Anita, Jaya and Nisha are partners sharing profits and losses in the ratio of 1:1:1 Jaya retires from the firm. Anita and Nisha decided to share the profit in future in the ratio 4:3. Calculate the gaining ratio.
The Old Profit Sharing Ratio of Anita, Jaya, and Nisha is 1:1:1. Jaya retires, and the continuing partners, Anita and Nisha, decide on a New Profit Sharing Ratio of 4:3. To find the Gaining Ratio, we calculate the difference between the new share and the old share for each continuing partner using the formula: Gaining Share = New Share – Old Share.
Anita’s Gaining Share = (4/7) - (1/3) = (12 - 7)/21 = 5/21. Nisha’s Gaining Share = (3/7) - (1/3) = (9 - 7)/21 = 2/21. Therefore, the Gaining Ratio between Anita and Nisha is 5:2.
Explanation
The solution follows the method illustrated in the provided context (specifically Illustration 5). The gaining ratio is calculated by deducting the partner's old share from their new share. Anita's old share was 1/3, and her new share is 4/7. Nisha's old share was 1/3, and her new share is 3/7. The difference between these shares represents their gain, resulting in a ratio of 5:2.
Solution Steps
Step 1: Determine the Old Share of continuing partners (Anita and Nisha) from the ratio 1:1:1. Old Share = 1/3 each.
Step 2: Determine the New Share from the future ratio 4:3. Anita's New Share = 4/7; Nisha's New Share = 3/7.
Step 3: Calculate Gaining Share using the formula: New Share - Old Share.
Step 4: Anita's Gain = (4/7) - (1/3) = (12-7)/21 = 5/21.
Step 5: Nisha's Gain = (3/7) - (1/3) = (9-7)/21 = 2/21.
Step 6: Gaining Ratio = 5/21 : 2/21 = 5:2.