A train takes 53 seconds to cross a bridge of length 288 m. if the same train takes 17 seconds to cross a sign board, find the length of the train

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

Speed of train which takes 53 seconds to cross a bridge of length 288 m = $$s=\frac{288+l}{53}$$ -----------(i)

Also, $$s=\frac{l}{17}$$ --------------(ii)

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

=> $$\frac{l}{17}=\frac{288+l}{53}$$

=> $$53l=(288\times17)+17l$$

=> $$53l-17l=36l=288\times17$$

=> $$l=\frac{288\times17}{36}=136$$

$$\therefore$$ Length of train = 136 m

=> Ans - (D)