Radha and Rukmani are partners in a firm sharing profits in 3:2 ratio. They admitted Gopi as a new partner. Radha surrendered 1/3 of her share in favour of Gopi and Rukmani surrendered 1/4 of her share in favour of Gopi. Calculate new profit sharing ratio?
New Profit Sharing Ratio is 4:3:3
Explanation
The calculation follows the pattern established in Illustration 3 and Illustration 4 provided in the context. The key is to calculate the share surrendered by each partner as a fraction of their own share, not the total share. Radha surrenders 1/3 of her 3/5 share, and Rukmani surrenders 1/4 of her 2/5 share. The new ratio is derived by subtracting these surrendered portions from the old shares and combining the remaining shares with the new partner's acquired share.
Solution Steps
Radha's Surrender: Radha's old share is 3/5. She surrendered 1/3 of her share in favour of Gopi. Share surrendered = 1/3 of 3/5 = 1/5.
Rukmani's Surrender: Rukmani's old share is 2/5. She surrendered 1/4 of her share in favour of Gopi. Share surrendered = 1/4 of 2/5 = 1/10.
Gopi's Share: Gopi acquires his share from both partners. Gopi's Share = Radha's surrendered share + Rukmani's surrendered share = 1/5 + 1/10 = 2/10 + 1/10 = 3/10.
New Shares of Old Partners: Radha's New Share = Old Share - Surrendered Share = 3/5 - 1/5 = 2/5. Rukmani's New Share = Old Share - Surrendered Share = 2/5 - 1/10 = 4/10 - 1/10 = 3/10.
New Profit Sharing Ratio: The ratio between Radha, Rukmani, and Gopi will be: Radha : Rukmani : Gopi 2/5 : 3/10 : 3/10 Converting to common denominator 10: 4/10 : 3/10 : 3/10 New Ratio = 4:3:3.