CAT (QA) PYQs

Rahul starts on his journey at 5 pm at a constant speed so that he reaches his destination at 11 pm the same day. However, on his way, he stops for 20 minutes, and after that, increases his speed by 3 km per hour to reach on time. If he had stopped for 10 minutes more, he would have had to increase his speed by 5 km per hour to reach on time. His initial speed, in km per hour, was

A train travelled a certain distance at a uniform speed. Had the speed been $6$ km per hour more, it would have needed $4$ hours less. Had the speed been $6$ km per hour less, it would have needed $6$ hours more. The distance, in km, travelled by the train is

John jogs on track $A$ at $6$ kmph and Mary jogs on track $B$ at $7.5$ kmph. The total length of tracks $A$ and $B$ is $325$ metres. While John makes $9$ rounds of track $A$, Mary makes $5$ rounds of track $B$. In how many seconds will Mary make one round of track $A$?