A train X crosses another train Y travelling in the opposite direction in 15 seconds. The speed of train Y was 72 km/h and the length of train Y is 80% of the length of train X. If train X was moving at a speed of 16 m/s, then the length (in m ) of train X is:

Given:

Speed of train Y = 72 km/h = 72 × (1000/3600) m/s = 20 m/s

Speed of train X = 16 m/s

Length of train Y = 0.8 × Length of train X

Time taken to cross each other = 15 seconds

Formula Used:

Relative Speed when moving in opposite directions = Speed of Train X + Speed of Train Y

Distance = Relative Speed × Time

Total Distance = Length of Train X + Length of Train Y

Calculation:

Relative Speed = 16 m/s + 20 m/s = 36 m/s

Total Distance = 36 m/s × 15 s = 540 m

Let Length of Train X be L. Then, Length of Train Y = 0.8L

Total Distance = L + 0.8L

540 = 1.8L

⇒ L = 540 / 1.8

⇒ L = 300 m

The length of train X is 300 meters.