The ratio of speeds of a goods train and passenger train is 11:13 in the same direction. If the passenger train crosses the goods train in 90 seconds, while a passenger in the passenger train observes that he crosses the goods train in 75 seconds. Find the ratio of length of goods train to passenger train?

Let lengths be Lg and Lp. Speeds in ratio 11:13, so relative speed = 13-11 = 2 units. From outside, passenger train crosses goods train in 90s: (Lg + Lp)/2 = 90, so Lg + Lp = 180. From inside passenger train, only goods train's length passes: Lg/2 = 75, so Lg = 150. Then Lp = 180 - 150 = 30. Ratio Lg:Lp = 150:30 = 5:1. The key is recognizing that from inside, only the other train's length matters.