CAT 2022 Slot 1 Paper

$\mathrm{M}$ - First meeting point
Let the speeds of trains $\mathrm{A}$ and $\mathrm{B}$ be ' $\mathit{a}$ ' and ' $\mathit{b}$ ', respectively.
$\frac{\mathit{x}}{\mathit{a}}=\frac{\mathit{D}-\mathit{x}}{\mathit{b}}$
It is given,
$\frac{\mathrm{D}}{\mathit{a}}=10$ and $\frac{\mathit{x}}{\mathit{b}}=9$
$\frac{\mathit{x}}{\frac{\mathrm{D}}{10}}=\frac{\mathrm{D}-\mathit{x}}{\frac{\mathit{x}}{9}}$
$\frac{10\mathit{x}}{\mathrm{D}}=\frac{9\mathrm{D}-9\mathit{x}}{\mathit{x}}$
$10{\mathit{x}}^2=9{\mathrm{D}}^2-9\mathrm{D}\mathit{x}$
$10{\mathit{x}}^2+9\mathrm{D}\mathit{x}-9{\mathrm{D}}^2=0$
Solving, we get $\mathit{x}=\frac{3\mathrm{D}}{5}$
$\frac{\mathit{x}}{\mathit{b}}=9$
$\frac{3\mathrm{D}}{\mathit{b}\times 5}=9$
$\frac{\mathrm{D}}{\mathit{b}}=15$
The total time taken by train $\mathit{B}$ to travel from station $\mathrm{Y}$ to station $\mathrm{X}$ is 15 minutes.
The answer is option B