Question

Two trains whose respective lengths are 200 m and 250 m cross each other in 18 seconds when they are travelling in the opposite direction and in 1 minute when they are travelling in the same direction. What is the speed of faster train?
1. 59.5 km/hr
2. 58.5 km/hr
3. 68.5 km/hr
4. 54.5 km/hr

Answer 1

Correct Answer - Option 2 : 58.5 km/hr

Given:

Length of trains = 200 m and 250 m

Time taken to cross if travelling in opposite direction = 18 seconds

Time taken to cross if travelling in same direction = 60 seconds

Concept used:

When to bodies are moving in the opposite direction, the relative speed is calculated by adding the speed of both the bodies.

When two bodies are moving in the same direction, the relative speed is computed by their difference

Calculation:

Let speeds of both trains be x m/s and y m/s

Now, according to question,

⇒ x + y = 450/18 = 25 m/s     ----(i)

⇒ x – y = 450/60 = 7.5 m/s     ----(ii)

Adding equation (i) and (ii)

2x = 32.5

⇒ x = 16.25 m/s = 16.25 × (18/5) km/hr

⇒ 58.5 km/hr

∴ The speed of faster train is 58.5 km/hr