, as a retiring partner's claim is not just limited to capital but extends to other entitlements as well. Thus, Assertion is false, but Reason is true.

Key Concept: Revaluation Account

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
\begin{itemize}

Key Concept: Hidden Goodwill, Multiple Retirements

b) \$35,000, M contributes \$21,000 and N contributes \$14,000
[Solution Description]
Hidden goodwill for O = \$70,000 - \$50,000 = \$20,000
Hidden goodwill for P = \$45,000 - \$30,000 = \$15,000
Total hidden goodwill = \$20,000 + \$15,000 = \$35,000
Old ratio of M and N was 4:3. New ratio is 3:2.
Gaining ratio for M = 3/5 - 4/7 = (21 - 20)/35 = 1/35
Gaining ratio for N = 2/5 - 3/7 = (14 - 15)/35 = -1/35. Since N's share decreases, only M gains. So, M's gain = 1/35 of total profit.
However, in practice, when two partners retire, the continuing partners adjust the goodwill based on their new ratio. Here, since M and N have a new ratio of 3:2, they will share the goodwill in this ratio.
M's contribution = (3/5) * \$35,000 = \$21,000
N's contribution = (2/5) * \$35,000 = \$14,000
Journal entries:
M's Capital A/c Dr. \$21,000
N's Capital A/c Dr. \$14,000
To O's Capital A/c \$20,000
To P's Capital A/c \$15,000

Key Concept: Total Capital Calculation, New Capital Allocation

d) \$480,000
[Solution Description]
Step 1: Sum the existing capitals of A and B along with the amount payable to C and additional cash.
$180,000 + 120,000 + 150,000 + 30,000 = 480,000$
So, the total capital of the new firm is \$480,000.

Key Concept: Sacrifice made by Continuing Partner

d) Neither X nor Y sacrificed
[Solution Description]
First, calculate the old ratio: X ($\frac{2}{10}$), Y ($\frac{3}{10}$), Z ($\frac{5}{10}$).
New ratio: X ($\frac{1}{3}$), Y ($\frac{2}{3}$).
Gaining ratio = New ratio - Old ratio.
For X: $\frac{1}{3} - \frac{2}{10} = \frac{10}{30} - \frac{6}{30} = \frac{4}{30}$ (Gain).
For Y: $\frac{2}{3} - \frac{3}{10} = \frac{20}{30} - \frac{9}{30} = \frac{11}{30}$ (Gain).
Since both X and Y gained, no continuing partner sacrificed.

Key Concept: Gaining Ratio Application

c) \$15,000
[Solution Description]
First, calculate hidden goodwill: \$90,000 - \$60,000 = \$30,000. The gaining ratio between A and B is 1:1 (as they now share equally). Thus, A's share of hidden goodwill = (\$30,000 / 2) = \$15,000.

Key Concept: Partners' Capital Accounts Adjustment

d) \$0
[Solution Description]
Total capital = \$45,000 + \$30,000 = \$75,000
P's required capital = \$75,000 × 3/5 = \$45,000
Q's required capital = \$75,000 × 2/5 = \$30,000
P's capital already matches (\$45,000)
Q's capital also matches (\$30,000)
No cash needs to be brought in by Q

Key Concept: Adjustment of Capitals

c) \$100,000
[Solution Description]
The total capital of the new firm is \$200,000. The profit-sharing ratio between P and Q is $1 : 1$. Since the ratio is equal, the capital will also be divided equally:
$\text{P's Capital} = \frac{1}{1 + 1} \times 200,000 = \frac{1}{2} \times 200,000 = \$100,000$

Key Concept: Partners’ Capital Accounts

b) \$4,000
[Solution Description]
Revaluation loss is distributed among partners in their profit-sharing ratio. Here, since it is equally shared among three partners, each partner bears \$4,000 (\$12,000 ÷ 3).
Thus, X's Capital Account will be debited with \$4,000.

Key Concept: Calculation of Gaining Ratio

b) $2 : 1$
[Solution Description]
First, calculate the share acquired by A and C from B:
$\text{A's gain} = \frac{2}{3} \times \frac{1}{3} = \frac{2}{9}$
$\text{C's gain} = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$
The gaining ratio of A and C is $2 : 1$.

Key Concept: Hidden Goodwill Calculation

c) \$12,000
[Solution Description]
Hidden goodwill is calculated as the excess amount paid over the adjusted capital.
Step 1: Adjusted capital of Z = \$48,000
Step 2: Amount paid to Z = \$60,000
Step 3: Hidden goodwill = \$60,000 - \$48,000 = \$12,000
Thus, the hidden goodwill is \$12,000.

Key Concept: Goodwill Adjustment, Multiple Instalments, Interest Calculation

b) \$1,600 for full second year
[Solution Description]
Step 1: Calculate total due to R:
Capital = \$60,000
Assuming goodwill adjusted = \$60,000 × (1/6) = \$10,000
Total due = \$70,000
Step 2: First payment:
Paid = \$30,000
Remaining = \$40,000
Step 3: Two annual instalments of \$20,000 each
Step 4: Interest for first year on \$40,000:
$8/100 \times 40,000 = 3,200$
Step 5: After first instalment (20k principal + 3.2k interest):
New principal = \$20,000
Step 6: Interest for second year:
$8/100 \times 20,000 = 1,600$
The second instalment includes this \$1,600 interest.

Key Concept: Change in Profit Sharing Ratio on the Retirement of a Partner

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
Assertion (A) states that when a partner retires, the remaining partners acquire the retiring partner's share in their old profit-sharing ratio if no new ratio is specified. This is true as per the syllabus, which mentions that if the new profit-sharing ratio is not given, the retiring partner's share is acquired in the old ratio by the remaining partners. Reason (R) states that the gaining ratio determines how the retiring partner's share is distributed among the remaining partners. This is also true because the gaining ratio is calculated as the difference between the new ratio and the old ratio, showing how the share is acquired. However, the Reason does not directly explain why the old ratio is used when no new ratio is specified. Hence, both are true, but the Reason does not correctly explain the Assertion.

Key Concept: Calculation of Gaining Ratio

b) $2 : 1$
[Solution Description]
To find the gaining ratio, we subtract the old ratio from the new ratio for each partner.
$\text{X's gain} = \frac{7}{10} - \frac{5}{10} = \frac{2}{10} = \frac{1}{5}$
$\text{Z's gain} = \frac{3}{10} - \frac{2}{10} = \frac{1}{10}$
Thus, the gaining ratio of X and Z is $2 : 1$.

Key Concept: Journal Entry for Goodwill Adjustment

b) AS-26
[Solution Description]
As per the syllabus, adjusting goodwill without raising a Goodwill Account is done in compliance with AS-26 (Accounting Standard 26), which prohibits the recognition of internally generated goodwill in financial statements.

Key Concept: Retirement of a Partner

c) In accordance with an express agreement by the partners
[Solution Description]
According to Section 32 (1) of the Indian Partnership Act, 1932, a partner may retire: (a) with the consent of all other partners, (b) in accordance with an express agreement by the partners, or (c) in case of partnership at will, by giving written notice to all other partners of his intention to retire.

Key Concept: Sacrifice made by Continuing Partner

c) Gaining Partner's Capital A/c
[Solution Description]
According to the syllabus, when a partner retires and continuing partners also sacrifice their share, the gaining partner's capital account is debited, and the sacrificing partners' capital accounts are credited, including the retiring partner's capital account if they have sacrificed. The journal entry format is:
$\text{Gaining Partner's Capital A/c} \quad Dr. \\ \\ \quad \text{To Sacrificing Partner's Capital A/c (including retiring partner if applicable)}$

Key Concept: Revaluation Account

b) \$10,000
[Solution Description]
The profit on revaluation is calculated by subtracting the old value from the new value. Here, the building's value increased from \$50,000 to \$60,000. So the profit is \$60,000 - \$50,000 = \$10,000.

Key Concept: Retirement of Partner: Settlement via Loan Account

c) Dr. Charu's Capital A/c \$27,000; Cr. Charu's Loan A/c \$27,000
[Solution Description]
Step 1: Since no cash is paid, the entire amount is transferred to Charu's Loan A/c.
Step 2: The journal entry will debit Charu's Capital A/c and credit Charu's Loan A/c with \$27,000.

Key Concept: Gaining Ratio Calculation

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that when the new profit sharing ratio is not specified, the gaining ratio is taken as the old profit sharing ratio of the remaining partners. This is correct because, in such cases, it is standard practice to assume that the continuing partners acquire the outgoing partner's share in their existing profit-sharing ratio. The reason provided explains that this assumption simplifies calculations and maintains continuity, which is a valid justification for the assertion. Therefore, both the assertion and reason are true, and the reason correctly explains the assertion.

Key Concept: Hidden Goodwill

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
According to the concept of hidden goodwill, when a retiring partner is paid an amount greater than his adjusted capital, the excess is treated as his share of goodwill. Here, the retiring partner's adjusted capital is \textbackslash\$ 70,000, but he receives \textbackslash\$ 90,000, so the difference (\textbackslash\$ 20,000) is hidden goodwill. The reason correctly states that this goodwill is recorded by debiting the gaining partners' capital accounts (as per the gaining ratio). Thus, both Assertion and Reason are true, and Reason correctly explains the Assertion.

Key Concept: Gaining Ratio Calculation

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the gaining ratio is calculated by subtracting the old ratio from the new ratio, which is correct as per the formula: $Gaining\ ratio = New\ ratio - Old\ ratio$. The reason explains the purpose of the gaining ratio, which is to determine how the remaining partners acquire the outgoing partner's share. Both statements are true, and the reason correctly explains the assertion.

Key Concept: Revaluation Account, Profit/Loss Distribution

b) Partner A's capital increases by \$4,000.
[Solution Description]
Step 1: Calculate the increase in asset value. Original assets = \$200,000; Undervaluation = 10\%. Increase = \$200,000 × 10\% = \$20,000.
Step 2: Calculate the decrease in liability value. Original liabilities = \$50,000; Overvaluation = 20\%. Decrease = \$50,000 × 20\% = \$10,000.
Step 3: Prepare Revaluation Account. Credit for asset increase (\$20,000) and debit for liability decrease (\$10,000). Net profit = \$20,000 - \$10,000 = \$10,000.
Step 4: Distribute profit in old ratio (2:2:1). Total parts = 2 + 2 + 1 = 5. Partner A's share = (2/5) × \$10,000 = \$4,000.

Key Concept: Hidden Goodwill Calculation

c) \$20,000
[Solution Description]
Hidden goodwill is calculated as the excess amount paid to the retiring partner over his adjusted capital. Here, R's adjusted capital is \$80,000, and he is paid \$1,00,000. Therefore, hidden goodwill = \$1,00,000 - \$80,000 = \$20,000.

Key Concept: New Profit-Sharing Ratio with Multiple Retirements

a) $11 : 14$
[Solution Description]
Total profit-sharing ratio parts = $3 + 2 + 1 + 4 = 10$. P's share = $\frac{3}{10}$, R's share = $\frac{1}{10}$. Total retiring partners' share = $\frac{4}{10}$. Q gains $\frac{3}{5} \times \frac{4}{10} = \frac{12}{50} = \frac{6}{25}$. S gains $\frac{2}{5} \times \frac{4}{10} = \frac{8}{50} = \frac{4}{25}$. Q's new share = $\frac{2}{10} + \frac{6}{25} = \frac{10}{50} + \frac{12}{50} = \frac{22}{50} = \frac{11}{25}$. S's new share = $\frac{4}{10} + \frac{4}{25} = \frac{20}{50} + \frac{8}{50} = \frac{28}{50} = \frac{14}{25}$. New ratio between Q and S is $\frac{11}{25} : \frac{14}{25} = 11 : 14$.

Key Concept: Revaluation of Assets and Liabilities, Retirement of a Partner

b) Rs.50,000
[Solution Description]
The profit on revaluation is shared equally among all partners, including the retiring partner.
Revaluation Profit = Rs.7,50,000 - Rs.6,00,000 = Rs.1,50,000
Z's share = $\frac{1}{3} \times Rs.1,50,000 = Rs.50,000$
Hence, Rs.50,000 will be credited to Z's capital account.

Key Concept: Retirement of a Partner

c) The discontinuation of a partner from the firm
[Solution Description]
Retirement of a partner means that the partner discontinues being a partner in the firm. According to Section 32(1) of the Indian Partnership Act, 1932, a partner may retire with the consent of all other partners, as per an express agreement, or by giving notice in writing in case of a partnership at will.

Key Concept: Calculation of Interest

d) \$16,000
[Solution Description]
To calculate the interest on the outstanding loan amount, we use the formula: $\text{Interest} = \text{Principal} \times \text{Rate} \times \frac{\text{Time}}{1}$. Here, Principal = \$200,000, Rate = 8\%, Time = 1 year.
Step-by-step calculation:
\begin{itemize}

Key Concept: Super Profits, Goodwill Calculation

c) \$12,000
[Solution Description]
Super profits = Average Profit - Normal Profit = \$45,000 - \$25,000 = \$20,000. Goodwill = Super Profits $\times$ No. of years' purchase = \$20,000 $\times$ 3 = \$60,000. R's share of goodwill = \$60,000 $\times$ (2/10) = \$12,000.

Key Concept: New Profit Sharing Ratio Calculation

b) 23:17
[Solution Description]
T's share is $\frac{1}{10}$ (from 5:4:1). This share is divided between R and S in 3:1.
R gains $\frac{3}{4} \times \frac{1}{10} = \frac{3}{40}$.
S gains $\frac{1}{4} \times \frac{1}{10} = \frac{1}{40}$.
R's new share $= \frac{5}{10} + \frac{3}{40} = \frac{20}{40} + \frac{3}{40} = \frac{23}{40}$.
S's new share $= \frac{4}{10} + \frac{1}{40} = \frac{16}{40} + \frac{1}{40} = \frac{17}{40}$.
The new ratio is $\frac{23}{40} : \frac{17}{40}$ or 23:17.

Key Concept: Adjustment of Capitals

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
When a partner retires or dies, the remaining partners may need to adjust their capital contributions to align with the new profit-sharing ratio. This is done to maintain fairness in the distribution of profits and losses among the remaining partners. The assertion is true as it correctly states the necessity of adjusting capital contributions. The reason is also true because the adjustment indeed ensures that the capital balances are proportionate to the new profit-sharing ratio, justifying the assertion. Therefore, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: Goodwill Adjustment Entry

b) P's Capital A/c Dr. \$8,000; Q's Capital A/c Dr. \$4,000; To R's Capital A/c \$12,000
[Solution Description]
The gaining ratio determines how R's share of goodwill (\$12,000) is debited to P and Q.
P's share = $\frac{2}{3} \times 12,000 = \$8,000$
Q's share = $\frac{1}{3} \times 12,000 = \$4,000$
Journal entry:
P's Capital A/c Dr. \$8,000
Q's Capital A/c Dr. \$4,000
To R's Capital A/c \$12,000

Key Concept: Goodwill Adjustment, Revaluation

a) \$14,000
[Solution Description]
Old ratio is $4:3:2$, new ratio is $3:2$.
Gaining ratio for X: $\frac{3}{5} - \frac{4}{9} = \frac{27 - 20}{45} = \frac{7}{45}$
Gaining ratio for Z: $\frac{2}{5} - \frac{2}{9} = \frac{18 - 10}{45} = \frac{8}{45}$
Total goodwill = \$90,000. Y's share = $\frac{3}{9} \times 90000 = 30000$.
This amount will be shared by X and Z in their gaining ratio ($7:8$).
Amount debited to X's capital account = $\frac{7}{15} \times 30000 = 14000$.

Key Concept: Calculation of New Profit Sharing Ratio

b) 5 : 4
[Solution Description]
The given ratio is $\frac{5}{12} : \frac{4}{12} : \frac{3}{12}$, which simplifies to $5 : 4 : 3$ when multiplied by 12. When Z retires, his share of $\frac{3}{12}$ is removed. The remaining shares are $\frac{5}{12}$ for X and $\frac{4}{12}$ for Y. The new ratio is calculated as $\frac{5}{9}$ for X and $\frac{4}{9}$ for Y (since $5 + 4 = 9$). Thus, the new ratio is $5 : 4$.

Key Concept: Distribution of Revaluation Profit/Loss

c) \$3,000
[Solution Description]
The total revaluation loss is \$9,000, shared equally among the three partners. Each partner's share of the loss is calculated as \$9,000 / 3 = \$3,000.

Key Concept: Reconstitution of Firm

d) A new partnership comes into existence among the remaining partners
[Solution Description]
Retirement of a partner results in the reconstitution of the firm. The old partnership ends, but the firm continues, and a new partnership comes into existence among the remaining partners.

Key Concept: Liability of Retiring Partner

b) If he does not give public notice of his retirement
[Solution Description]
A retiring partner remains liable for the firm's debts if he does not give public notice of his retirement. However, this rule does not apply to sleeping partners, who need not give such notice.

Key Concept: New Profit Sharing Ratio Calculation

c) 4:3
[Solution Description]
First, convert the fractions to whole numbers for simplicity. Multiply each term by 8 to get the ratio as 4:3:1. When Z retires, the remaining ratio between X and Y is 4:3.

Key Concept: Calculation of Sacrificing Ratio

a) $\frac{1}{24}$ Gain
[Solution Description]
Calculate sacrificing ratio using the formula:
$\text{Sacrificing Ratio} = \text{Old Ratio} - \text{New Ratio}$
For B: Old Ratio = $\frac{2}{6}$, New Ratio = $\frac{3}{8}$.
$\text{Sacrificing Ratio} = \frac{2}{6} - \frac{3}{8} = \frac{16}{48} - \frac{18}{48} = -\frac{2}{48} = -\frac{1}{24} \text{(Gain)}$
Thus, B gains $\frac{1}{24}$ share.

Key Concept: Goodwill Appears in the Books

b) Debit: X's Capital A/c \textbackslash(\textbackslash$35,000\textbackslash), Y's Capital A/c \textbackslash(\textbackslash$ 25,000\textbackslash), Z's Capital A/c \textbackslash(\textbackslash$20,000\textbackslash); Credit: Goodwill A/c \textbackslash(\textbackslash$ 80,000\textbackslash)
[Solution Description]
The existing goodwill of \textbackslash(\textbackslash$80,000\textbackslash) must be written off in the old profit-sharing ratio (7:5:4). Total parts = 7 + 5 + 4 = 16. X's share =$\frac{7}{16} \times 80,000 = \textbackslash(\textbackslash$35,000\textbackslash), Y's share =$\frac{5}{16} \times 80,000 = \textbackslash(\textbackslash$25,000\textbackslash), Z's share =$\frac{4}{16} \times 80,000 = \textbackslash(\textbackslash$ 20,000\textbackslash). The journal entry will debit all partners' capital accounts and credit the goodwill account.

Key Concept: Adjustment of Accumulated Losses

c) Debited to all partners in old profit-sharing ratio
[Solution Description]
Undistributed losses (such as a debit balance in Profit and Loss A/c) are debited to all partners' capital/current accounts in their old profit-sharing ratio. The journal entry is:
$\text{All Partners’ Capital/Current A/cs Dr.}$
$\text{To Profit and Loss A/c}$

Key Concept: Hidden Goodwill Calculation

c) \$20,000
[Solution Description]
Hidden goodwill is calculated as the amount paid to the retiring partner minus his adjusted capital.
$\text{Hidden Goodwill} = 70,000 - 50,000 = \$20,000$

Key Concept: Hidden Goodwill, Gaining Ratio

b) \$6,000
[Solution Description]
Hidden goodwill is calculated as the excess amount paid over the retiring partner's adjusted capital. Here, Z receives \$78,000, while his capital is \$60,000. So, hidden goodwill = \$78,000 - \$60,000 = \$18,000. This represents Z's share of goodwill. Since the gaining ratio between X and Y is 2:1, X's share = \$18,000 $\times$ (2/3) = \$12,000, and Y's share = \$18,000 $\times$ (1/3) = \$6,000. Therefore, Y's capital account will be debited by \$6,000.

Key Concept: Surplus/Deficit Adjustment, New Capital Allocation

b) Bring in \$100,000
[Solution Description]
Step 1: Calculate the total ratio parts as $3 + 2 = 5$.
Step 2: Determine Partner X's new capital share:
$500,000 \times \frac{3}{5} = 300,000$
Step 3: Subtract existing capital from new capital:
$300,000 - 200,000 = 100,000$
This means Partner X needs to bring in \$100,000.

Key Concept: Liability of Retiring Partner

d) After giving a public notice of retirement or if they were a sleeping partner.
[Solution Description]
A retiring partner remains liable for the firm's acts until a public notice of retirement is given, unless they were a sleeping partner.

Key Concept: Interest Calculation on Partner’s Loan

b) \$`5,000$`
[Solution Description]
First, calculate the outstanding loan amount at the beginning of the first year (\$`50,000$`). The interest for the first year is calculated as:$\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} = 50,000 \times \frac{10}{100} \times 1 = \$`5,000$`.

Key Concept: Liability of Retiring Partner

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a retiring partner is not liable for the firm's acts after retirement, which is true as per the syllabus. The reason states that the retiring partner remains liable to third parties until a public notice of retirement is given, which is also true as per the syllabus. Furthermore, the reason correctly explains why the assertion is true - because liability ceases only after public notice is given. Therefore, both assertion and reason are true, and the reason correctly explains the assertion.

Key Concept: New Profit Sharing Ratio, Equal Acquisition

a) $13 : 11$
[Solution Description]
Step 1: Calculate P's share = $\frac{5}{12}$.
Step 2: Q's gain = $\frac{1}{2} \times \frac{5}{12} = \frac{5}{24}$.
Step 3: R's gain = $\frac{1}{2} \times \frac{5}{12} = \frac{5}{24}$.
Step 4: New share for Q = $\frac{4}{12} + \frac{5}{24} = \frac{8}{24} + \frac{5}{24} = \frac{13}{24}$.
Step 5: New share for R = $\frac{3}{12} + \frac{5}{24} = \frac{6}{24} + \frac{5}{24} = \frac{11}{24}$.
Thus, the new ratio is $\frac{13}{24} : \frac{11}{24} = 13 : 11$.

Key Concept: Gaining Ratio with New Ratio Given

a) 5 : 7
[Solution Description]
Gaining ratio = New ratio - Old ratio.
P's new share = $\frac{7}{12}$, old share = $\frac{4}{9}$.
P's gain = $\frac{7}{12} - \frac{4}{9} = \frac{21 - 16}{36} = \frac{5}{36}$
R's new share = $\frac{5}{12}$, old share = $\frac{2}{9}$.
R's gain = $\frac{5}{12} - \frac{2}{9} = \frac{15 - 8}{36} = \frac{7}{36}$
Thus, gaining ratio = 5 : 7

Key Concept: Gaining Ratio Calculation

b) 8:13
[Solution Description]
Calculate X’s gain: $\frac{4}{7} - \frac{4}{9} = \frac{8}{63}$. Calculate Z’s gain: $\frac{3}{7} - \frac{2}{9} = \frac{13}{63}$. Hence, the gaining ratio is 8:13.

Key Concept: New Ratio Calculation

a) $11 : 14$
[Solution Description]
Total shares of retiring partners P ($3/10$) and R ($1/10$) = $4/10$.
Step 1: Q's gaining share = $(3/5) \times (4/10) = 12/50$.
Step 2: S's gaining share = $(2/5) \times (4/10) = 8/50$.
Step 3: Q's new share = Old share + Gaining share = $2/10 + 12/50 = 22/50$.
Step 4: S's new share = $4/10 + 8/50 = 28/50$.
New ratio = $22 : 28$ or simplified as $11 : 14$.

Key Concept: Payment of Amount Due to Retiring Partner

c) Retiring Partner’s Loan A/c
[Solution Description]
When the amount due to a retiring partner is not paid immediately, the retiring partner’s capital account is debited and his loan account is credited. The journal entry is:
$\text{Retiring Partner’s Capital A/c} \quad \text{Dr.} \quad \text{To Retiring Partner’s Loan A/c}$
This transfers the unpaid amount to the retiring partner’s loan account.

Key Concept: Super Profit Calculation

d) \$45,000
[Solution Description]
Super profit is calculated as the difference between average profit and normal profit.
$\text{Super Profit} = 40,000 - 25,000 = \$15,000$
Goodwill is then calculated as 3 times the super profit.
$\text{Goodwill} = 15,000 \times 3 = \$45,000$

Key Concept: New Profit Sharing Ratio

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
In this case, the assertion is true because when a partner retires and nothing is specified about the new profit sharing ratio, the remaining partners continue to share profits in their original proportion, excluding the retired partner's share. The reason is also true and correctly explains the assertion as it describes the necessity of recalculating the ratio to reflect the absence of the retired partner.

Key Concept: Retirement of Partner: Partial Payment

a) Dr. Mona's Capital A/c \$24,000; Cr. Cash/Bank A/c \$12,000; Cr. Mona's Loan A/c \$12,000
[Solution Description]
Step 1: Calculate the cash paid to Mona immediately. Half of \$24,000 is \$12,000.
Step 2: Determine the remaining amount transferred to Loan A/c. Remaining amount = \$24,000 - \$12,000 = \$12,000.
Step 3: The journal entry will be: Dr. Mona's Capital A/c \$24,000; Cr. Cash/Bank A/c \$12,000; Cr. Mona's Loan A/c \$12,000.

Key Concept: Goodwill Written Off

d) In the old profit-sharing ratio
[Solution Description]
Existing goodwill is written off in the old profit-sharing ratio of the partners. The amount debited to the partners' capital accounts is based on their old ratio.

Key Concept: Adjustment of Capitals: Capital Adjustment Entry

c) \$50,000
[Solution Description]
Total capital of the new firm = \$250,000.
R's share = $\frac{1}{5}$ (from $2 : 2 : 1$ ratio).
Therefore, R's capital = $\frac{1}{5} \times 250,000 = \$50,000$.
Since R is bringing fresh capital, he must contribute \$50,000.

Key Concept: Interest Calculation, Journal Entries

a) \$8,000
[Solution Description]
Step 1: Calculate interest for the year.
Interest = 8\% of \$50,000 = \$4,000.
Step 2: Determine principal repayment.
Total instalment = \$12,000.
Principal repaid = \$12,000 - \$4,000 (interest) = \$8,000.
Step 3: Verify closing balance.
New loan balance = \$50,000 - \$8,000 = \$42,000.
Portion of principal repayment: \$8,000.

Key Concept: Hidden Goodwill, Gaining Ratio

b) \$30,000, gaining ratio 3:2
[Solution Description]
Hidden goodwill is calculated as the excess payment over the adjusted capital of the retiring partner. Here, C's adjusted capital is \$90,000, but he is paid \$120,000. So, hidden goodwill = \$120,000 - \$90,000 = \$30,000.
To find the gaining ratio:
Old ratio of A and B was 3:2. After C's retirement, new ratio will be their old ratio since nothing else is specified. So, gaining ratio remains 3:2.
Journal entry:
A's Capital A/c Dr. \$18,000 (3/5 of \$30,000)
B's Capital A/c Dr. \$12,000 (2/5 of \$30,000)
To C's Capital A/c \$30,000

Key Concept: Interest on Unpaid Amount to Retiring Partner

b) 6\% p.a.
[Solution Description]
According to Section 37 of the Partnership Act, 1932, in the absence of an agreement, the outgoing partner is entitled to receive interest at 6\% p.a. on the unpaid amount until the date of payment or a share of the profit attributable to the use of their money, whichever is higher.

Key Concept: Calculation of New Profit Sharing Ratio, Reconstitution of Partnership

c) Assertion is true, but Reason is false.
[Solution Description]
First, convert the given profit-sharing ratio $\frac{1}{3} : \frac{1}{6} : \frac{1}{2}$ into whole numbers by finding the LCM of denominators (3, 6, 2), which is 6. Multiply each term by 6:
$P = \frac{1}{3} \times 6 = 2, \quad Q = \frac{1}{6} \times 6 = 1, \quad R = \frac{1}{2} \times 6 = 3.$
The simplified ratio is $2 : 1 : 3$. When Q retires, his share ($1$) is distributed between P and R in their old ratio ($2 : 3$).
P's gain = $\frac{2}{5} \times 1 = \frac{2}{5}$
R's gain = $\frac{3}{5} \times 1 = \frac{3}{5}$
New share of P = Old share + Gained share = $\frac{2}{6} + \frac{2}{5} \times \frac{1}{6} = \frac{10}{30} + \frac{2}{30} = \frac{12}{30} = \frac{2}{5}$
New share of R = Old share + Gained share = $\frac{3}{6} + \frac{3}{5} \times \frac{1}{6} = \frac{15}{30} + \frac{3}{30} = \frac{18}{30} = \frac{3}{5}$
Hence, the new ratio is $2 : 3$, confirming Assertion (A) is true. However, Reason (R) is false because the remaining partners do not always acquire the retiring partner's share in their old ratio unless specified; they may acquire it equally or in another agreed ratio.

Key Concept: Construction of Partner’s Loan Account

a) Transferring the balance from the capital account to the loan account
[Solution Description]
The first step involves transferring the balance of the retiring partner's capital account to their loan account. This ensures that the amount due to the retiring partner is recorded as a liability and will be paid in instalments with interest.

Key Concept: Change in Profit Sharing Ratio

a) $5 : 3$
[Solution Description]
When B retires, his share ($4/12$) is to be distributed among A and C in their old ratio of $5 : 3$.
Step 1: Calculate total parts = $5 + 4 + 3 = 12$.
Step 2: B's share = $4/12$.
Step 3: A's gaining share = $(5/8) \times (4/12) = 20/96 = 5/24$.
Step 4: C's gaining share = $(3/8) \times (4/12) = 12/96 = 3/24$.
Step 5: A's new share = Old share + Gaining share = $5/12 + 5/24 = 15/24$.
Step 6: C's new share = $3/12 + 3/24 = 9/24$.
New ratio = $15 : 9$ or simplified as $5 : 3$.

Key Concept: Accounting Treatment of Undistributed Profits and Losses

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
According to the accounting treatment for undistributed profits at the time of retirement, all accumulated profits (e.g., General Reserve, Profit and Loss A/c credit balance) must be distributed among all partners, including the retiring partner, in their old profit-sharing ratio. This ensures that the retiring partner receives their rightful share of profits earned during their tenure in the firm. The Reason correctly justifies the Assertion, as it explains why the retiring partner is included in the distribution.

Key Concept: Termination of Old Partnership and Continuation of Firm

d) A new partnership is formed among the remaining partners, and the firm continues.
[Solution Description]
The old partnership comes to an end, but the firm continues with the remaining partners forming a new partnership.

Key Concept: Calculation of New Profit Sharing Ratio

b) $23 : 17$
[Solution Description]
C's share is $\frac{1}{10}$ (since $5 + 4 + 1 = 10$). A gains $\frac{3}{4} \times \frac{1}{10} = \frac{3}{40}$. B gains $\frac{1}{4} \times \frac{1}{10} = \frac{1}{40}$. A's new share = $\frac{5}{10} + \frac{3}{40} = \frac{20}{40} + \frac{3}{40} = \frac{23}{40}$. B's new share = $\frac{4}{10} + \frac{1}{40} = \frac{16}{40} + \frac{1}{40} = \frac{17}{40}$. The new ratio of A to B is $\frac{23}{40} : \frac{17}{40} = 23 : 17$.

Key Concept: New Profit Sharing Ratio

b) $1 : 1$
[Solution Description]
Step 1: Shakti's share is $\frac{3}{10}$.
Step 2: Since Sadhana acquires Shakti's entire share, her new share becomes $\frac{2}{10} + \frac{3}{10} = \frac{5}{10}$ or $\frac{1}{2}$.
Step 3: Shiv's share remains unchanged at $\frac{5}{10}$ or $\frac{1}{2}$.
Step 4: The new profit-sharing ratio is $\frac{1}{2} : \frac{1}{2}$ or $1 : 1$.

Key Concept: Gaining Ratio Calculation

c) $1 : 1$
[Solution Description]
X's share = $1/2$ is divided equally between Y and Z.
Step 1: Y's gaining share = $1/2 \times 1/2 = 1/4$.
Step 2: Z's gaining share = $1/2 \times 1/2 = 1/4$.
Gaining ratio = $1/4 : 1/4$ or simplified as $1 : 1$.

Key Concept: Balance Sheet Impact, New Capital Allocation

c) \$480,000
[Solution Description]
Step 1: Total new capital after adjustment is $240,000 + 160,000 = 400,000$.
Step 2: Add the goodwill amount to get total assets:
$400,000 + 80,000 = 480,000$
The total assets will now be \$480,000.

Key Concept: Hidden Goodwill Calculation

c) \$20,000
[Solution Description]
Hidden goodwill is calculated as the difference between the settlement amount and the adjusted capital of the retiring partner. Here, the settlement amount is \$70,000 and the adjusted capital is \$50,000. Therefore, hidden goodwill = \$70,000 - \$50,000 = \$20,000.

Key Concept: Specific Reserve, Gaining Ratio

c) \$0
[Solution Description]
First, determine the gaining ratio:
Old ratio of X and Y = 4:3, New ratio = 3:2.
Gaining ratio:
For X: $\frac{3}{5} - \frac{4}{7} = \frac{21 - 20}{35} = \frac{1}{35}$.
For Y: $\frac{2}{5} - \frac{3}{7} = \frac{14 - 15}{35} = -\frac{1}{35}$ (Y sacrifices).
Since Y is sacrificing, they do not gain anything. The entire surplus is adjusted to X.
However, if undistributed, the reserve would be split in the old ratio 4:3 initially.
But since the question asks about the gaining ratio adjustment, Y gains nothing.

Key Concept: Construction of Partner’s Loan Account, Interest Calculation

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that interest for the first year is calculated on the full outstanding amount before any instalment payment. This is correct because when the capital balance is initially transferred to the Loan Account, the entire amount is outstanding until the first instalment is paid.
The reason states that the loan repayment agreement specifies interest is calculated on the opening balance at the start of each financial year. This is also true and correctly explains the assertion, as the interest calculation method aligns with standard accounting practices where interest is computed based on the principal amount (opening balance) before any repayments are made during the year.
Therefore, both the assertion and reason are true, and the reason correctly explains the assertion.

Key Concept: Calculation of Gaining Ratio

b) $0 : 1$
[Solution Description]
New profit sharing ratio of P and R after Q's retirement is $1 : 1$.
$\text{P's gain} = \frac{1}{2} - \frac{3}{6} = \frac{1}{2} - \frac{1}{2} = 0$
$\text{R's gain} = \frac{1}{2} - \frac{1}{6} = \frac{3}{6} - \frac{1}{6} = \frac{2}{6} = \frac{1}{3}$
Thus, the gaining ratio of P and R is $0 : 1$.

Key Concept: Adjustment of Capitals, Revaluation Account

d) Assertion is false, but Reason is true.
[Solution Description]
The assertion states that the total capital of the new firm after retirement is equal to the sum of the adjusted capitals of the remaining partners. This is false because the total capital of the new firm is determined based on the agreement among the remaining partners and may not necessarily be equal to the sum of their adjusted capitals. The reason states that the adjustment of capitals ensures proportionality with the new profit-sharing ratio, which is true. However, the assertion itself is false. Thus, the correct answer is that the Assertion is false, but the Reason is true.

Key Concept: Specific Reserve Adjustment

c) Distributed to all partners in old ratio
[Solution Description]
The surplus in Workmen Compensation Reserve after adjusting the liability (\$35,000) is distributed to all partners in their old profit-sharing ratio (3:2). Calculation:
Partner A share = \$35,000 $\times \frac{3}{5}$ = \$21,000
Partner B share = \$35,000 $\times \frac{2}{5}$ = \$14,000
Journal Entry:
$\text{Workmen’s Compensation Reserve A/c Dr. 35,000}$
$\text{To Partner A’s Capital A/c 21,000}$
$\text{To Partner B’s Capital A/c 14,000}$

Key Concept: Calculation of New Profit Sharing Ratio

d) Assertion is false, but Reason is true.
[Solution Description]
The Assertion states that the new profit sharing ratio is always calculated by adding the old share to the acquired share when a partner retires. However, this is not always true because if nothing is mentioned about the new ratio, the remaining partners continue with their existing ratio by simply removing the retiring partner's share (as per Illustration 1 in the syllabus). Thus, the Assertion is false.
The Reason provides the correct formula for calculating the new profit sharing ratio when the remaining partners acquire the retiring partner's share. This is true as per the syllabus. Therefore, the Assertion is false, but the Reason is true.

Key Concept: Goodwill Appears in the Books

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that when goodwill appears in the books at the time of a partner's retirement, it is written off by debiting the Partners' Capital Accounts in their old profit-sharing ratio. This is correct as per accounting standards. The reason given is that the existing goodwill must be removed from the books to reflect the true financial position of the firm. This is also correct and provides the justification for the assertion. Thus, both Assertion and Reason are true, and Reason correctly explains the Assertion.

Key Concept: Sacrifice made by Continuing Partner

b) \$\9,000
[Solution Description]
Old ratio: A ($\frac{4}{10}$), B ($\frac{3}{10}$), C ($\frac{3}{10}$).
New ratio: A ($\frac{3}{5}$), B ($\frac{2}{5}$).
Gaining ratio = New ratio - Old ratio.
For A: $\frac{3}{5} - \frac{4}{10} = \frac{6}{10} - \frac{4}{10} = \frac{2}{10}$ (Gain).
For B: $\frac{2}{5} - \frac{3}{10} = \frac{4}{10} - \frac{3}{10} = \frac{1}{10}$ (Gain).
Only C sacrificed ($\frac{3}{10}$).
Total goodwill = \$90,000.
Amount to be debited to B's Capital Account: $\$90,000 \times \frac{1}{10} = \$9,000$.

Key Concept: Goodwill Appears in the Books, Gaining Ratio

c) Assertion is true, but Reason is false.
[Solution Description]
The Assertion states that the goodwill appearing in the books (\$60,000) will be debited to Partners' Capital Accounts (P, Q, R) in their old profit-sharing ratio (3:2:1). This is correct as per accounting standards for writing off goodwill. However, the Reason claims that the existing goodwill is transferred in the gaining ratio, which is false because it should be written off in the old ratio, not the gaining ratio. Therefore, Assertion is true, but Reason is false.

Key Concept: Gaining Ratio - Basic Calculation

c) 5 : 2
[Solution Description]
Since the new profit sharing ratio is not given, the gaining ratio will be the same as their old profit sharing ratio.
X's gain = $\frac{5}{8}$ of Y's share ($\frac{3}{10}$) which gives $\frac{5}{8} \times \frac{3}{10} = \frac{15}{80}$
Z's gain = $\frac{3}{8}$ of Y's share ($\frac{2}{10}$) which gives $\frac{3}{8} \times \frac{2}{10} = \frac{6}{80}$
Thus, the gaining ratio between X and Z is $15 : 6 = 5 : 2$

Key Concept: Multi-concept: Sacrifice by continuing partner, Capital adjustment, Gaining ratio

c) \$4,000
[Solution Description]
Old ratio from capitals: 120:80:40 = 3:2:1. New ratio A:B=3:2. Gain calculation: For A=(3/5)-(3/6)=(18-15)/30=3/30 gain. For B=(2/5)-(2/6)=(12-10)/30=2/30 gain. Total gain=5/30=1/6. C's share is 1/6 being acquired. B's gain portion=2/5 of total gain. So credit to B's capital=\$60,000 × (2/5)×(1/6)= \$4,000. Also since B sacrifices 2/30, but gains 2/30, net effect is zero. Thus only A's sacrifice needs consideration.

Key Concept: Effect of Retirement

c) The retiring partner continues to be liable until a public notice of retirement is given
[Solution Description]
A retiring partner remains liable to third parties for the acts of the firm even after retirement until a public notice of retirement is given. However, if the partner was a sleeping partner, no public notice is required.

Key Concept: Retirement of a Partner, Liability after Retirement

c) Assertion is true, but Reason is false.
[Solution Description]
The Assertion states that a retiring partner remains liable for the firm's debts incurred before his retirement even if he gives public notice of his retirement. This is true because a retiring partner is liable for the firm's acts done before his retirement, regardless of whether a public notice is given or not.
The Reason states that according to Section 32 (1) of the Indian Partnership Act, 1932, a retiring partner is absolved of all liabilities once he retires with mutual consent and issues a public notice. This is false because Section 32 (1) only specifies the conditions under which a partner can retire, but does not state that a retiring partner is automatically absolved of all liabilities upon retirement. Further, as per the syllabus, a retiring partner continues to be liable to third parties for the firm's acts until a public notice is given regarding his retirement.
Thus, the Assertion is true, but the Reason is false.

Key Concept: Undistributed Profits, Workmen’s Compensation Reserve

c) \$13,333.33
[Solution Description]
First, calculate the surplus in Workmen’s Compensation Reserve:
Surplus = Total Reserve - Actual Liability = \$30,000 - \$10,000 = \$20,000.
Next, distribute the General Reserve (\$60,000) and the surplus (\$20,000) in the ratio 3:2:1.
Total distributed amount = \$60,000 + \$20,000 = \$80,000.
Partner C's share = $\frac{1}{6}$ of \$80,000 = \$13,333.33.
Therefore, Partner C receives \$13,333.33.

Key Concept: Revaluation Account Preparation

b) \$3,333.33
[Solution Description]
First calculate total revaluation profit/loss:
Building appreciation = \$60,000 - \$50,000 = \$10,000 gain
Machinery depreciation = \$25,000 - \$30,000 = \$5,000 loss
Net revaluation profit = \$10,000 - \$5,000 = \$5,000
X's share = \$5,000 × 2/3 = \$3,333.33

Key Concept: Accounting Treatment of Undistributed Profits

c) Transferred to all partners in old profit sharing ratio
[Solution Description]
Undistributed profits such as General Reserve are transferred to all partners' capital/current accounts in their old profit sharing ratio. The journal entry for transferring General Reserve would be:
$\text{General Reserve A/c Dr.}$
$\text{To All Partners’ Capital/Current A/cs}$
This ensures that even the retiring partner receives their share of accumulated profits from the period they were part of the firm.

Key Concept: Explicitly Given Gaining Ratio

b) 14 : 9
[Solution Description]
C's share is $\frac{1}{6}$.
A gains $\frac{3}{4} \times \frac{1}{6} = \frac{3}{24} = \frac{1}{8}$
B gains $\frac{1}{4} \times \frac{1}{6} = \frac{1}{24}$
New ratio for A = $\frac{3}{6} + \frac{1}{8} = \frac{14}{24} = \frac{7}{12}$
New ratio for B = $\frac{2}{6} + \frac{1}{24} = \frac{9}{24} = \frac{3}{8}$
Thus, new ratio = $\frac{7}{12} : \frac{3}{8} = 14 : 9$

Key Concept: Accounting Treatment of Hidden Goodwill

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The Assertion states that hidden goodwill arises when the amount paid to a retiring partner includes an unrecorded premium for goodwill, which is correct as it represents inferred goodwill. The Reason states that only purchased goodwill can be recorded in the books as per AS-26, which is also true. However, the Reason does not explain why hidden goodwill arises; it merely states a separate accounting rule. Thus, both statements are true, but the Reason is not the correct explanation of the Assertion.

Key Concept: Payment of Amount Due to Retiring Partner

d) Assertion is false, but Reason is true.
[Solution Description]
According to Section 37 of the Indian Partnership Act, 1932, if there is no agreement regarding interest on the unpaid amount due to a retiring partner, the partner has the option to receive either interest at 6\% per annum or a share of the profits attributable to the use of their money. The assertion states that the loan account must carry interest at 6\% p.a., but this is not entirely accurate because the retiring partner can choose between interest or profit share. However, the reason correctly cites the legal provision under the Partnership Act. Therefore, the assertion is false, but the reason is true.

Key Concept: Revaluation Account, Partners' Capital Adjustment

c) \$60,000
[Solution Description]
First, calculate the gain on revaluation: New asset value (\$600,000) - Old asset value (\$500,000) = \$100,000. Liabilities remain unchanged.
Revaluation profit = Gain on assets - Increase in liabilities = \$100,000 - \$0 = \$100,000.
Partner A's share = \$100,000 $\times$ (3/5) = \$60,000.
Therefore, Partner A's capital account will be credited with \$60,000.

Key Concept: Adjustment of Capital

a) Credit Partner A's capital with \$2,000
[Solution Description]
A debit balance in the capital account means the partner owes the firm. To adjust, Partner A needs to contribute cash equal to the debit balance, i.e., \$2,000, which will be credited to their capital account.

Key Concept: Hidden Goodwill, Gaining Ratio

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The Assertion (A) states that hidden goodwill is recorded when a firm pays a lump sum amount to the retiring partner exceeding his adjusted capital balance, which aligns with the definition of hidden goodwill. The Reason (R) correctly mentions that Accounting Standard 26 allows only purchased goodwill to be recorded in books.
Step-by-step reasoning:
1) Hidden goodwill arises when the payment to the retiring partner includes an amount beyond his adjusted capital, representing his share of firm's goodwill.
2) AS-26 permits recording goodwill only if it is purchased, not self-generated. However, this applies to recording goodwill as an asset, whereas hidden goodwill adjustment is handled via partners' capital accounts without raising a goodwill account.
3) While both statements are true, the Reason does not directly explain why hidden goodwill is recorded—it merely states the accounting standard restriction on goodwill recognition.

Key Concept: Sacrifice by Continuing Partner

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that when a partner retires, the continuing partner's capital account is debited if they gain a share in profits. This is true because the gaining partner needs to compensate the retiring partner and other sacrificing partners. The reason explains that the gaining partner compensates the sacrificing partners by debiting their capital account, which correctly justifies the assertion. Therefore, both the assertion and reason are true, and the reason is the correct explanation of the assertion.

Key Concept: Retirement of Partner: Calculation of Amount Payable

c) \$13,000
[Solution Description]
Step 1: Determine Rahul's share of goodwill. Goodwill amount is \$60,000. Rahul's share = (1 / 6) * \$60,000 = \$10,000.
Step 2: Find Rahul's share of undistributed profits. Total profit is \$18,000. Rahul's share = (1 / 6) * \$18,000 = \$3,000.
Step 3: Add both amounts to get the total payable. Total payable = \$10,000 + \$3,000 = \$13,000.

Key Concept: Change in Profit Sharing Ratio

b) $23 : 13$
[Solution Description]
Step 1: Calculate Q's share which is $\frac{4}{12}$ or $\frac{1}{3}$.
Step 2: P acquires $\frac{2}{3} \times \frac{1}{3} = \frac{2}{9}$ of Q's share.
Step 3: R acquires $\frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$ of Q's share.
Step 4: New share of P = Old share ($\frac{5}{12}$) + Acquired share ($\frac{2}{9}$). Convert to common denominator 36: $\frac{15}{36} + \frac{8}{36} = \frac{23}{36}$.
Step 5: New share of R = Old share ($\frac{3}{12}$ or $\frac{1}{4}$) + Acquired share ($\frac{1}{9}$). Convert to common denominator 36: $\frac{9}{36} + \frac{4}{36} = \frac{13}{36}$.
Step 6: New profit-sharing ratio is $\frac{23}{36} : \frac{13}{36}$ or simplified to $23 : 13$.

Key Concept: Gaining Ratio

b) By subtracting the old ratio from the new ratio
[Solution Description]
The gaining ratio is calculated as the difference between the new profit sharing ratio and the old profit sharing ratio of the remaining partners. The formula is: $Gaining\ Ratio = New\ Ratio - Old\ Ratio$.

Key Concept: Accounting Treatment of Goodwill, Retirement of a Partner

c) Dr. P’s Capital A/c Rs.10,000 and Q’s Capital A/c Rs.10,000; Cr. R’s Capital A/c Rs.20,000
[Solution Description]
R's share of goodwill = $\frac{1}{5} \times Rs.1,00,000 = Rs.20,000$
The gaining ratio is 1:1, so P and Q will compensate R equally.
Dr. P's Capital A/c Rs.10,000
Dr. Q's Capital A/c Rs.10,000
Cr. R's Capital A/c Rs.20,000
No other adjustment is made since goodwill is not raised in the books.

Key Concept: Change in Profit Sharing Ratio

c) By subtracting the old ratio from the new ratio for each remaining partner.
[Solution Description]
The gaining ratio is calculated as $\text{Gaining Ratio} = \text{New Ratio} - \text{Old Ratio}$ for the remaining partners.

Key Concept: Gaining Ratio, New Profit Sharing Ratio

c) Assertion is true, but Reason is false.
[Solution Description]
To determine the correctness of the assertion and reason:
1. Old ratio of X, Y, Z = $5:3:2$ or $\frac{5}{10}:\frac{3}{10}:\frac{2}{10}$.
2. Since Y and Z acquire X's share ($\frac{5}{10}$) equally, each gains $\frac{5}{20}$ ($=\frac{5}{10} \times \frac{1}{2}$).
3. Thus, the gaining ratio is $\frac{5}{20}:\frac{5}{20} = 1:1$.
4. However, the Reason is incorrect because the gaining ratio equals the new profit sharing ratio only when the continuing partners acquire the outgoing partner's share in their old ratio. In this case, they acquired it equally (not in old ratio), making the Reason false.

Key Concept: Journal Entry for Goodwill Adjustment

c) \$27,000
[Solution Description]
The total hidden goodwill is \$36,000, which is to be borne by A and B in the gaining ratio of 3:1. First, calculate the total parts of the gaining ratio: 3 + 1 = 4. A's share = (3/4) $\times$ \$36,000 = \$27,000. Thus, A’s Capital Account will be debited with \$27,000.

Key Concept: Revaluation Account, Partners' Capital Accounts

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The Assertion is true because according to accounting standards, when the value of an asset increases, the Revaluation Account is credited to record the gain. The Reason is also true as this gain is transferred to the partners' capital accounts in their profit-sharing ratio. However, the Reason does not explain why the Revaluation Account is credited; it only explains the distribution of the gain. Therefore, both statements are true, but the Reason is not the correct explanation of the Assertion.

Key Concept: Revaluation Profit/Loss, Partner's Capital Adjustment

b) Partner Q's capital increases by \$30,000.
[Solution Description]
Step 1: Calculate the increase in land value. Original value = \$500,000; Undervaluation = 20\%. Increase = \$500,000 × 20\% = \$100,000.
Step 2: Calculate the decrease in loan value. Original loan = \$100,000; Overvaluation = 10\%. Decrease = \$100,000 × 10\% = \$10,000.
Step 3: Prepare Revaluation Account. Credit for land increase (\$100,000) and debit for loan decrease (\$10,000). Net profit = \$100,000 - \$10,000 = \$90,000.
Step 4: Distribute profit equally (1:1:1). Partner Q's share = (1/3) × \$90,000 = \$30,000.

Key Concept: Revaluation Entries, Multi-step Calculation

b) Dr. Revaluation A/c \$30,000; Cr. Machinery A/c \$30,000.
[Solution Description]
Step 1: Calculate the decrease in machinery value. Original value = \$120,000; Overvaluation = 25\%. Decrease = \$120,000 × 25\% = \$30,000.
Step 2: The journal entry for decrease in asset value is: Dr. Revaluation A/c \$30,000; Cr. Machinery A/c \$30,000.

Key Concept: Effect of Retirement on Liability

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The assertion is true as per the syllabus: a retiring partner remains liable for the firm's acts post-retirement until public notice is given (except for sleeping partners). The reason is also true because Section 32(1) provides legal backing to this requirement. However, the reason does not fully explain why the liability exists—it merely confirms the procedure. Thus, both are true, but the reason is not the correct explanation of the assertion.

Key Concept: Accounting Treatment of Undistributed Losses

c) Debited to all partners' accounts in old ratio
[Solution Description]
The undistributed loss (\$20,000) is distributed to all partners in their old profit-sharing ratio (2:1:1). The calculation is as follows:
Partner 1 share = \$20,000 $\times \frac{2}{4}$ = \$10,000
Partner 2 share = \$20,000 $\times \frac{1}{4}$ = \$5,000
Partner 3 share = \$20,000 $\times \frac{1}{4}$ = \$5,000
Journal Entry:
$\text{Partner 1’s Capital A/c Dr. 10,000}$
$\text{Partner 2’s Capital A/c Dr. 5,000}$
$\text{Partner 3’s Capital A/c Dr. 5,000}$
$\text{To Profit and Loss A/c 20,000}$

Key Concept: Accounting Treatment of Goodwill including Hidden Goodwill

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description] The Assertion states that goodwill is valued as per agreement among the partners at the time of retirement, which is true because the valuation of goodwill depends on mutual agreement. The Reason states that goodwill cannot be recorded in books unless consideration is paid for it, which is also true as per Accounting Standard 26. However, the Reason does not directly explain why goodwill is valued as per agreement at retirement; it only explains a separate accounting principle about recording goodwill. Thus, both are true, but the Reason is not the correct explanation of the Assertion.

Key Concept: Adjustment of Capitals: Revaluation Account

b) \$11,429
[Solution Description]
Total goodwill = \$90,000.
C's share of goodwill = $\frac{2}{9} \times 90,000 = \$20,000$.
This amount will be debited to A and B in their new profit-sharing ratio (if unchanged, it remains $4 : 3$).
A's sacrifice = $\frac{4}{7} \times 20,000 = \$11,428.57$.

Key Concept: Calculation of New Profit Sharing Ratio

c) 3 : 2
[Solution Description]
The original profit-sharing ratio is $3 : 2 : 1$ for P, Q, and R respectively. When R retires, his share $\frac{1}{6}$ ($1$ part out of $3 + 2 + 1 = 6$ parts) is removed. The remaining partners continue sharing in their original ratio of $3 : 2$. Therefore, the new ratio is simplified to $3 : 2$.

Key Concept: Gaining Ratio Calculation

c) $1 : 1$
[Solution Description]
Shakti's share is $\frac{3}{10}$. Since Sadhana takes Shakti's entire share, her gain is $\frac{3}{10}$. Her original share is $\frac{2}{10}$. Gaining ratio for Sadhana is the ratio in which she acquires Shakti's share, which is $1$ (since she gains all of it). Thus, the gaining ratio is $1 : 1$ (since Shiv does not gain anything).

Key Concept: Partial Payment, Asset Transfer, Capital Adjustment

b) \$7,500 from revaluation profit
[Solution Description]
Step 1: Record machinery revaluation:
Machinery Dr. \$25,000
To Revaluation \$25,000
Step 2: Transfer revaluation profit (4:3:3):
Revaluation Dr. \$25,000
To X \$10,000 (\$25,000×4/10)
To Y \$7,500 (\$25,000×3/10)
To Z \$7,500 (\$25,000×3/10)
Step 3: Partial settlement with Z:
Z's Capital Dr. \$67,500 (\$60,000 + \$7,500)
To Cash \$20,000
To Machinery \$25,000
To Z's Loan \$22,500
Y's Capital Account will be credited with \$7,500 from revaluation.

Key Concept: Partial Payment and Loan Transfer

c) Retiring Partner’s Capital A/c Dr. To Cash/Bank A/c and Retiring Partner’s Loan A/c
[Solution Description]
For partial payment in cash and transferring the remaining balance to the loan account, the correct journal entry is:
$\text{Retiring Partner’s Capital A/c} \quad \text{Dr.} \quad \text{To Cash/Bank A/c} \quad \text{To Retiring Partner’s Loan A/c}$
This entry records both the partial cash payment and the transfer of the remaining amount to the loan account.

Key Concept: Adjustment of Capitals: Calculating New Capital

c) \$75,000
[Solution Description]
Total capital of the new firm = \$150,000.
New profit-sharing ratio of X and Y = $1 : 1$.
Therefore, X's new capital = $\frac{1}{2} \times 150,000 = \$75,000$.
Since X's existing capital is \$60,000, he needs to bring in an additional \$15,000.

Key Concept: Accounting Treatment of Revaluation of Assets and Liabilities

c) Assertion is true, but Reason is false.
[Solution Description]
The assertion states that the revaluation account is prepared to record changes in the value of assets and liabilities, which is true as per accounting principles. The reason states that the profit or loss from revaluation is transferred to the partners' capital accounts in their new profit-sharing ratio, which is false because it should be transferred in the old profit-sharing ratio. Therefore, the assertion is true, but the reason is false.

Key Concept: Gaining Ratio Calculation

a) $3 : 1$
[Solution Description]
First, calculate the old shares of X and Y:
X's old share = $\frac{3}{6} = \frac{1}{2}$
Y's old share = $\frac{2}{6} = \frac{1}{3}$
New shares after Z's retirement:
X's new share = $\frac{5}{8}$
Y's new share = $\frac{3}{8}$
Gaining ratio = New ratio - Old ratio
X's gain = $\frac{5}{8} - \frac{1}{2} = \frac{5}{8} - \frac{4}{8} = \frac{1}{8}$
Y's gain = $\frac{3}{8} - \frac{1}{3} = \frac{9}{24} - \frac{8}{24} = \frac{1}{24}$
Gaining ratio of X and Y = $\frac{1}{8} : \frac{1}{24} = 3 : 1$ after multiplying both by 24.

Key Concept: Adjustment of Capitals

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The assertion (A) states that the remaining partners must adjust their capital contributions to match their new profit sharing ratio when a partner retires or dies. This is true because the partners may decide to realign their capital as per the new profit-sharing arrangement. However, the reason (R) only explains how the total capital of the new firm is calculated and does not directly support the assertion about adjusting individual capitals. Therefore, both statements are true, but Reason is not the correct explanation of Assertion.

Key Concept: Sacrifice made by Continuing Partner

b) \$\36,000
[Solution Description]
Old ratio: P ($\frac{3}{10}$), Q ($\frac{2}{10}$), R ($\frac{3}{10}$), S ($\frac{2}{10}$).
New ratio: P ($\frac{3}{10}$), Q ($\frac{1}{10}$), S ($\frac{6}{10}$).
Gaining ratio = New ratio - Old ratio.
For P: $\frac{3}{10} - \frac{3}{10} = 0$ (No change).
For Q: $\frac{1}{10} - \frac{2}{10} = -\frac{1}{10}$ (Sacrifice).
For S: $\frac{6}{10} - \frac{2}{10} = \frac{4}{10}$ (Gain).
R’s share of goodwill: $\$120,000 \times \frac{3}{10} = \$36,000$.
Amount credited to R's Capital Account: \$36,000.

Key Concept: Loan Account Balancing, Multiple Instalments

a) \$24,000
[Solution Description]
Step 1: Interest for Year 1 on \$1,20,000 at 10\%:
Interest = 10\% of \$1,20,000 = \$12,000.
Closing balance = \$1,20,000 - \$40,000 = \$80,000.
Step 2: Interest for Year 2 on \$80,000 at 10\%:
Interest = 10\% of \$80,000 = \$8,000.
Closing balance = \$80,000 - \$40,000 = \$40,000.
Step 3: Interest for Year 3 on \$40,000 at 10\%:
Interest = 10\% of \$40,000 = \$4,000.
Total interest = \$12,000 + \$8,000 + \$4,000 = \$24,000.

Key Concept: Partner’s Loan Account

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion (A) states that interest on a retiring partner’s loan is calculated on the outstanding balance at the end of each financial year, which is correct as per standard accounting practices. The Reason (R) explains that this interest compensates the retiring partner for the delay in receiving their dues, which is also accurate. Furthermore, the Reason provides the correct justification for why interest is calculated annually on the outstanding balance, linking it to the concept of compensating for delayed payments. Hence, both Assertion and Reason are true, and Reason correctly explains the Assertion.

Key Concept: Journal Entry for Hidden Goodwill

c) X's Capital A/c Dr. \$12,000; Y's Capital A/c Dr. \$6,000; To Z's Capital A/c \$18,000
[Solution Description]
Hidden goodwill = \$63,000 - \$45,000 = \$18,000. X's share = (2/3) * \$18,000 = \$12,000; Y's share = (1/3) * \$18,000 = \$6,000. The journal entry is:
X's Capital A/c Dr. \$12,000
Y's Capital A/c Dr. \$6,000
To Z's Capital A/c \$18,000.

Key Concept: Loan Account Preparation, Interest Calculation

a) \$30,000
[Solution Description]
Step 1: Calculate the loan amount transferred.
Total capital = \$80,000, immediate payment = \$20,000.
Loan amount = \$80,000 - \$20,000 = \$60,000.
Step 2: Calculate annual instalment (principal only).
Instalment = \$60,000 / 4 = \$15,000 per year.
Step 3: Interest for Year 1 on \$60,000 at 12\%:
Interest = 12\% of \$60,000 = \$7,200.
Payment = \$15,000 (principal) + \$7,200 (interest) = \$22,200.
Closing balance = \$60,000 - \$15,000 = \$45,000.
Step 4: Interest for Year 2 on \$45,000 at 12\%:
Interest = 12\% of \$45,000 = \$5,400.
Payment = \$15,000 (principal) + \$5,400 (interest) = \$20,400.
Closing balance = \$45,000 - \$15,000 = \$30,000.
Final closing balance after second instalment: \$30,000.

Key Concept: Retirement of Partner - Goodwill Adjustment

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that a retiring partner is entitled to his share of goodwill at retirement, which is correct as per partnership accounting principles. The Reason explains that since the retiring partner will not share future profits (which may include benefits from existing goodwill), he should be compensated. This is also true and correctly explains why the Assertion holds. Thus, both statements are true, and the Reason is the correct explanation of the Assertion.

Key Concept: Adjustment of Hidden Goodwill

b) \$12,000
[Solution Description]
Step 1: Hidden goodwill = Amount paid - Adjusted capital = \$66,000 - \$54,000 = \$12,000.
Step 2: Total hidden goodwill is \$12,000, which needs to be adjusted in the gaining ratio.
The question only asks for the total hidden goodwill, not its distribution.

Key Concept: Hidden Goodwill, Profit Sharing Ratio

b) \$30,000, X contributes \$20,000 and Y contributes \$10,000
[Solution Description]
Hidden goodwill = Payment to Z - Adjusted capital of Z = \$105,000 - \$75,000 = \$30,000.
New profit-sharing ratio between X and Y is 2:1. Therefore, the gaining ratio is also 2:1 as there is no change except the retirement of Z.
Contribution by X = (2/3) * \$30,000 = \$20,000
Contribution by Y = (1/3) * \$30,000 = \$10,000
Journal entry:
X's Capital A/c Dr. \$20,000
Y's Capital A/c Dr. \$10,000
To Z's Capital A/c \$30,000

Key Concept: Calculation of New Profit Sharing Ratio

b) 7 : 5
[Solution Description]
The original profit-sharing ratio is $7 : 5 : 3$ for A, B, and C respectively. When C retires, his share $\frac{3}{15}$ ($3$ parts out of $7 + 5 + 3 = 15$ parts) is removed. The remaining partners continue sharing in their original ratio of $7 : 5$. Therefore, the new ratio remains $7 : 5$.

Key Concept: Retiring Partner's Loan Account, Interest on Loan, Profit Sharing Ratio

b) \$20,000 as profit share
[Solution Description]
Under Section 37 of Partnership Act, C can choose either:
1. Interest @6\% p.a. on unpaid amount:
$6/100 \times 50,000 = 3,000$
2. Profit share attributable to his capital:
Total profit = \$80,000
C's share = $(50,000/200,000) \times 80,000 = 20,000$
Since \$20,000 > \$3,000, C would prefer profit share option.

Key Concept: Undistributed Losses, Profit and Loss Adjustment

b) Debit each partner’s capital by \$15,000 and credit Profit and Loss A/c by \$45,000
[Solution Description]
Since the loss is shared equally, each partner bears \$15,000 (\$45,000 / 3).
The journal entry will be:
$A's Capital A/c \quad Dr. \quad 15,000$
$B's Capital A/c \quad Dr. \quad 15,000$
$C's Capital A/c \quad Dr. \quad 15,000$
$To Profit and Loss A/c \quad 45,000$
Thus, each partner's capital account is debited by \$15,000.

Key Concept: Revaluation Account

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion is true because the Revaluation Account is indeed used to record changes in the value of assets and liabilities during revaluation. The Reason is also true because any increase in the value of assets is credited to the Revaluation Account as per accounting principles. Moreover, the Reason correctly explains why the Revaluation Account is used for recording such changes.
Therefore, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: Revaluation Account

c) Credit balance of \$15,000
[Solution Description]
Increase in asset (machinery) is credited to the Revaluation Account: + \$10,000. Decrease in liability (creditors) is also credited to the Revaluation Account: + \$5,000. Net effect is a credit balance of \$15,000.

Key Concept: Interest on Retiring Partner’s Loan

d) \$50,000
[Solution Description]
Under Section 37 of the Partnership Act, if an outgoing partner opts for a share of profit, the calculation is based on the proportion of his unpaid amount to the total capital employed.
Total capital employed = \$50,000 (Z’s unpaid amount) + Any additional capital by remaining partners (not mentioned here). Assuming only Z’s capital was used:
$\text{Z's Share of Profit} = \frac{50,000}{50,000} \times 100,000 = \$50,000$
However, if other partners contributed capital, the denominator increases, reducing Z’s share.

Key Concept: Sacrifice made by Continuing Partner, Gaining ratio, Goodwill adjustment

c) \$10,500
[Solution Description]
First calculate old ratios: X=5/10, Y=3/10, Z=2/10. New ratio X:Y=7:12. Gaining ratio = New - Old. For X: (7/12)-(5/10)=(35-30)/60=5/60 gain. For Y: (5/12)-(3/10)=(25-18)/60=7/60 gain. Total gain=12/60=1/5. Z's share is 2/10 which equals 1/5 being acquired. Since Y gains more (7/60) than X (5/60), Y will bear more debit. Amount to be debited to Y = (7/12)*\$90,000*(1/5) = \$10,500.

Key Concept: Payment of Amount Due to Retiring Partner

d) Retiring Partner’s Capital A/c Dr. To Cash/Bank A/c
[Solution Description]
The correct journal entry for paying the full amount due to a retiring partner in cash is:
$\text{Retiring Partner’s Capital A/c} \quad \text{Dr.} \quad \text{To Cash/Bank A/c}$
This records the payment of the retiring partner's capital in full.

Key Concept: Interest on Loan, Instalment Payment

b) `19,500
[Solution Description]
Each instalment is $\frac{45,000}{3} = `15,000$. Interest for the first year is $45,000 \times 10\% = `4,500$. Total first instalment: $15,000 + 4,500 = `19,500$.

Key Concept: Payment of Amount Due to Retiring Partner, Interest on Unpaid Amount

A share of the profits attributable to the use of their capital in the business,
[Solution Description]
According to Section 37 of the Partnership Act, 1932, if the retiring partner's capital is not settled immediately and is transferred to a loan account, the outgoing partner has the option to claim either:
\begin{enumerate}

Key Concept: Effect of Retirement of a Partner, Gaining Ratio, Goodwill Adjustment