2026 · Q6
A train completely crossed two persons X and Y moving in the same direction as the train in 8 seconds and 8.1 seconds respectively. X is walking at a uniform speed of 3 km/hr and Y is walking at a uniform speed of 4 km/hr. What is the speed of the train?
Elementary MathematicsTime, Speed and Distance
- A81 km/hr
- B82 km/hr
- C83 km/hr
- D84 km/hr
Explanation
Let the train's speed be v km/h and its length L km. Overtaking X (same direction) uses the relative speed v − 3: L = (v − 3)(8/3600). Overtaking Y gives L = (v − 4)(8.1/3600). Equating the two expressions, 8(v − 3) = 8.1(v − 4), i.e. 8v − 24 = 8.1v − 32.4. Solving gives 0.1v = 8.4, so v = 84 km/h, option D.