A 214 m long train crosses a man walking at a speed of 5.7 km/h in the opposite direction in 9 seconds. What is the speed (in km/h) of the train?

Correct option is A

Given:

Length of train = 214 m
Speed of man = 5.7 km/h
Time taken to cross = 9 seconds

Formula used:
Relative speed (opposite direction) = Speed of train + Speed of man
Speed = $$\frac{\text{Distance }}{\text{ Time}}$$​​

Solution:
Let speed of train = x 

Speed of man = 5.7 km/h = 5.7 × $$\frac 5{18}$$​m/s = 1.583 m/s

Relative speed =$$\frac{214}9$$​ m/s

x (in m/s) + 1.583 = 23.78

x (in m/s) = 23.78 − 1.583 = 22.197

Convert to km/h: 22.197 × $$\frac{18}5$$​= 79.9 km/h    

Speed of train = 79.9 km/h