To solve this question, we need to consider the relative motion of the train and the man on the platform.
Given:
Length of the train = 300m
Time taken by the train to cross the man = 10 seconds
Let's first find the speed of the train. We know that speed = distance / time.
Speed of the train = 300m / 10s = 30 m/s
Now, we need to find the time taken by the train to cross a platform of length 120m.
When the train is crossing the platform, it covers the distance equal to its own length (300m) plus the length of the platform (120m).
Total distance = 300m + 120m = 420m
The time taken can be found using the formula: time = distance / speed.
Time taken = 420m / 30 m/s = 14 seconds
Therefore, the time taken by the train to cross the platform of length 120m is 14 seconds.
Comparing this with the options given:
A) 3 seconds - incorrect
B) 3.5 seconds - incorrect
C) 4 seconds - correct
D) 4.5 seconds - incorrect
So, the correct answer is C) 4 seconds.