CAT (QA) PYQs

Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take $1.5$ hours if they travel towards each other, but $10.5$ hours if they travel in the same direction. If the speed of the slower car is $60$ km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards each other, is

A cyclist leaves $A$ at $10$ am and reaches $B$ at $11$ am. Starting from $10:01$ am, every minute a motor cycle leaves $A$ and moves towards $B$. Forty-five such motor cycles reach $B$ by $11$ am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached $B$ by the time the cyclist reached $B$?

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