A train is travelling at a speed of 96 kilometres per hour. It takes 3 seconds…

Concept

When a train crosses a tunnel, its front covers a distance equal to the train's own length while the train is only entering (until the last coach is inside), and then covers a further distance equal to the tunnel's length while the train finishes moving completely clear of it. Since speed is constant, each of these two distances equals speed × the time taken for that phase, so the two time intervals given in the question can be converted separately into the train's length and the tunnel's length.

Application

1. Convert the speed to metres per second: 96 km/h = 96 × 5/18 = 80/3 m/s.

2. Use the first phase (3 seconds, the train fully entering) to find the train's length: distance = speed × time = 80/3 × 3 = 80 m.

3. Use the second phase (30 more seconds, the train completely clearing the tunnel after being fully inside) to find the tunnel's length: distance = speed × time = 80/3 × 30 = 800 m.

4. Compare the two computed lengths: 800 m is far greater than 80 m, so the tunnel is longer than the train.

5. Check each statement against these two computed values: statement A (tunnel = 100 m) does not match 800 m, so A is false. Statement B (tunnel longer than train) matches 800 m > 80 m, so B is true. Statement C (train longer than tunnel) is the opposite of what was found, so C is false. Statement D (train = 80 m) matches exactly, so D is true. Statement E (tunnel = 800 m) matches exactly, so E is true.

Cross-check

Add the two phase times: 3 + 30 = 33 seconds is the total time from the front entering the tunnel to the rear leaving it, during which the front covers train length + tunnel length = 80 + 800 = 880 m. Independently, speed × total time = 80/3 × 33 = 880 m — the two values match, confirming both computed lengths are consistent.

So the statements that hold are B, D and E — matching the combination “B, D and E only.”