Two trains are moving in opposite directions at speeds of 50 km/h and 110 km/h. The length of one train is 500 m. The time taken by them to cross each other is 12 seconds. The length (in m) of the other train, correct to 2 decimal places, is:

Question

Question

This question was previously asked in

SSC GD Constable 2025 Official Paper (Held On: 06 Feb, 2025 Shift 2)

Answer 1

Given:

Speed of train 1 (S₁) = 50 km/h

Speed of train 2 (S₂) = 110 km/h

Length of train 1 (L₁) = 500 m

Time to cross (t) = 12 seconds

Formula used:

Relative speed (opposite direction) = S₁ + S₂

Distance = Speed × Time

1 km/h = 5/18 m/s

When two trains cross each other, the total distance covered is the sum of their lengths.

Calculation:

Relative speed = 50 km/h + 110 km/h = 160 km/h

Convert relative speed to m/s:

⇒ 160 km/h = 160 × \(\frac{5}{18}\) m/s

⇒ Relative speed = \(\frac{800}{18}\) m/s = \(\frac{400}{9}\) m/s

Let the length of train 2 be L₂.

Total distance covered = L₁ + L₂ = 500 + L₂ meters

Using Distance = Speed × Time:

⇒ 500 + L₂ = \(\frac{400}{9}\) × 12

⇒ 500 + L₂ = \(\frac{400 \times 4}{3}\)

⇒ 500 + L₂ = \(\frac{1600}{3}\)

⇒ 500 + L₂ = 533.33

⇒ L₂ = 533.33 - 500

⇒ L₂ = 33.33

∴ The length of the other train is 33.33 m.

Download Solution PDF