A train takes 18 sec to cross a man who is standing on a platform . While it takes 35 sec to cross a 170 meter long platform . Find length of the train .

180 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 35 sec to cross a 170 meter long platform, total distance = 170 + x 

 Speed = \(\frac{170\;+\;x}{35}\)      ---------- ( 2 ) 

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

 \(\frac{x}{18}\)    =   \(\frac{170\;+\;x}{35}\)

35x = 3060 + 18x 

17x = 3060    ⇒  x = 180 m 

so, length of train = 180 m