Murli, Naveen and Omprakesh are partners sharing profits in the ratio of $\frac{3}{8}$, $\frac{1}{2}$ and $\frac{1}{8}$. Murli retires and surrenders $\frac{2}{3}\text{rd}$ of his share in favour of Naveen and the remaining share in favour of Omprakesh. The gaining ratio of the remaining partners is-

First, let's establish the common old profit sharing ratios:Murli's Share = $\frac{3}{8}$ Naveen's Share = $\frac{1}{2}=\frac{4}{8}$ Omprakesh's Share = $\frac{1}{8}$ When Murli retires, he surrenders his share in the following breakdown:Share surrendered to Naveen = $\frac{2}{3}\text{ of Murli’s Share}=\frac{2}{3}\times \frac{3}{8}=\frac{6}{24}$ Remaining share surrendered to Omprakesh = $\left(1-\frac{2}{3}\right)\text{ of Murli’s Share}=\frac{1}{3}\times \frac{3}{8}=\frac{3}{24}$ The gaining ratio matches the exact proportion of shares acquired by the continuing partners:
$$\text{Gaining Ratio of Naveen and Omprakesh}=\frac{6}{24}:\frac{3}{24}=6:3=2:1$$