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

A man leaves his home and walks at a speed of $12$ km per hour, reaching the railway station $10$ minutes after the train had departed. If instead he had walked at a speed of $15$ km per hour, he would have reached the station $10$ minutes before the train's departure. The distance (in km) from his home to the railway station is

A boat takes $2$ hours to travel downstream a river from port A to port B , and $3$ hours to return to port A . Another boat takes a total of $6$ hours to travel from port $B$ to port $A$ and return to port $B$. If the speeds of the boats and the river are constant, then the time, in hours, taken by the slower boat to travel from port $A$ to port $B$ is