Two trains having lengths of 410 m and 390 m are running at speeds of 80 km/h and 100 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 C

Given:

Length of first train = 410 m

Length of second train = 390 m

Speed of first train = 80 km/h

Speed of second train = 100 km/h

Concept Used:

$$\text{Relative Speed} = \text{Speed of faster train} - \text{Speed of slower train}\\ \ \\\text{Time} = \frac{\text{Sum of train lengths}}{\text{Relative speed}}$$​

Solution:

Length of both train = 390 + 410 = 800  

Both train, same direction that's why Difference = 100 - 80 = 20 km/hr 

​Total = $$\frac{\text{Total Distance }}{\text{Total time}}\times\frac{18}5$$​    

= $$\frac{800}{20}\times\frac{18}5 = 144 sec$$​

In 60 sec = 1 min
144 sec = $$\frac{1}{60}\times 144 = 2.4 \text{min}$$