CMAT Exam 2023 Shift 1 Solved Paper

Statement A:
$\mathrm{x}:\mathrm{y}=3:1$
${\mathit{x}}^3-{\mathit{y}}^3={\left(3\mathit{k}\right)}^3-{\mathit{k}}^3=26{\mathit{k}}^3$
This implies value of ${\mathit{x}}^3-{\mathit{y}}^3$ cannot be determined from the given information. Therefore, statement $\mathrm{A}$ is incorrect.
Statement B:
It is given,

Let $\mathit{x}=3\mathit{k}$ and $\mathit{y}=2\mathit{k}$
$3\mathit{k}=2\mathit{k}+12$
$\mathit{k}=12$

It is given, $\mathit{z}:\mathit{y}=1:3$
$\mathit{z}=\frac{24}{3}=8$
$\mathit{z}+\mathit{x}=36+8=44$
Therefore, statement B is correct.
Statement C:
It is given, $3\mathit{x}=8\mathit{y}$ and $5\mathit{y}=9\mathit{z}$
$\mathit{x}:\mathit{y}=8:3=24:9$
$\mathit{y}:\mathit{z}=9:5$
$\mathit{x}:\mathit{y}:\mathit{z}=24:9:5$
$\mathit{x}:\mathit{z}=24:5=72:15$
Therefore, statement $\mathrm{C}$ is correct.
The answer is option C.