CAT (QA) PYQs

Arun drove from home to his hostel at $60$ miles per hour. While returning home he drove half way along the same route at a speed of $25$ miles per hour and then took a bypass road which increased his driving distance by $5$ miles, but allowed him to drive at $50$ miles per hour along this bypass road. If his return journey took $30$ minutes more than his onward journey, then the total distance traveled by him is

The distance from $B$ to $C$ is thrice that from $A$ to $B$. Two trains travel from $A$ to $C$ via $B$. The speed of train $2$ is double that of train $1$ while traveling from $A$ to $B$ and their speeds are interchanged while traveling from $B$ to $C$. The ratio of the time taken by train $1$ to that taken by train $2$ in travelling from $A$ to $C$ 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