Two trains are moving in opposite directions at speeds of 50 km/h and 110 km/h. The
length of one train is 500 m. The time taken by them to cross each other is 12 seconds. The length (in m) of the other train, correct to 2 decimal places, is:

Correct option is A

Given:
Speed of train 1, v₁ = 50 km/h
Speed of train 2, v₂ = 110 km/h
Length of train 1, L₁ = 500 m
Time taken to cross each other, t = 12 seconds
Length of train 2, L₂ = ? 
Formula Used:
Relative speed when trains move in opposite directions: v₁ + v₂
Distance covered when crossing each other = L₁ + L₂
​$$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$​​
Convert speeds from km/h to m/s:
​$$v \, \text{(m/s)} = v \, \text{(km/h)} \times \frac{5}{18}\\$$​​
Solution:
Relative speed = $$(50 + 110) \times \frac{5}{18} = 160 \times \frac{5}{18} \, \text{m/s}\\$$​​
Distance covered in 12 seconds:
​$$\text{Distance} = \text{Speed} \times \text{Time} = 160 \times \frac{5}{18} \times 12 = 533.33 \, \text{m}\\$$​​
$$L_1 + L_2 = 533.33\\L_2 = 533.33 - 500 = 33.33 \, \text{m}\\$$​​
The length of the other train is 33.33 meters.