A 200 m long train is running with a speed of 50 km/h. In what time will it pass a man who is running at 5 km/h in the direction opposite to that in which the train is going ?

Firstly, we can solve this question by assuming that the length of the man is negligible and that only the length of the train matters. 
If the man and the train move in opposite directions, the relative velocity will increase.

200m is 0.2km. The speed of the train is 50 kmph, and that of the man is 5 kmph. 
Effective relative velocity will be 55 kmph.  

Time taken to cover 0.2km will be 0.2/55=1/275 hours. 

An hour has 3600 seconds. 3600/275=144/11 seconds. 

Hence, the answer is Option C.