CAT (QA) PYQs

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 $B$ ?

In a race of three horses, the first beat the second by $11$ metres and the third by $90$ metres. If the second beat the third by $80$ metres, what was the length, in metres, of the racecourse?

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