Puja, Priya, Pratistha are partners sharing profits and losses in the ratio of 5:3:2. Priya retires. Her share is taken by Priya and Pratistha in the ratio of 2:1. Calculate the new profit sharing ratio.
Old Profit Sharing Ratio of Puja, Priya, and Pratistha is 5:3:2. Priya's Share = 3/10. Since Priya retires, her share is acquired by the remaining partners, Puja and Pratistha, in the ratio of 2:1.
Share Acquired by Puja: = 2/3 of 3/10 = 6/30
Share Acquired by Pratistha: = 1/3 of 3/10 = 3/30
New Share Calculation: New Share = Old Share + Acquired Share
Puja's New Share: = 5/10 + 6/30 = 15/30 + 6/30 = 21/30
Pratistha's New Share: = 2/10 + 3/30 = 6/30 + 3/30 = 9/30
New Profit Sharing Ratio (Puja:Pratistha): = 21/30 : 9/30 = 21 : 9 = 7 : 3
Explanation
The solution follows the method illustrated in Illustration 2 of the provided context, where the retiring partner's share is distributed to the continuing partners in a specific ratio. Note: The question text in the context contains a typo stating 'Priya and Pratistha' acquire the share; logically, since Priya is retiring, the acquiring partners are Puja and Pratistha. The calculation adds the acquired portion to the existing shares of the remaining partners to find the new ratio.
Solution Steps
Step 1: Determine the retiring partner's share. Priya's share is 3/10.
Step 2: Calculate the share acquired by remaining partners. Puja acquires 2/3 of 3/10 = 6/30. Pratistha acquires 1/3 of 3/10 = 3/30.
Step 3: Calculate new shares by adding acquired share to old shares. Puja = 5/10 + 6/30 = 21/30. Pratistha = 2/10 + 3/30 = 9/30.
Step 4: Determine the New Profit Sharing Ratio by simplifying the fraction 21/30 : 9/30 to 7:3.