A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is

Step 1: Let the length of the first train be L meters

Speed of first train = 48 km/h = (48 × 1000) / 3600 = 13.33 m/s

Speed of second train = 42 km/h = (42 × 1000) / 3600 = 11.67 m/s

Step 2: Total relative speed = 13.33 + 11.67 = 25 m/s

Time to cross each other = 12 seconds

Distance = Speed × Time = 25 × 12 = 300 meters

Step 3: Let the second train’s length be L/2

L + (L/2) = 300
(3L/2) = 300 ⇒ L = 200 meters

Step 4: Now use platform crossing time

Total time to cross the platform = 45 seconds

Speed = 13.33 m/s, Length of train = 200 meters

Distance = Speed × Time = 13.33 × 45 = 599.85 ≈ 600 meters

Length of platform = 600 - 200 = 400 meters

Answer: 400 meters

The length of the platform is 400 meters.

This question tests your understanding of speed, distance, and time with relative motion. It is common in competitive exams, and understanding how to separate the distances covered in different parts (with another train vs a platform) is key to solving it.