Question

Pari, Param, and Prizleen are partners sharing profits and losses in the ratio of 5:3:2. Param retires. Her share is taken by Pari and Prizleen in the ratio of 2:1. Calculate the new profit sharing ratio of Pari and Prizleen.

• A. 7:3
• B. 3:7
• C. 5:2
• D. 2:1

Answer 1

The Correct Option is A

Provided Information:
Partners Pari, Param, and Prizleen share profits and losses in a 5:3:2 ratio.
Param retires, and her share is acquired by Pari and Prizleen in a 2:1 ratio.
Step 1: Determine Param's share. Total ratio: 5 + 3 + 2 = 10. Param's profit share is: \[ \text{Param's Share} = \frac{3}{10} \]
Step 2: Allocate Param's share to Pari and Prizleen. Param's share is distributed between Pari and Prizleen in a 2:1 ratio. Total distribution ratio: 2 + 1 = 3.
Pari's portion of Param's share: \[ \text{Pari's share of Param's share} = \frac{2}{3} \times \frac{3}{10} = \frac{6}{30} = \frac{1}{5} \]
Prizleen's portion of Param's share: \[ \text{Prizleen's share of Param's share} = \frac{1}{3} \times \frac{3}{10} = \frac{3}{30} = \frac{1}{10} \]
Step 3: Calculate the new profit-sharing ratio. New shares for Pari and Prizleen are calculated as follows:
- Pari's new share = Original share + Share acquired from Param \[ \text{Pari's new share} = \frac{5}{10} + \frac{1}{5} = \frac{5}{10} + \frac{2}{10} = \frac{7}{10} \]
- Prizleen's new share = Original share + Share acquired from Param \[ \text{Prizleen's new share} = \frac{2}{10} + \frac{1}{10} = \frac{3}{10} \]
Step 4: New profit-sharing ratio. The revised profit-sharing ratio between Pari and Prizleen is: \[ \text{New ratio} = 7:3 \]

The final answer is (1): 7:3.