Two trains of lengths 120 m and 180 m are moving in opposite directions at 54 km/h and 72 km/h respectively. How long will they t…

Question

Two trains of lengths 120 m and 180 m are moving in opposite directions at 54 km/h and 72 km/h respectively. How long will they take to cross each other?

1. A. 12 sec
2. B. 9 sec (Correct answer)
3. C. 15 sec
4. D. 20 sec

Correct Answer

Option B — 9 sec

Detailed Solution & Explanation

The correct answer is 9 sec.

Key Points

• When two trains move in opposite directions, their speeds add (relative speed), and to cross each other they must together cover the sum of their lengths.
• Total length = 120 + 180 = 300 m.
• Convert speeds to m/s (×5/18): 54 km/h = 15 m/s, 72 km/h = 20 m/s.
• Relative speed (opposite directions) = 15 + 20 = 35 m/s.
• Time = distance ÷ relative speed = 300 ÷ 35 ≈ 8.57 s, which rounds to the nearest option, 9 seconds.
• trains crossing = total length ÷ relative speed.
• Relative speed is the sum for opposite directions and the difference for the same direction.

Exam Tip

• always convert km/h to m/s with the factor 5/18 before dividing by the length in metres, and pick the closest option when the arithmetic gives a near value.