Question

Mita, Veena, and Atul were partners in a firm sharing profits and losses in the ratio \(3 : 2 : 1\). Atul retired, and his share was taken over by Mita and Veena in the ratio \(1 : 4\). The new profit-sharing ratio between Mita and Veena after Atul's retirement will be:

• A. \(3 : 2\)
• B. \(8 : 7\)
• C. \(7 : 3\)
• D. \(2 : 3\)

Hint:

When a retiring partner’s share is redistributed, calculate the additional shares for remaining partners and add them to their original shares to find the new ratio.

Answer 1

The Correct Option is B

- Atul's allocated portion is \(1/6\) of the total, given the combined ratio of \(3 + 2 + 1 = 6\).
- Initially, Mita's portion was \(3/6 = 1/2\), and Veena's was \(2/6 = 1/3\).
- Mita and Veena acquired Atul's share in a \(1 : 4\) ratio.
- Mita received an additional \(\frac{1}{6} \times \frac{1}{5} = \frac{1}{30}\) of the total.
- Veena received an additional \(\frac{1}{6} \times \frac{4}{5} = \frac{4}{30} = \frac{2}{15}\) of the total.
- Mita's revised portion is \(1/2 + 1/30 = 15/30 + 1/30 = 16/30 = 8/15\).
- Veena's revised portion is \(1/3 + 2/15 = 5/15 + 2/15 = 7/15\).
- The updated profit-sharing ratio is \(8 : 7\).