Aman, Naman and Neel were partners in a firm sharing profits in the ratio of 1:2:1. Neel retires and he surrenders 2/3 of his share in favour of Aman and the remaining share in fav... Aman, Naman and Neel were partners in a firm sharing profits in the ratio of 1:2:1. Neel retires and he surrenders 2/3 of his share in favour of Aman and the remaining share in favour of Naman. Calculate the new profit sharing ratio of Aman and Naman. Read more

Steps to Solve

1. Identify Initial Shares
   The initial profit sharing ratio of Aman, Naman, and Neel is 1:2:1.
   Let the total shares be represented as follows:

• Aman = 1x
• Naman = 2x
• Neel = 1x

2. Calculate Neel's Share to Surrender
   Neel surrenders $\frac{2}{3}$ of his share.
   His share is $1x$, thus the surrendered share is:
   $$ \text{surrendered share} = \frac{2}{3} \times 1x = \frac{2}{3}x $$

3. Determine Remaining Share of Neel
   The remaining share of Neel after surrendering part of his share is:
   $$ \text{remaining share} = 1x - \frac{2}{3}x = \frac{1}{3}x $$

4. Redistribute the Surrendered Share
   The surrendered share is divided between Aman and Naman. Aman receives the entire surrendered amount, making his new share:
   $$ \text{Aman's new share} = 1x + \frac{2}{3}x = \frac{5}{3}x $$
   Naman retains his original share, which is:
   $$ Naman's share = 2x $$

5. Calculate the New Profit Sharing Ratio
   Now, the new profit sharing ratio of Aman and Naman is:
   $$ \text{New Ratio} = \frac{5/3x}{2x} = \frac{5/3}{2} = \frac{5}{6} $$
   To express this as a ratio:
   $$ Aman : Naman = \frac{5}{3} : 2 = 5 : 6 $$