Question

A train crosses a 655 metres long platform in 55 seconds and the same train crosses a 455 metres long platform in 45 seconds. What is the length of the train?
1. 654 m
2. 445 m
3. 545 m
4. 345 m
5. None of these

Answer 1

Correct Answer - Option 2 : 445 m

Given:

Length of the first platform = 655 metres

Length of the second platform = 455 metres

The time taken to cross the first platform = 55 seconds

The time taken to cross the second platform = 45 seconds

Concept used:

When a train crosses a platform,

Speed of train = (Length of train + Length of platform)/Time taken to cross the platform

Calculation:

Let the length of the train be x metres and the speed of the train be y m/sec.

Speed of train when it crosses 655 m long platform = (x + 655)/55

⇒ y = (x + 655)/55

Speed of train when it crosses 455 m long platform = (x + 455)/45

⇒ y = (x + 455)/45

⇒ (x + 655)/55 = (x + 455)/45

⇒ 9(x + 655) = 11(x + 455)

⇒ 9x + 5895 = 11x + 5005

⇒ 11x – 9x = 5895 – 5005

⇒ 2x = 890

⇒ x = 445 m

∴ Length of the train = 445 metres