CAT (QA) PYQs

Two cars travel the same distance starting at $10:00$ am and $11:00$ am, respectively, on the same day. They reach their common destination at the same point of time. If the first car travelled for at least $6$ hours, then the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is

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

Mira and Amal walk along a circular track, starting from the same point at the sometime. If they walk in the same direction, then in $45$ minutes, Amal completes exactly $3$ more rounds than Mira. If they walk in opposite directions, then they meet for the first time exactly after $3$ minutes. The number of rounds Mira walks in one hour is