Two trains having lengths of 240 m and 410 m are running at speeds of 80 km/h and 110 km/h, respectively, in the same direction. The time taken (in minutes) by the faster train, coming from behind, to completely cross the other train is:

Correct option is D

Given:

Length of first train = 240 m

Length of second (faster) train = 410 m

Speed of first train = 80 km/h

Speed of second train = 110 km/h

Both trains are moving in the same direction

Formula Used:

When two objects move in the same direction, relative speed = difference of their speeds.

The total distance to be covered = sum of the lengths of the two trains.

Time = Distance ÷ Relative Speed

Solution:

Relative Speed = 110 - 80 = 30 km/h = $$\frac{30 \times 5}{18} = \frac{25}3 \, \text{m/s}$$​​

Total Distance = 240 + 410 = 650  m

Time (in seconds) = $$\frac{650}{25/3}$$​ = 78 seconds

​$$= \frac{78}{60} \approx 1.3\, \text{ minutes}$$​​