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?
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?
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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.
Updated On: Jan 13, 2026
- \( \frac{1}{10} \)
- \( \frac{2}{10} \)
- \( \frac{3}{10} \)
- \( \frac{4}{10} \)
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The Correct Option is A
Solution and Explanation
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 \(\frac{1}{10}\).
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