Question

Sudama, Sharma and Varun were partners in a firm sharing profits and losses in the ratio of 6 : 4 : 3. Sharma retired from the firm on 31st March, 2025. The gaining ratio of Sudama and Varun will be:

• A. 3 : 2
• B. 2 : 1
• C. 1 : 2
• D. 2 : 3

Hint:

When a partner retires and no new ratio is specified, the continuing partners continue in their old ratio. Gaining Ratio = New Share - Old Share. It represents how much each continuing partner gains from the retiring partner's share.

Answer 1

The Correct Option is B

We need to find the gaining ratio of Sudama and Varun after Sharma's retirement.
Step 1: Understand the concept of gaining ratio.
Gaining ratio is the ratio in which the continuing partners gain the share of the retiring partner. It is calculated as: \[ \text{Gaining Ratio} = \text{New Share} - \text{Old Share} \] Step 2: Identify the old profit sharing ratio.
Old ratio of Sudama : Sharma : Varun = 6 : 4 : 3
Total of old ratio = 6 + 4 + 3 = 13

• Sudama's old share = \(\frac{6}{13}\)
• Sharma's old share = \(\frac{4}{13}\)
• Varun's old share = \(\frac{3}{13}\)

Step 3: Determine the new ratio after retirement.
When a partner retires, the remaining partners continue with each other. Unless specified otherwise, they continue in their old ratio. So, Sudama and Varun will share profits in their old ratio of 6 : 3, which simplifies to 2 : 1. New ratio of Sudama : Varun = 2 : 1

• Sudama's new share = \(\frac{2}{3}\)
• Varun's new share = \(\frac{1}{3}\)

Step 4: Calculate the gaining ratio.
\[ \text{Gain} = \text{New Share} - \text{Old Share} \] For Sudama: \[ \text{Gain} = \frac{2}{3} - \frac{6}{13} = \frac{26 - 18}{39} = \frac{8}{39} \] For Varun: \[ \text{Gain} = \frac{1}{3} - \frac{3}{13} = \frac{13 - 9}{39} = \frac{4}{39} \] Gaining ratio = \(\frac{8}{39} : \frac{4}{39} = 8 : 4 = 2 : 1\) Final Answer: (B) 2 : 1