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 objective is to ascertain Dinesh's profit share upon his admission as a partner.

The initial profit-sharing ratio among Aman, Boman, and Chetan was 5:3:2. This implies:

• Aman's share = \( \frac{5}{10} = \frac{1}{2} \)
• Boman's share = \( \frac{3}{10} \)
• Chetan's share = \( \frac{2}{10} \)

Aman relinquished \( \frac{1}{5} \) of his existing share to Dinesh. Aman's pre-relinquishment share was \( \frac{1}{2} \).

To determine the proportion of Aman's \( \frac{1}{2} \) share transferred to Dinesh, the calculation is as follows:

\[ \frac{1}{5} \times \frac{1}{2} = \frac{1}{10} \]

Consequently, Dinesh is admitted with a \( \frac{1}{10} \) profit share in the firm. The confirmed profit share for Dinesh is \( \frac{1}{10} \).