CAT (QA) PYQs

A man leaves his home and walks at a speed of $12$ km per hour, reaching the railway station $10$ minutes after the train had departed. If instead he had walked at a speed of $15$ km per hour, he would have reached the station $10$ minutes before the train's departure. The distance (in km) from his home to the railway station is

In a car race, car $A$ beats car $B$ by $45 \mathrm{~km}$, car $B$ beats car $C$ by $50$km, and car $A$ beats $C$ by $90 \mathrm{~km}$. the distance (in km) over which the race has been conducted is

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