A train takes 18 sec to cross a man who is standing on a platform . While it takes 30 sec to cross a 300 meter long platform . Find length of the train .

450 m

Let length of train = x meter

Time taken to cross a man is 18 sec . so total distance traveled is only length of train 

Distance = Speed × Time 

Speed = \(\frac{x}{18}\)       ------ ( 1 ) 

 Train takes 30 sec to cross a 300 meter long platform, total distance = 300 + x 

 Speed = \(\frac{300\;+\;x}{30}\)      ---------- ( 2 ) 

Speed of train is same so put equation 1 equals to equation 2 

 \(\frac{x}{18}\)    =   \(\frac{300\;+\;x}{30}\)

30x = 5400 + 18x 

12x = 5400    ⇒  x = 450 m 

so, length of train = 450 m