CAT (QA) PYQs

Arvind travels from town $A$ to town $B$, and Surbhi from town B to town $A$, both starting at the same time along the same route. After meeting each other, Arvind takes $6$ hours to reach town $B$ while Surbhi takes $24$ hours to reach town $A$. If Arvind travelled at a speed of $54 \mathrm{~km} / \mathrm{h}$, then the distance, in km, between town $A$ and town $B$ is

Two trains $A$ and $B$ were moving in opposite directions, their speeds being in the ratio $5: 3$. The front end of $A$ crossed the rear end of $B$ $46$ seconds after the front ends of the trains had crossed each other. It took another $69$ seconds for the rear ends of the trains to cross each other. The ratio of length of train $A$ to that of train $B$ 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