A train takes 20 sec to cross a man who is standing on a platform . While it takes 25 sec to cross a 200 meter long platform . Find length of the train .

800 m

Let length of train = x meter

Time taken to cross a man is 20 sec . so total distance traveled is only length of train 

Distance = Speed × Time 

Speed = \(\frac{x}{20}\)       ------ ( 1 ) 

 Train takes 25 sec to cross a 200 meter long platform, total distance = 200 + x 

 Speed = \(\frac{200\;+\;x}{25}\)      ---------- ( 2 ) 

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

 \(\frac{x}{20}\)    =   \(\frac{200\;+\;x}{25}\)

25x = 4000+ 20x 

5x = 4000    ⇒  x = 800 m 

so, length of train = 800 m