A 280 m long train overtakes a man moving at a speed of 5 km/h (in same direction) in 42 seconds. How much time (in seconds) will it take this train to completely cross another 500 m long train, moving in the opposite direction at a speed of 43 km/h?

Correct option is C

Given:

Length of Train A = 280 m

Man's speed = 5 km/h

Overtaking time = 42 seconds

Train B length = 500 m

Train B speed = 43 km/h (opposite direction)

Formula Used:

Relative speed (same direction) = Speed of Train A − Speed of man

Speed = $$\frac{Distance} { Time}$$​​

Convert km/h to m/s:  $$1 \text{ km/h} = \frac{5}{18} \text{ m/s}$$​​

Relative speed (opposite direction) = Sum of both speeds

Solution:

Relative speed(train and men) = $$\frac{280}{42} = \frac{20}{3}$$​m/s

Converting  man's speed(into m/s) = $$5 \times \frac{5}{18} = \frac{25}{18}$$​m/s

Train A speed =$$\frac{20}{3} +\frac{25}{18} = \frac{145}{18}$$​ m/s

Now, 

Convert Train B speed(into m/s) =$$43 \times \frac{5}{18} = \frac{215}{18}$$​ m/s

Relative speed =$$\frac{145}{18} + \frac{215}{18}$$​ = 20  m/s

Total length to cross = 280 + 500 = 780 m

Time = $$\frac{780}{20} = 39 \text{ seconds}$$​​

Thus, The train will take 39 seconds to cross the other train.