CAT (QA) PYQs

The distance from $A$ to $B$ is $60 \mathrm{~km}$. Partha and Narayan start from $A$ at the same time and move towards $B$. Partha takes four hours more than Narayan to reach $B$. Moreover, Partha reaches the mid-point of $A$ and $B$ two hours before Narayan reaches $B$. The speed of Partha, in km per hour, is

In a race of three horses, the first beat the second by $11$ metres and the third by $90$ metres. If the second beat the third by $80$ metres, what was the length, in metres, of the racecourse?

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