Xavier Aptitude Test 2020 Paper

Let the part of the amount divided between $\mathrm{Y}$ and $\mathrm{Z}$ be $5\mathit{k}$ ⇒ $\mathrm{Y}$ gets $2\mathit{k}$ and $\mathrm{Z}$ gets $3\mathit{k}$.
The overall profit is $\mathrm{Rs}200000$.
Hence the remaining profit is $\mathrm{Rs}200000-5\mathit{k}$
Left over profit of $2-5\mathit{k}$ is divided in the ratio $2.5:3.5:4$
The final profit distribution among $\mathrm{X}$, $\mathrm{Y}$ and $\mathrm{Z}$
$\Rightarrow$ Finally, $\mathrm{X}$ gets $\frac{2.5}{10}\left(200000-5\mathit{k}\right)$ , $\mathrm{Y}$ gets $2\mathit{k}+\frac{3.5}{10}\left(200000-5\mathit{k}\right)$ and $\mathrm{Z}$ gets $3\mathit{k}+\frac{4}{10}\left(200000-5\mathit{k}\right)$
Given the ratio of profit distribution of $\mathrm{X}$ and $\mathrm{Z}$ is $1:4$
Given, $3\mathit{k}+\frac{4}{10}\left(20000-5\mathit{k}\right)=4\left(\frac{2.5}{10}\left(200000-5\mathit{k}\right)\right)\Rightarrow 3\mathit{k}=\frac{6}{10}\left(200000-5\mathit{k}\right)$
$\Rightarrow 10\mathit{k}=400000-10\mathit{k}\Rightarrow 20\mathit{k}=400000\Rightarrow \mathit{k}=20000$
∴ Share of $\mathrm{Y}=2\mathit{k}+\frac{3.5}{10}\left(200000-5\mathit{k}\right)=75000$