A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same direction and completely passes them in 8 seconds and 9 seconds respectively. What is the length of the tram?

Let tram length be L meters and tram speed be v km/hr. Relative to X (3 km/hr): (v − 3) km/hr × 8 sec = L; converting, (v − 3) × 5/18 × 8 = L, so L = 40(v−3)/18 = 20(v−3)/9. Relative to Y (4 km/hr): (v − 4) × 5/18 × 9 = L, so L = 45(v−4)/18 = 5(v−4)/2. Equating: 20(v−3)/9 = 5(v−4)/2. Cross-multiplying: 40(v−3) = 45(v−4), so 40v − 120 = 45v − 180, giving 5v = 60, v = 12 km/hr. Then L = 5(12−4)/2 = 5 × 8/2 = 20 m.