A train running at 75 km/hr crosses another train running at 30 km/hr in the same direction in 108 seconds. If the length of the fast-moving train is 950 m, then what is the length (in m) of the slow-moving train?

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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 fast train (S₁) = 75 km/hr

Speed of slow train (S₂) = 30 km/hr

Direction = Same

Time to cross (t) = 108 seconds

Length of fast train (L₁) = 950 m

Formula used:

Relative speed (same direction) = |S₁ - S₂|

Distance = Speed × Time

1 km/hr = \(\frac{5}{18}\) m/s

When two trains cross each other, the total distance covered is the sum of their lengths (L₁ + L₂).

Calculation:

Relative speed = 75 km/hr - 30 km/hr = 45 km/hr

Convert relative speed to m/s:

⇒ 45 km/hr = 45 × \(\frac{5}{18}\) m/s

⇒ Relative speed = \(\frac{225}{18}\) m/s = \(\frac{25}{2}\) m/s = 12.5 m/s

Let the length of the slow train be L₂.

Total distance = L₁ + L₂ = 950 + L₂ meters

Using Distance = Speed × Time:

⇒ 950 + L₂ = 12.5 × 108

⇒ 950 + L₂ = 1350

⇒ L₂ = 1350 - 950

⇒ L₂ = 400 m

∴ The length of the slow-moving train is 400 m.