Question

A train 100m long passes a bridge in 10 seconds at 72 km/hr. The length of the bridge is:

• A. 100m
• B. 150m
• C. 200m
• D. 50m

Hint:

To convert km/hr to m/s, multiply by $5/18$. To convert m/s to km/hr, multiply by $18/5$.

Answer 1

The Correct Option is A

Step 1: Understand the Concept
To solve problems involving a train crossing an object with its own length (like a bridge, platform, or tunnel), we use the basic formula: Speed = Distance / Time. The key point here is that the Total Distance covered by the train to completely clear the bridge is the sum of the length of the train and the length of the bridge itself.

Step 2: Analysis & Unit Conversion
First, we must ensure all units are consistent. Since the length and time are given in meters and seconds, we convert the speed from km/hr to m/s:
Speed = $72 \text{ km/hr} = 72 \times \frac{5}{18} = 20 \text{ m/s}$.

Next, we calculate the total distance covered in 10 seconds at this speed:
Total Distance = $\text{Speed} \times \text{Time} = 20 \text{ m/s} \times 10 \text{ s} = 200 \text{ m}$.

Since the Total Distance is the sum of the train and bridge lengths, we find the bridge length by subtracting the train's length from the total:
Length of Bridge = $200 \text{ m (Total)} - 100 \text{ m (Train)}$.

Step 3: Conclusion
The calculation ($200 - 100$) results in 100 meters. Therefore, the length of the bridge is 100m.

Final Answer: (A)