CAT (QA) PYQs

Arvind travels from town $A$ to town $B$, and Surbhi from town B to town $A$, both starting at the same time along the same route. After meeting each other, Arvind takes $6$ hours to reach town $B$ while Surbhi takes $24$ hours to reach town $A$. If Arvind travelled at a speed of $54 \mathrm{~km} / \mathrm{h}$, then the distance, in km, between town $A$ and town $B$ is

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

On a long stretch of east-west road, $A$ and $B$ are two points such that $B$ is $350$ km west of $A$. One car starts from $A$ and another from $B$ at the same time. If they move towards each other, then they meet after $1$ hour. If they both move towards east, then they meet in $7 \mathrm{hrs}$. The difference between their speeds, in km per hour, is