Question

A and B are partners sharing profits in the ratio of 3:2. Their capitals after all adjustments are Rs. 3,60,000 and Rs. 2,40,000 respectively. C is admitted for 1/5th share and brings Rs. 1,50,000 as his capital.
The total capital of the new firm on the basis of C's capital will be:

• A. Rs. 6,00,000
• B. Rs. 7,50,000
• C. Rs. 8,00,000
• D. Rs. 9,00,000

Hint:

When finding the total capital of the firm on the basis of a new partner's capital, ignore all other information about existing partners' capitals.
Simply multiply the new partner's capital by the reciprocal of their profit share.
This simple step avoids unnecessary calculations and saves valuable exam time.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
In this question, we are asked to find the total capital of the newly constituted firm based on the capital of the incoming partner, C.
A and B share profits in the ratio of 3:2, and their adjusted capitals are Rs. 3,60,000 and Rs. 2,40,000.
C is admitted for a 1/5th share of profits and brings Rs. 1,50,000 as his capital contribution.
Our objective is to find the capitalized value of the entire firm using C's share and capital.

Step 2: Key Formula or Approach:
1. The total capital of the firm based on the new partner's capital is calculated by multiplying the new partner's capital by the reciprocal of his profit share.
\[ \text{Total Capital of the New Firm} = \text{New Partner's Capital} \times \frac{1}{\text{New Partner's Share}} \]

Step 3: Detailed Explanation:
1. We identify the details of the incoming partner C from the question.
C's Capital Contribution = Rs. 1,50,000.
C's Profit Share = \(\frac{1}{5}\).
2. We apply the formula for the total capital of the new firm on the basis of C's capital:
\[ \text{Total Capital} = \text{Rs. } 1,50,000 \times \frac{5}{1} = \text{Rs. } 7,50,000 \]
3. Let us analyze why the adjusted capitals of A and B (Rs. 3,60,000 and Rs. 2,40,000) are given in the problem.
Sometimes, these values are used to find if the existing partners' capitals are in proportion to their new profit-sharing ratio.
Let us check the new profit-sharing ratio:
If C's share is \(\frac{1}{5}\), the remaining share is:
\[ 1 - \frac{1}{5} = \frac{4}{5} \]
This remaining share of \(\frac{4}{5}\) is divided between A and B in their old ratio of 3:2:
\[ \text{A's New Share} = \frac{4}{5} \times \frac{3}{5} = \frac{12}{25} \]
\[ \text{B's New Share} = \frac{4}{5} \times \frac{2}{5} = \frac{8}{25} \]
\[ \text{C's Share} = \frac{1}{5} = \frac{5}{25} \]
The new profit-sharing ratio is \(12:8:5\).
Based on a total capital of Rs. 7,50,000, A and B's proportionate capitals should be:
\[ \text{A's proportionate capital} = \text{Rs. } 7,50,000 \times \frac{12}{25} = \text{Rs. } 3,60,000 \]
\[ \text{B's proportionate capital} = \text{Rs. } 7,50,000 \times \frac{8}{25} = \text{Rs. } 2,40,000 \]
The adjusted capitals given in the question (Rs. 3,60,000 and Rs. 2,40,000) match these proportionate capitals, meaning no further adjustment of capital is required.
However, the question only asks for the total capital based on C's contribution, which is Rs. 7,50,000.

Step 4: Final Answer:
The total capital of the new firm on the basis of C's capital is Rs. 7,50,000.
Therefore, Option (B) is the correct answer.