CAT 2022

Slot 1

QA

Question & Solution

M - First meeting point

Let the speeds of trains A and B be 'a' and 'b', respectively.

$\frac{x}{a}=\ \frac{\ D-x}{b}$

It is given,

$\frac{D}{a}=10$ and $\frac{x}{b}=9$

$\frac{x}{\frac{D}{10}}=\ \frac{\ D-x}{\frac{x}{9}}$

$\frac{10x}{D}=\ \frac{\ 9D-9x}{x}$

$10x^2=\ \ 9D^2-9Dx$

$10x^2+9Dx-9D^2=\ 0$

Solving, we get $x=\frac{3D}{5}$

$\frac{x}{b}=9$

$\frac{3D}{b\times5}=9$

$\frac{D}{b}=15$ 

The total time taken by train B to travel from station Y to station X is 15 minutes.

The answer is option B