Question

Two trains running in opposite directions cross a man standing on the platform in 19 seconds and 29 seconds respectively. If they cross each other in 23 seconds, what is the ratio of their speeds?

1. 2:1
2. 1:2
3. 3:2
4. 2:3

Answer 1

Correct Answer - Option 3 : 3:2

Given:

Time is taken to cross a man = 19 sec. and 29 sec.

Train crosses each other = 23 sec.

Formula used:

Speed = Distance/ Time

Calculation:

Let’s assume L₁ and L₂ be the lengths of both trains respectively.

Speed of first train = L₁/19

Speed of second train = L₂/29

Relative speed ⇒ L₁/19 + L₂/29 = (L₁ + L₂)/23

⇒ L₁/19 – L₁/23 = L₂/23 - L₂/29

⇒ L₁ × 4/(19 × 23) = L₂ × 6/(23 × 29)

⇒ (L₁/19) × 2 = (L₂/29) × 3

⇒ (L₁/19)/ (L₂/29) = 3/2

∴ The ratio of their speeds = 3:2.