Assume that in this question, $A = 20, B = 30, C = 50$.
They find $\$100$ and want to split by ratios such that the one with the least amount at the moment gets the most. $A$ will get the most, $B$ after that, and $C$ the least and this division will be relative to the money they currently have.
If the ratios are not inverted they come out to be $2:3:5$, But how to invert it so $C$ gets the least as he has the most at the moment.
Surely it would just be
\begin{align}&\color{white}=\frac1{20}:\frac1{30}:\frac1{50}\\\\ &=\frac{300}{20}:\frac{300}{30}:\frac{300}{50}\\\\ &=15:10:6\end{align}
Therefore \begin{align}A&\text{ gets } \frac{15}{31}\times 100 \approx \$48.387\cdots\\ B&\text{ gets } \frac{10}{31}\times 100 \approx \$32.258\cdots\\ C&\text{ gets } \frac{6}{31}\times 100 \approx \$19.354\cdots\end{align}