Correct Answer: 400 m
Explanation:
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.
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