Question

Aaroh, Bhuvan, and Charu were partners in a firm sharing profits and losses in the ratio of \( 1 : 2 : 6 \). Charu died. Aaroh and Bhuvan acquired Charu’s share in the ratio of \( 2 : 1 \). The new profit-sharing ratio between Aaroh and Bhuvan after Charu’s death will be:

• A. 2 : 1
• B. 1 : 2
• C. 5 : 4
• D. 4 : 5

Hint:

When a partner’s share is redistributed, always calculate the shares proportionally based on the given ratio and add them to the remaining partners’ original shares.

Answer 1

The Correct Option is C

1. Original Shares of Aaroh, Bhuvan, and Charu: Aaroh’s share = \( \frac{1}{9} \), Bhuvan’s share = \( \frac{2}{9} \), Charu’s share = \( \frac{6}{9} \). 2. Charu’s Share Distribution: Total share of Charu = \( \frac{6}{9} \). Aaroh and Bhuvan acquired Charu’s share in the ratio of \( 2 : 1 \). - Aaroh’s share from Charu = \( \frac{2}{3} \times \frac{6}{9} = \frac{12}{27} = \frac{4}{9}. \) - Bhuvan’s share from Charu = \( \frac{1}{3} \times \frac{6}{9} = \frac{6}{27} = \frac{2}{9}. \) 3. New Shares of Aaroh and Bhuvan: - Aaroh’s new share = \( \frac{1}{9} + \frac{4}{9} = \frac{5}{9}. \) - Bhuvan’s new share = \( \frac{2}{9} + \frac{2}{9} = \frac{4}{9}. \) 4. New Profit-Sharing Ratio: \[ \text{Aaroh : Bhuvan} = \frac{5}{9} : \frac{4}{9} = 5 : 4. \]