To solve this problem, we can use the concept of speed and time being inversely proportional to each other.
Let's assume the length of the train is 'L' meters.
When the train is running at a speed of 72 km/h, it crosses a pole in 30 seconds. Since the train crosses the pole, the distance covered by the train is equal to its length (L).
Speed = Distance/Time
Converting the speed from km/h to m/s: 72 km/h = (72 * 1000) m/3600 s = 20 m/s
Using the formula, we have: 20 m/s = L/30 s
Now, let's find the time taken by the train to cross the pole when its speed is 54 km/h.
Converting the speed from km/h to m/s: 54 km/h = (54 * 1000) m/3600 s = 15 m/s
Using the formula, we have: 15 m/s = L/t
Since the length of the train (L) remains the same, we can equate the two equations:
L/30 = L/t
Simplifying, we get: t = 30 * (15/20) t = 22.5 seconds
Therefore, it would take the same train 22.5 seconds to cross the pole when its speed is 54 km/h.