Two trains are moving in the same direction at the speed of 73 km/hr and 123 km/hr. The time taken by faster train to cross a man sitting in the slower train is 27 seconds. What will be the length of the faster train?

Speed of the slower train ($$v_1$$​) = 73 km/hr

Speed of the faster train ($$v_2$$​​) = 123 km/hr

Time taken to cross the man = 27 seconds

The relative speed of the two trains is the difference in their speeds because they are moving in the same direction.

Relative Speed = $$v_2 – v_1$$​​

Length of the train = Relative speed × Time taken to cross

Solution: 

Relative speed = 123 - 73 = 50 km/hr

Converting 50 km/hr in m/sec = $$50 \times \frac{5}{18} = \frac{125}{9} \, m/sec$$ 

Now, length of the faster train;

 $$=\frac{125}{9} \times 27 = 375$$ 

Thus, the length of the faster train is 375 m.