CAT (QA) PYQs

One can use three different transports which move at $10$, $20$, and $30$ kmph, respectively. To reach from $A$ to $B$, Amal took each mode of transport $1/3$ of his total journey time, while Bimal took each mode of transport $1/3$ of the total distance. The percentage by which Bimal's travel time exceeds Amal's travel time is nearest to

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

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