Two trains having lengths of 110 m and 390 m are running at speeds of 120 km/h and 130 km/h in the same direction. The faster train, coming from behind, completely crosses the other in how many minutes?

Correct option is A

Given:
Length of trains = 110 m and 390 m
Speeds = 120 km/h and 130 km/h
Same direction → use relative speed = difference of speeds
Formula Used:
​$$\text{Time} = \frac{\text{Distance}}{\text{Relative Speed}}$$​​
Relative Speed (m/s) = (Difference in km/h × $$\frac 5{18}$$​)
Solution:
Relative speed = (130 − 120) km/h = 10 km/h
= 10 × $$\frac 5{18} = \frac {50}{18}$$​ = 2.78 m/s
Total distance to be covered = 110 + 390 = 500 m
Time = $$\frac{500}{ 2.78}$$​ ≈ 180 sec
= 180 ÷ 60 = 3 minutes