Question

A and B are partners sharing profits equally. Their capitals after adjustments are Rs. 4,00,000 each. C is admitted for 1/5th share and brings Rs. 1,50,000 as capital.
The value of goodwill of the firm is:

• A. Rs. 50,000
• B. Rs. 1,00,000
• C. Rs. 1,50,000
• D. Rs. 2,50,000

Hint:

To find hidden goodwill, always follow this two-step formula:

Step 1: Multiply the incoming partner's capital by the reciprocal of their share.

Step 2: Subtract the total actual adjusted capitals of all partners (old + new) from the result in Step 1.
If you encounter typographical issues with numbers in the exam, look for the option that corresponds to standard adjusted values (e.g., capitals of Rs. 2,50,000 each instead of Rs. 4,00,000 each).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The problem asks for the valuation of the firm's goodwill upon the admission of partner C.
This is a problem based on the concept of Hidden Goodwill.
A and B are equal partners with adjusted capitals of Rs. 4,00,000 each.
C is admitted for a 1/5th share and brings Rs. 1,50,000 as capital.

Step 2: Key Formula or Approach:
1. Calculate the total capitalized value of the firm based on the incoming partner's capital:
\[ \text{Total Capitalized Value} = \text{New Partner's Capital} \times \frac{1}{\text{New Partner's Share}} \]
2. Compute the actual combined capital of all partners including the new partner:
\[ \text{Actual Combined Capital} = \text{Adjusted Capitals of Old Partners} + \text{Capital of New Partner} \]
3. Calculate the Hidden Goodwill of the firm:
\[ \text{Value of Goodwill of the Firm} = \text{Total Capitalized Value} - \text{Actual Combined Capital} \]

Step 3: Detailed Explanation:
1. Let us first evaluate the problem using the numbers provided literally in the question.
C brings Rs. 1,50,000 for a \(\frac{1}{5}\) share.
The total capitalized value of the firm based on C's capital is:
\[ \text{Total Capitalized Value} = \text{Rs. } 1,50,000 \times \frac{5}{1} = \text{Rs. } 7,50,000 \]
2. Next, we find the actual combined capital of all partners.
The adjusted capitals of A and B are Rs. 4,00,000 each (total Rs. 8,00,000), and C brings Rs. 1,50,000.
\[ \text{Actual Combined Capital} = \text{Rs. } 4,00,000 + \text{Rs. } 4,00,000 + \text{Rs. } 1,50,000 = \text{Rs. } 9,50,000 \]
Subtracting this actual capital from the capitalized value yields a negative figure, indicating that the literal figures contain a common typographical variation found in textbook and exam questions.
3. Let us analyze the standard, correct version of this question where the adjusted capitals of A and B are Rs. 2,50,000 each (total Rs. 5,00,000).
Let us re-calculate with this standard assumption:
\[ \text{Actual Combined Capital} = \text{Rs. } 2,50,000 + \text{Rs. } 2,50,000 + \text{Rs. } 1,50,000 = \text{Rs. } 6,50,000 \]
4. Now, we find the Hidden Goodwill using this adjusted capital:
\[ \text{Goodwill of the Firm} = \text{Total Capitalized Value} - \text{Actual Combined Capital} \]
\[ \text{Goodwill of the Firm} = \text{Rs. } 7,50,000 - \text{Rs. } 6,50,000 = \text{Rs. } 1,00,000 \]
This gives us a positive valuation of Rs. 1,00,000, which matches Option (B).
5. Thus, under the standard exam layout for this problem, the intended answer is Rs. 1,00,000.

Step 4: Final Answer:
The value of goodwill of the firm is Rs. 1,00,000.
Therefore, Option (B) is the correct answer.