Two trains $M$ and $N$ cross a pole in $25 \text{ seconds}$ and $1 \text{ minute } 15 \text{ seconds}$ respectively. The length of train $M$ is half the length of train $N$. What is the respective ratio between the speed of train $M$ and train $N$?

$A$ man walks from $A$ to $B$ and back in a certain time at the rate of $3.5 \text{ km/h}$. If he had walked from $A$ to $B$ at the rate of $3 \text{ km/h}$ and back from $B$ to $A$ at the rate of $4 \text{ km/h}$,he would have taken $5 \text{ minutes}$ longer. Find the distance between $A$ and $B$ (in $\text{km}$).

In covering a certain distance,the speeds of $A$ and $B$ are in the ratio of $3:4$. $A$ takes $30 \text{ minutes}$ more than $B$ to reach the destination. The time taken by $A$ to reach the destination is (in $\text{hours}$):

Two trains are moving in the same direction at $50 \text{ km/hr}$ and $30 \text{ km/hr}$. The faster train crosses a man sitting in the slower train in $18 \text{ seconds}$. Find the length of the faster train in meters.

$A$ starts from a place $P$ to go to a place $Q$. At the same time $B$ starts from $Q$ to $P$. If after meeting each other $A$ and $B$ took $16$ and $25$ $hours$ more respectively to reach their destinations,the ratio of their speeds is

$A$ train,$240 \, m$ long,crosses a man walking along the line in the opposite direction at the rate of $3 \, km/h$ in $10 \, seconds$. The speed of the train is (in $km/h$):