CAT (QA) PYQs

Ravi is driving at a speed of $40$ km/h on a road. Vijay is $54$ meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of $50$ km/h and is $225$ meters away from Ravi. The speed, in km/h, at which Vijay should drive so that all the three cross each other at the same time, 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

Two persons are walking beside a railway track at respective speeds of $2$ and $4 \mathrm{~km}$ per hour in the same direction. A train came from behind them and crossed them in $90$ and $100$ seconds, respectively. The time, in seconds, taken by the train to cross a stationary object?