A train takes 52 seconds to cross a bridge of length 204 m. if the same train takes 18 seconds to cross a sign board, find the length of the train. (in metre)

Let length of train = $$l$$ m and speed = $$s$$ m/s

Speed of train which takes 52 seconds to cross a bridge of length 204 m = $$s=\frac{204+l}{52}$$ -----------(i)

Also, $$s=\frac{l}{18}$$ --------------(ii)

Substituting value of $$s$$ from equation (ii) in (i), we get :

=> $$\frac{l}{18}=\frac{204+l}{52}$$

=> $$52l=(204\times18)+18l$$

=> $$52l-18l=34l=204\times18$$

=> $$l=\frac{204\times18}{34}=108$$

$$\therefore$$ Length of train = 108 m

=> Ans - (D)