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

We are given the following information:
Pari, Param, and Prizleen are partners sharing profits and losses in the ratio of 5:3:2.
Param retires, and her share is taken by Pari and Prizleen in the ratio of 2:1.
Step 1: Calculate Param's share Since the total profit-sharing ratio is 5 + 3 + 2 = 10, Param’s share of the profits is: \[ \text{Param's Share} = \frac{3}{10} \] ### Step 2: Distribute Param's share between Pari and Prizleen Param's share is taken by Pari and Prizleen in the ratio of 2:1. The total ratio for the distribution is 2 + 1 = 3.
Pari's share 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 share 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 Now, let's calculate the new shares for Pari and Prizleen: - Pari’s new share = Original share + Share taken 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 taken from Param \[ \text{Prizleen's new share} = \frac{2}{10} + \frac{1}{10} = \frac{3}{10} \] Step 4: New profit-sharing ratio The new profit-sharing ratio between Pari and Prizleen is: \[ \text{New ratio} = 7:3 \]

Thus, the correct answer is (1): 7:3.

Answer 2

1. Calculate Param’s share: - Total ratio parts = 5 + 3 + 2 = 10 - Param’s share \(= \frac{3}{10}\) of the total profit.
2. Distribution of Param’s share: - Pari takes \(\frac{2}{3}\) of Param’s share. - Prizleen takes \(\frac{1}{3}\) of Param’s share.
3. New shares: - Pari’s new share = Original share + Pari’s part of Param’s share 
Prizleen’s new share \(=\frac{2}{10} + \frac{1}{3} \times \frac{3}{10} = \frac{2}{10} + \frac{1}{10} = \frac{3}{10}\)
4. New profit-sharing ratio of Pari and Prizleen: - New ratio = Pari’s share : Prizleen’s share \(\frac{7}{10}: \frac{3}{10} = \frac{7}{3}\)