A 210-meter-long Train P crosses a pole in 14 seconds. The speed of Train Q is 40% more than the speed of Train P, and the ratio of the length of Train P to Train Q is 7 : 9. If Train Q crosses a platform in 25 seconds, find the length of the platform.

ATQ, Train P crosses a pole in 14 seconds. So, speed of Train P = Length / Time Speed of Train P = 210/14 = 15 m/s The speed of Train Q is 40% more than Train P. So, speed of Train Q = 15 × 140/100 = 21 m/s The ratio of the length of Train P to Train Q is 7 : 9. Length of Train P = 210 meters = 7 parts. So, 1 part = 210/7 = 30 meters. Length of Train Q = 9 parts = 9 × 30 = 270 meters. Train Q crosses a platform in 25 seconds. Distance covered by Train Q in 25 seconds = Speed × Time Distance covered = 21 × 25 = 525 meters. When a train crosses a platform, distance covered = length of train + length of platform. So, Length of Train Q + Length of platform = 525 270 + Length of platform = 525 Length of platform = 525 − 270 = 255 meters.