Question

Anju, Divya, and Bobby were partners in a firm sharing profits and losses in the ratio of \(3 : 2 : 1\). Bobby retired. The new profit-sharing ratio between Anju and Divya after Bobby's retirement was \(5 : 3\). The gaining ratio of the remaining partners will be:

• A. \(3 : 2\)
• B. . \(5 : 3\)
• C. . \(3 : 1\)
• D. . \(2 : 3\)

Hint:

To calculate gaining ratios, subtract the old share from the new share for each partner. Simplify for clarity.

Answer 1

The Correct Option is D

- Bobby's share was \(1/6\) (as the total ratio is \(3+2+1 = 6\)).
- Anju's original share = \(3/6 = 1/2\), and Divya's original share = \(2/6 = 1/3\).
- After Bobby retires, the new profit-sharing ratio between Anju and Divya is \(5 : 3\).
- Total share of Anju and Divya = \(1 - \frac{1}{6} = \frac{5}{6}\).
- New share of Anju = \(\frac{5}{6} \times \frac{5}{8} = \frac{25}{48}\).
New share of Divya = \(\frac{5}{6} \times \frac{3}{8} = \frac{15}{48}\).
- Gaining ratio = \((\text{New Share - Old Share})\):
- Anju's gain = \(\frac{25}{48} - \frac{1}{2} = \frac{25}{48} - \frac{24}{48} = \frac{1}{48}\).
- Divya's gain = \(\frac{15}{48} - \frac{1}{3} = \frac{15}{48} - \frac{16}{48} = -\frac{1}{48}\).
- Gaining ratio = \(3 : 1\).