CAT (QA) PYQs

Arun drove from home to his hostel at $60$ miles per hour. While returning home he drove half way along the same route at a speed of $25$ miles per hour and then took a bypass road which increased his driving distance by $5$ miles, but allowed him to drive at $50$ miles per hour along this bypass road. If his return journey took $30$ minutes more than his onward journey, then the total distance traveled by him is

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

A motorbike leaves point $A$ at $1$ pm and moves towards point $B$ at a uniform speed. A car leaves point $B$ at $2$ pm and moves towards point $A$ at a uniform speed which is double that of the motorbike. They meet at $3:40$ pm at a point which is $168 \mathrm{~km}$ away from $A$ . What is the distance, in km, between $A$ and $B$ ?