Amit, Dinesh, and Gagan are partners sharing profits in the ratio of $5:3:2$. Dinesh retires. Amit and Gagan decide to share the profits of the new firm in the ratio of $3:2$. The gaining ratio between Amit and Gagan will be:

The formula for calculating the Gaining Share is:
$$\text{Gaining Share}=\text{New Share}-\text{Old Share}$$
Given details:Old Ratio of Amit, Dinesh, and Gagan = $5:3:2$ Old Shares: Amit = $\frac{5}{10}$, Gagan = $\frac{2}{10}$ New Ratio of Amit and Gagan = $3:2$ New Shares: Amit = $\frac{3}{5}$, Gagan = $\frac{2}{5}$ Calculating the gaining shares:Amit's Gain = $\frac{3}{5}-\frac{5}{10}=\frac{6-5}{10}=\frac{1}{10}$ Gagan's Gain = $\frac{2}{5}-\frac{2}{10}=\frac{4-2}{10}=\frac{2}{10}$ Comparing the gains of Amit and Gagan:
$$\frac{1}{10}:\frac{2}{10}=1:2$$