X, Y and Z are partners sharing profits in the ratio of 5:3:2. X wants to retire and goodwill is valued…

The old profit-sharing ratio of X, Y, and Z is $5:3:2$, and the new ratio of continuing partners Y and Z is $1:1$ ($\frac{5}{10} : \frac{5}{10}$). Y's gain is $\frac{5}{10} - \frac{3}{10} = \frac{2}{10}$ and Z's gain is $\frac{5}{10} - \frac{2}{10} = \frac{3}{10}$, giving a gaining ratio of $2:3$. Retiring partner X's share of goodwill is $1{,}00{,}000 \times \frac{5}{10} = \text{Rs. } 50{,}000$, which is debited to Y (Rs. 20,000) and Z (Rs. 30,000) in their gaining ratio $2:3$, giving "Y's Capital A/c Dr. 20,000, Z's Capital A/c Dr. 30,000; To X's Capital A/c 50,000".