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

• Train A speed = 48 km/h
• Train B speed = 42 km/h (opposite direction)
• Train B length = half of Train A
• Two trains completely cross in 12 s
• Train A crosses a platform in 45 s

Step 1: Find Train A's length
Relative speed (opposite) = (48 + 42) km/h = 90 km/h = 90 × (5/18) = 25 m/sTotal distance when two trains cross = L + L/2 = 1.5L1.5L = 25 × 12 = 300 ⇒ L = 300/1.5 = 200 m

Step 2: Find platform length
Speed of Train A = 48 × (5/18) = 13.333… m/sDistance in 45 s while crossing platform = 13.333… × 45 = 600 mL + Platform = 600 ⇒ Platform = 600 − 200 = 400 m

Notes

• When crossing a platform, add train and platform lengths.
• Always convert km/h to m/s by × 5/18.