A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

We are given the following:

• Length of the first train = 270 m
• Speed of the first train = 120 km/h
• Speed of the second train = 80 km/h
• Time taken to cross = 9 seconds
• We need to find: Length of the second train

Step 1: Convert the combined speed into meters per second

When two trains move in opposite directions, their relative speed = sum of their speeds.
Relative Speed = 120 + 80 = 200 km/h
To convert km/h to m/s, multiply by (1000 / 3600):
=> 200 × (1000 / 3600) = 55.56 m/s

Step 2: Use the speed-distance-time formula

Distance = Speed × Time
Total distance covered in 9 seconds = 55.56 × 9 = 500.04 meters

Step 3: Understand what distance is covered

The total distance covered while crossing = length of first train + length of second train
Let the length of the second train = x meters
Then, 270 + x = 500.04
=> x = 500.04 - 270 = 230.04 meters

Final Answer:

The length of the other train is approximately 230 meters