CAT (QA) PYQs

The distance from $A$ to $B$ is $60 \mathrm{~km}$. Partha and Narayan start from $A$ at the same time and move towards $B$. Partha takes four hours more than Narayan to reach $B$. Moreover, Partha reaches the mid-point of $A$ and $B$ two hours before Narayan reaches $B$. The speed of Partha, in km per hour, is

Two ants $A$ and $B$ start from a point $P$ on a circle at the same time, with $A$ moving clock-wise and $B$ moving anti-clockwise. They meet for the first time at $10:00$ am when $A$ has covered $60$ of the track. If $A$ returns to $P$ at $10:12$ am, then $B$ returns to $P$ at

The distance from $B$ to $C$ is thrice that from $A$ to $B$. Two trains travel from $A$ to $C$ via $B$. The speed of train $2$ is double that of train $1$ while traveling from $A$ to $B$ and their speeds are interchanged while traveling from $B$ to $C$. The ratio of the time taken by train $1$ to that taken by train $2$ in travelling from $A$ to $C$ is