Q9. 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 the speed of the tram be 'T' km/hr and its length be 'L' meters. When the tram overtakes a person moving in the same direction, the relative speed is the difference between their speeds.

The distance covered is the length of the tram. Convert speeds from km/hr to m/s by multiplying by 5/18. Person X's speed = 3 km/hr = 3 × (5/18) = 5/6 m/s. Person Y's speed = 4 km/hr = 4 × (5/18) = 10/9 m/s.

Let the tram's speed be 't' m/s. For person X: Relative speed = (t - 5/6) m/s. Time taken = 8 seconds. Length of tram (L) = Relative speed × Time = (t - 5/6) × 8 --- (1) For person Y: Relative speed = (t - 10/9) m/s.

Time taken = 9 seconds. Length of tram (L) = Relative speed × Time = (t - 10/9) × 9 --- (2) Equating (1) and (2): 8t - 40/6 = 9t - 90/9 8t - 20/3 = 9t - 10 10 - 20/3 = 9t - 8t t = (30 - 20)/3 = 10/3 m/s.

Now substitute 't' back into equation (1) to find L: L = (10/3 - 5/6) × 8 L = (20/6 - 5/6) × 8 L = (15/6) × 8 L = (5/2) × 8 L = 20 meters. This question tests the application of relative speed concepts in time, speed, and distance problems, specifically involving trains/trams overtaking objects, a common topic in UPSC CSAT.