Question

A and B are partners sharing profits in the ratio of 3:2. They admit C for 1/5th share in profits. The Balance Sheet shows a debit balance of Profit and Loss Account of Rs. 25,000. Goodwill of the firm is valued at Rs. 1,00,000. C brings his share of goodwill in cash.
The amount credited to A's Capital Account on account of goodwill is:

• A. Rs. 12,000
• B. Rs. 15,000
• C. Rs. 18,000
• D. Rs. 20,000

Hint:

Whenever the problem specifies a new partner's share without mentioning how it is acquired, the sacrificing ratio is always equal to the old profit-sharing ratio.
This allows you to bypass calculating the new profit-sharing ratio entirely, saving valuable time during the exam.
Additionally, keep accumulated items (like P&L debit balances) separate from goodwill adjustments as they do not affect each other's calculations.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
In this problem, we need to calculate the exact amount of premium for goodwill that will be credited to partner A's capital account upon the admission of the new partner, C.
The old profit-sharing ratio between partners A and B is given as 3:2.
The incoming partner, C, is admitted for a 1/5th share in the profits of the firm.
The total goodwill of the firm is valued at Rs. 1,00,000, and C brings his share of this goodwill in cash.
Additionally, the Balance Sheet contains an accumulated loss represented by a debit balance in the Profit and Loss Account of Rs. 25,000.
We must identify the share of goodwill brought in by C and distribute it in the sacrificing ratio of the existing partners.

Step 2: Key Formula or Approach:
1. Calculate the premium for goodwill brought in by the new partner:
\[ \text{New Partner's Share of Goodwill} = \text{Total Goodwill of the Firm} \times \text{New Partner's Share} \]
2. Identify the sacrificing ratio of the existing partners.
When no separate agreement or new profit-sharing ratio is mentioned, the old profit-sharing ratio is assumed to be the sacrificing ratio.
3. Distribute the incoming partner's share of goodwill among the sacrificing partners:
\[ \text{Partner's Share of Goodwill} = \text{New Partner's Share of Goodwill} \times \text{Partner's Sacrificing Ratio Share} \]

Step 3: Detailed Explanation:
1. First, we compute the total amount of goodwill that C needs to bring in.
The total valuation of the firm's goodwill is Rs. 1,00,000.
C is admitted for a 1/5th share of profits.
Applying the formula:
\[ \text{C's Share of Goodwill} = \text{Rs. } 1,00,000 \times \frac{1}{5} = \text{Rs. } 20,000 \]
Hence, C brings Rs. 20,000 in cash as his share of premium for goodwill.
2. Second, we determine the sacrificing ratio of A and B.
Since there is no other information regarding how C acquires his share from A and B, the sacrificing ratio is identical to their old profit-sharing ratio, which is 3:2.
3. Third, we allocate C's share of goodwill of Rs. 20,000 to A's capital account.
The share of A is calculated as follows:
\[ \text{Amount credited to A's Capital Account} = \text{Rs. } 20,000 \times \frac{3}{5} = \text{Rs. } 12,000 \]
Similarly, the share of B would be:
\[ \text{Amount credited to B's Capital Account} = \text{Rs. } 20,000 \times \frac{2}{5} = \text{Rs. } 8,000 \]
4. Fourth, we note the treatment of the debit balance in the Profit and Loss Account.
The accumulated loss of Rs. 25,000 shown in the Balance Sheet must be debited to the old partners' capital accounts in their old profit-sharing ratio of 3:2.
This does not affect the premium for goodwill credited to A's capital account, which remains Rs. 12,000.

Step 4: Final Answer:
The amount credited to A's Capital Account on account of goodwill is Rs. 12,000.
Thus, Option (A) is the correct answer.