CAT (QA) PYQs

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

The minor angle between the hours hand and minutes hand of a clock was observed at 8:48 am. The minimum duration, in minutes, after $8.48$ am when this angle increases by $50 \%$ 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 $A$?