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

To solve this problem, we need to determine the share of profits Dinesh receives in the firm after being admitted as a partner.

Aman, Boman, and Chetan originally shared profits in the ratio of 5:3:2. This means:

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

It is given that Aman surrendered \(\frac{1}{5}\)th of his share to Dinesh. Aman's share before surrendering is \(\frac{1}{2}\).

To find out what fraction of this \(\frac{1}{2}\) Aman gives to Dinesh, we calculate \(\frac{1}{5}\)th of \(\frac{1}{2}\):

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

Therefore, Dinesh is admitted with a \(\frac{1}{10}\) share in the profits of the firm. The correct answer is \(\frac{1}{10}\).