A train running at 75 km/hr crosses another train running at 30 km/hr in the same direction in 108 seconds. If the length of the fast-moving train is 950 m, then what is the length (in m) of the slow-moving train?

Correct option is A

Given:
Speed of fast train, v₁ = 75 km/h
Speed of slow train, v₂ = 30 km/h
Time taken to cross each other, t = 108 seconds
Length of fast train, L₁ = 950 m
Length of slow train, L₂ = ?
Formula Used:
Relative speed when trains run in the same direction: v₁ - v₂
Distance covered when crossing each other = L₁ + L₂
Time = Distance / Speed
Convert speeds from km/h to m/s:
​$$v \, \text{(m/s)} = v \, \text{(km/h)} \times \frac{5}{18}$$​​
Solution:
Relative speed = $$(75 - 30) \times \frac{5}{18} = 45 \times \frac{5}{18} = \frac{225}{18} = 12.5 \, \text{m/s}$$​​
Distance covered in 108 seconds  $$= \text{Speed} \times \text{Time} = 12.5 \times 108 = 1350 \, \text{m}$$​​
Sum of lengths =  $$L_1 + L_2$$​ = 1350 
​$$L_2 = 1350 - 950 = 400 \, \text{m}$$​​
Answer: The length of the slow-moving train is 400 meters.