A train takes 18 sec to cross a man who is standing on a platform . While it takes 25 sec to cross a 210 meter long platform . Find length of the train .

540m

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 25 sec to cross a 210 meter long platform, total distance = 210 + x 

 Speed = \(\frac{210\;+\;x}{25}\)      ---------- ( 2 ) 

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

 \(\frac{x}{18}\)    =   \(\frac{210\;+\;x}{25}\)

25x = 3780 + 18x 

7x = 3780    ⇒  x = 540 m 

so, length of train = 540 m