A train travelling at 90 km/h takes 10 seconds to cross a bridge of length 100 m. What is the length (in metres) of the train?

Introduction / Context:
This quantitative aptitude question is about finding the length of a train using its speed and the time taken to cross a bridge. It combines basic speed, distance, and time concepts that are very common in problems on trains.

Given Data / Assumptions:

• Speed of the train = 90 km/h.
• Length of the bridge = 100 m.
• Time taken to completely cross the bridge = 10 seconds.
• The train moves at constant speed in a straight line.
• The train length plus bridge length is the total distance covered during the crossing.

Concept / Approach:
To find the train length, we calculate how much distance the train covers in 10 seconds at a speed of 90 km/h. The train must cover its own length plus the length of the bridge, so total distance equals train length plus 100 m. We first convert the speed from km/h to m/s, then use distance = speed * time, and finally subtract the bridge length to get the train length.

Step-by-Step Solution:
Step 1: Convert 90 km/h to m/s using the factor 5/18. Step 2: Speed in m/s = 90 * 5 / 18 = 25 m/s. Step 3: Distance covered in 10 seconds = speed * time = 25 * 10 = 250 m. Step 4: Total distance while crossing the bridge = train length + bridge length. Step 5: So train length + 100 = 250. Step 6: Train length = 250 - 100 = 150 m.

Verification / Alternative check:
Recheck by forward calculation. If the train is 150 m long and the bridge is 100 m, total distance is 250 m. At 25 m/s, time = 250 / 25 = 10 seconds, which matches the given time exactly. Thus the train length is correctly found.

Why Other Options Are Wrong:

• 130 m: This would give total distance 230 m and a time less than 10 seconds.
• 120 m: This would give only 220 m, leading to a crossing time of 220 / 25 = 8.8 seconds.
• 140 m: This leads to 240 m, giving 240 / 25 = 9.6 seconds, still not equal to 10 seconds.

Common Pitfalls:
Many learners forget that the train must travel its own length plus the bridge length when crossing. Another common error is failing to convert km/h to m/s correctly, which leads to incorrect numbers. It is also important not to mix units and to always keep distances in metres and time in seconds when using m/s.

Final Answer:
The length of the train is 150 m.