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
- $12$
- $6$
- $15$
- $10$