CAT (QA) PYQs

Two trains $A$ and $B$ were moving in opposite directions, their speeds being in the ratio $5: 3$. The front end of $A$ crossed the rear end of $B$ $46$ seconds after the front ends of the trains had crossed each other. It took another $69$ seconds for the rear ends of the trains to cross each other. The ratio of length of train $A$ to that of train $B$ is

In a $10 \mathrm{~km}$ race. A, B, and C , each running at uniform speed, get the gold, silver, and bronze medals, respectively. If A beats B by $1 \mathrm{~km}$ and B beats C by $1 \mathrm{~km}$, then by how many metres does A beat C?

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