A train is moving with uniform speed crosses two tunnels of lengths 270 metres and 450 metres in 12 seconds and 15 seconds respectively. What is the speed (in km/hr) of the train?

Let speed of train = $$x$$ km/hr and length of train = $$l$$ km

Using, speed = distance/time

=> $$x=\frac{l+270}{12}$$ ----------(i)

and $$x=\frac{l+450}{15}$$ ---------(ii)

Comparing both equations, we get :

=> $$\frac{l+270}{12}=\frac{l+450}{15}$$

=> $$5l+1350=4l+1800$$

=> $$5l-4l=1800-1350$$

=> $$l=450$$

Substituting it in equation (ii), => $$x=\frac{450+450}{15}=\frac{900}{15}=60$$ m/s

= $$(60\times\frac{18}{5})=216$$ km/hr

=> Ans - (D)