Question 6.

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 $x = \frac{3D}{5}$

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

$\frac{3D}{5b} = 9$

$\frac{D}{b} = 15$

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