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, determine the surrendered shares and distribute them to the new partner, then simplify the resulting ratios.

Answer 1

The Correct Option is A

The combined share of Hema and Tara was 5 parts, with Hema holding 2 parts and Tara holding 3 parts. Hema's share following the surrender is calculated as: \[ Hema’s new share} = 2 - \frac{1}{3} \cdot 2 = \frac{4}{3} + \frac{2}{3} = \frac{8}{3} \] Tara's share following the surrender is calculated as: \[ Tara’s new share} = 3 - \frac{1}{2} \cdot 3 = \frac{6}{2} - \frac{3}{2} = \frac{9}{2} \] Ojas's share is calculated as: \[ Ojas’s share} = \frac{1}{3} \cdot 2 + \frac{1}{2} \cdot 3 = \frac{2}{3} + \frac{3}{2} = \frac{13}{6} \] The new shares for Hema, Tara, and Ojas are represented as: \[ \frac{8}{3} : \frac{9}{2} : \frac{13}{6} \] After finding a common denominator and simplifying, the new ratio is: \[ New Ratio} = 8 : 9 : 13 \]