Two trains 'A' and 'B' of length 'l' and '4 l' are travelling into a tunnel of length 'L' in parallel tracks from opposite directions with velocities 108 km / h and 72 km / h, respectively. If train 'A' takes 35 s less time than train 'B' to cross the tunnel then. length 'L' of tunnel is :
(Given L=60 l )

Solution

Physics sir · 4 steps

Each train crosses the tunnel on its own, so use ground speeds and add train length to tunnel length.

1. Distance to cross. A train has crossed the tunnel only when its last coach leaves it. So the front must travel the tunnel length plus the train's own length. A covers L + l = 61l and B covers L + 4l = 64l.
2. Speeds in m/s. 108 km/h = 30 m/s and 72 km/h = 20 m/s. The tunnel is fixed to the ground, so use these ground speeds. The relative velocity of the two trains plays no part here.

   t_B - t_A = 64l/20 - 61l/30 = (192l - 122l)/60 = 7l/6 = 35 s

3. Find l. 7l/6 = 35 gives l = 30 m.
4. So. L = 60l = 60 × 30 = 1800 m, which is option (c).

The idea to keep. To cross a tunnel or bridge, a train covers the tunnel length plus its own length. Relative velocity matters only when one moving object passes another moving object.

Answer from the NTA final answer key. Solution by PrepWiser.