CAT (QA) PYQs

Leaving home at the same time, Amal reaches the office at $10:15 am$ if he travels at $8 km/hr$, and at $9:40 am$ if he travels at $15 km/hr$. Leaving home at 9:10, at what speed, in $km/hr,$ must be travel so as to reach office exactly at $10 am?$

A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel time gets reduced by $75\%$. The ratio of the original speed of the motor boat to the speed of the river 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