A 252 m long train is running at a speed of 125 km/h. What is the time (in seconds) in which it will pass a man who starts from the engine running at the speed of 17 km/h in the same direction as that of the train?

The correct option is 8.4.

To find the time taken for the train to completely pass the man, we can analyze the motion of both objects relative to each other. Because both the train and the man are moving in the same direction, we can use the concept of relative speed.

Step 1: Identify the given values:
Length of the train = 252 m
Speed of the train = 125 km/h
Speed of the man = 17 km/h

Step 2: Calculate the relative speed of the train with respect to the man:
Since both are moving in the same direction, the relative speed is obtained by subtracting the speed of the man from the speed of the train:
$V_{\mathrm{relative}}=125-17=108\text{km/h}$

Step 3: Convert the relative speed into meters per second (m/s):
To convert a speed from km/h to m/s, we multiply by the conversion factor 5/18:
$V_{\mathrm{relative}}=108\times \frac{5}{18}$
Simplifying this:
$V_{\mathrm{relative}}=6\times 5=30\text{m/s}$

Step 4: Find the distance to be covered:
The man starts running from the engine (which is at the front of the train) in the same direction as the train. For the train to pass him completely, the rear end of the train must cross him. Therefore, the relative distance to be covered is equal to the length of the train:
Distance = 252 m

Step 5: Calculate the time taken:
Using the formula for time, we divide the relative distance by the relative speed:
$\text{Time}=\frac{\text{Distance}}{V_{\mathrm{relative}}}$
Substituting the values:
$\text{Time}=\frac{252}{30}=8.4\text{seconds}$
Thus, the train will pass the man in 8.4 seconds.