The time taken by a train to cross a man travelling in another train is 10 seconds, when the other train is travelling in the opposite direction. However, it takes 20 seconds, if both the trains are travelling in the same direction. The length of the first train is 200 m and that of the second train is 150 m. What is the speed of the first train ? 

Concept:

Relative speed:

If two trains are traveling with speeds of magnitude u & v respectively, then the relative speed will be

u + v,  if both trains are traveling in the opposite direction.

u - v,  if both trains are traveling in the same direction.

Formula used:

Speed = distance/ times

Calculation:

Let the speed of train 1 (of length 200 m) is 'u' m/s & speed of train 2

(of length 150 m) be 'v' m/s.

Given that, the man is sitting in the second train & a train of length 200 meters across a man (here, 150 m is irrelevant data).

By using the above concept,

When both trains are traveling in the same direction,

u - v = 200/20

u - v = 10           -----(1)

When both trains are traveling in the opposite direction,

u + v = 200/10 

u + v =  20         -----(2)

Adding both equations, we will get

2u = 30 or u =15 m/s

Since, 1 m/s = 3.6 km/hr

u = 15 × 3.6 = 54 km/hr

∴ The correct answer is 54 km/hr.