Question

Aditya, Vishesh, and Nimesh were partners in a firm sharing profits and losses equally. Aditya died on 1st July 2023. The remaining partners decided to continue the business of the firm and decided to share future profits in the ratio of 4:3. The gaining ratio of Vishesh and Nimesh will be:

• A. 4:3
• B. 3:2
• C. 5:2
• D. 1:1

Hint:

In partnership adjustments, always calculate the gaining ratio as the difference between the new and old ratios of the remaining partners. Simplify fractions to determine the correct ratio.

Answer 1

The Correct Option is C

When a partner retires or dies, the gaining ratio is calculated as the difference between the new ratio and the old ratio of the remaining partners. Step 1: Old ratio (equal sharing):
The firm originally shared profits and losses equally among Aditya, Vishesh, and Nimesh. The old ratio of Vishesh and Nimesh was: \[ \text{Old ratio of Vishesh and Nimesh} = \frac{1}{3} : \frac{1}{3}. \] Step 2: New ratio (after Aditya's exit):
After Aditya's death, the new profit-sharing ratio of Vishesh and Nimesh was agreed to be \(4:3\). Step 3: Gaining ratio:
The gaining ratio is calculated by subtracting the old ratio from the new ratio: \[ \text{Vishesh's gain} = \frac{4}{7} - \frac{1}{3} = \frac{12 - 7}{21} = \frac{5}{21}. \] \[ \text{Nimesh's gain} = \frac{3}{7} - \frac{1}{3} = \frac{9 - 7}{21} = \frac{2}{21}. \] Thus, the gaining ratio is: \[ \text{Gaining ratio of Vishesh : Nimesh} = 5:2. \] Conclusion:
The gaining ratio of Vishesh and Nimesh is \(5:2\).