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:

Given Data

• Train A speed = 48 km/hr; length = L
• Train B speed = 42 km/hr; length = L/2
• Opposite directions; they cross in 12 s
• Same train passes a platform in 45 s
• Required: platform length

Step 1: Find L using the two trains crossingRelative speed = 48 + 42 = 90 km/hr = 90 × (5/18) = 25 m/sDistance to cross = L + L/2 = 1.5LTime = 12 s ⇒ 1.5L ÷ 25 = 12 ⇒ 1.5L = 300 ⇒ L = 200 m

Step 2: Use platform crossing to get platform lengthSpeed of train A = 48 × (5/18) = 13.3333 m/sDistance in 45 s = 13.3333 × 45 = 600 m = L + platformPlatform length = 600 − 200 = 400 m

Checks & Common Pitfalls

• Opposite directions require adding speeds and adding lengths.
• When crossing a platform, distance equals train length plus platform length.

Final AnswerThe length of the platform is 400 m.