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. Initial Shares: Aaroh \( \frac{1}{9} \), Bhuvan \( \frac{2}{9} \), Charu \( \frac{6}{9} \). 2. Charu's Share Transfer: Charu's total share of \( \frac{6}{9} \) was distributed between Aaroh and Bhuvan in a \( 2 : 1 \) ratio. - Aaroh received \( \frac{2}{3} \) of Charu's share: \( \frac{2}{3} \times \frac{6}{9} = \frac{4}{9} \). - Bhuvan received \( \frac{1}{3} \) of Charu's share: \( \frac{1}{3} \times \frac{6}{9} = \frac{2}{9} \). 3. Revised Shares: - Aaroh's new share = Initial share + Share from Charu = \( \frac{1}{9} + \frac{4}{9} = \frac{5}{9} \). - Bhuvan's new share = Initial share + Share from Charu = \( \frac{2}{9} + \frac{2}{9} = \frac{4}{9} \). 4. New Profit-Sharing Ratio: \[ \text{Aaroh : Bhuvan} = \frac{5}{9} : \frac{4}{9} = 5 : 4. \]