Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is

M - First meeting point

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

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

It is given,

$$\dfrac{D}{a}=10$$ and $$\dfrac{x}{b}=9$$

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

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

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

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

Solving, we get $$x=\dfrac{3D}{5}$$

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

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

$$\dfrac{D}{b}=15$$ 

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

The answer is option B