Question

Hema and Tara were partners in a firm sharing profits and losses in the ratio of \( 2 : 3 \). They admitted Ojas as a new partner. Hema surrendered \( \frac{1}{3} \) of her share and Tara surrendered \( \frac{1}{2} \) of her share in favour of Ojas. The new profit-sharing ratio of Hema, Tara, and Ojas will be:

• A. \( 8 : 9 : 13 \)
• B. \( 3 : 2 : 5 \)
• C. \( 2 : 3 : 5 \)
• D. \( 2 : 3 : 25 \)

Hint:

To calculate the new profit-sharing ratio, first determine the surrendered shares and add the new partner’s share to find the adjusted ratios.

Answer 1

The Correct Option is B

The total share of Hema and Tara was 5 parts (2 parts for Hema and 3 parts for Tara). \[ Hema’s share after surrender} = 2 - \frac{1}{3} \cdot 2 = \frac{4}{3} \] \[ Tara’s share after surrender} = 3 - \frac{1}{2} \cdot 3 = \frac{3}{2} \] Ojas’s share = \( \frac{1}{3} \cdot 2 + \frac{1}{2} \cdot 3 = 2 \). The new shares of Hema, Tara, and Ojas become \( \frac{4}{3} : \frac{3}{2} : 2 \). Simplifying the ratio: \[ \frac{4}{3} : \frac{3}{2} : 2 = 3 : 2 : 5 \]