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 $10 am?$

Two persons are walking beside a railway track at respective speeds of $2$ and $4 \mathrm{~km}$ per hour in the same direction. A train came from behind them and crossed them in $90$ and $100$ seconds, respectively. The time, in seconds, taken by the train to cross a stationary object?

The wheels of bicycles $A$ and $B$ have radii $30$ cm and $40$ cm, respectively. While traveling a certain distance, each wheel of $A$ required $5000$ more revolutions than each wheel of $B$. If bicycle $B$ traveled this distance in $45$ minutes, then its speed, in km per hour, was