Question

A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds and him in 8 seconds. The length of the train is:

• A. 120 metres
• B. 160 metres
• C. 90 metres
• D. 100 metres

Hint:

When solving train-related problems, break the scenario into smaller parts: the time to cross the bridge and the time to cross the man. Use these two distances to solve for the unknown.

Answer 1

The Correct Option is A

Step 1: Understanding the scenario.
The train crosses the bridge in 20 seconds.
The man is standing on the bridge, so the total distance the train covers in these 20 seconds is the length of the train plus the length of the bridge. Let the length of the train be \( L \) meters.
The speed of the train can be calculated using the formula: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{180 + L}{20} \] Step 2: Understanding the man crossing.
The train also crosses the man in 8 seconds, which means the train covers a distance equal to its own length, \( L \), in 8 seconds. So, the speed of the train is also: \[ \text{Speed} = \frac{L}{8} \] Step 3: Equating the speeds.
Since both expressions represent the speed of the train, we can equate them: \[ \frac{180 + L}{20} = \frac{L}{8} \] Step 4: Solving for \( L \). Cross-multiply to solve for \( L \): \[ 8(180 + L) = 20L \] \[ 1440 + 8L = 20L \] \[ 1440 = 12L \] \[ L = \frac{1440}{12} = 120 \text{ meters} \] The correct length of the train is 120 meters. Hence, the correct answer is (1) 120 metres.