Given:
- Length of the train = 100 m
- Speed of the man = 5 m/s
- Time taken to overtake the man = 5 sec

To find:
- Time taken by the train to pass through the man when he runs in the opposite direction

Assumptions:
- The train and the man are moving in a straight line.
- The speeds mentioned are constant throughout.

Approach:
1. Find the speed of the train relative to the man.
2. Use the relative speed to calculate the time taken by the train to pass through the man when they are moving in the opposite direction.

Solution:
1. Speed of the train relative to the man = Speed of the train - Speed of the man
= 0 (since the speed of the train is constant and the man is running at a constant speed in the same direction)
2. When the train overtakes the man, the distance covered by the train is equal to the length of the train, i.e., 100 m.
Time taken by the train to cover this distance = 5 sec.
Therefore, the speed of the train = Distance/Time = 100/5 = 20 m/s.
3. Speed of the train relative to the man = 20 - 5 = 15 m/s.
4. Distance covered by the train to pass through the man when they are moving in the opposite direction = Length of the train + Length of the man
= 100 + 0 (since the man's length is negligible compared to the train's length)
= 100 m.
5. Time taken by the train to cover this distance = Distance/Speed = 100/15 = 6.67 sec (approximately).
Therefore, the time taken by the same train to pass through the same man when he runs in the opposite direction is approximately 6.67 seconds.

Answer:
The time taken by the same train to pass through the same man when he runs in the opposite direction is approximately 6.67 seconds. Thus, option a. 3.3s is incorrect.