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 share = \(1/6\) (as the total ratio is \(3 + 2 + 1 = 6\)).
- Mita's original share = \(3/6 = 1/2\), Veena's original share = \(2/6 = 1/3\).
- Atul's share was taken over by Mita and Veena in the ratio \(1 : 4\).
- Mita's additional share = \(\frac{1}{6} \times \frac{1}{5} = \frac{1}{30}\).
- Veena's additional share = \(\frac{1}{6} \times \frac{4}{5} = \frac{4}{30} = \frac{2}{15}\).
- New share of Mita = \(1/2 + 1/30 = 15/30 + 1/30 = 16/30 = 8/15\).
- New share of Veena = \(1/3 + 2/15 = 5/15 + 2/15 = 7/15\).
- New profit-sharing ratio = \(8 : 7\).