A passenger sitting in a train A moving at $$90$$ km h$$^{-1}$$ observes another train B moving in the opposite direction for $$8$$ s. If the velocity of the train B is $$54$$ km h$$^{-1}$$, then length of train B is:

Train A moves at 90 km/h and train B moves at 54 km/h in the opposite direction.

Relative velocity (since moving in opposite directions):

$$v_{rel} = 90 + 54 = 144 \text{ km/h} = 144 \times \frac{5}{18} = 40 \text{ m/s}$$

The passenger in train A observes train B passing for 8 seconds. The length of train B equals:

$$L_B = v_{rel} \times t = 40 \times 8 = 320 \text{ m}$$

The length of train B is $$\mathbf{320}$$ m.