Question

Aman, Boman and Chetan were partners in a firm sharing profits and losses in the ratio of 5:3:2. Dinesh was admitted as a new partner who acquired his share entirely from Aman. Aman surrendered \( \frac{1}{5} \)th of his share in the profits to Dinesh. Dinesh was admitted for which of the following share in the profits of the firm?

• A. \( \frac{1}{10} \)
• B. \( \frac{2}{10} \)
• C. \( \frac{3}{10} \)
• D. \( \frac{4}{10} \)

Hint:

Pay close attention to the wording. "Surrendered \( \frac{1}{5} \)th \textit{of his share}" means you multiply the fraction by the partner's existing share. If it said "surrendered \( \frac{1}{5} \)th share \textit{from his share}", it would mean Aman's share reduces by a fixed \( \frac{1}{5} \), which is different.

Answer 1

The Correct Option is A

The initial profit-sharing ratio of Aman, Boman, and Chetan is 5:3:2. Aman's share = \( \frac{5}{5+3+2} = \frac{5}{10} \).
Boman's share = \( \frac{3}{10} \).
Chetan's share = \( \frac{2}{10} \).
Dinesh is admitted and acquires his share entirely from Aman. Aman surrenders \( \frac{1}{5} \) \textit{of his share} to Dinesh. Share surrendered by Aman = \( \frac{1}{5} \times \text{Aman's share} \) \[ \text{Share surrendered by Aman} = \frac{1}{5} \times \frac{5}{10} = \frac{5}{50} = \frac{1}{10} \] Since Dinesh acquires his share entirely from Aman, the share surrendered by Aman is Dinesh's share in the firm. Therefore, Dinesh's share = \( \frac{1}{10} \).