A train P travelling at a speed of 15 m/s is able to cross a platform of 200 meter length completely in 30 seconds. Approximately how long will it take train P to cross a man who is coming towards the train on his bike at a speed of 27 km/h?
[Note: Ignore the length of the bike.]

A train P travelling at a speed of 15 m/s is able to cross a platform of 200 meter length completely in 30 seconds.

Speed of train = $$\frac{length\ of\ train+length\ of\ platform}{time}$$

$$15 = \frac{length\ of\ train+200}{30}$$

$$450=length\ of\ train+200$$

Time taken by train P to cross a man who is coming towards the train on his bike = $$\frac{length\ of\ train}{relative\ speed}$$

= $$\frac{250}{15+7.5}$$

= $$\frac{250}{22.5}$$

= $$\frac{2500}{225}$$

= 11.1 seconds (approx.)