The speed of a train T is 100 km per hour and the speed of a person P is 4 km per hour. T crosses P in 15 seconds, if P travels along the direction of motion of T. If P travels along the opposite direction of T, then in how much time does T cross P, in seconds, approximately?
- (a) 13·51
- (b) 13·65
- (c) 13·85 ✓ UPSC's answer
- (d) 14·05
Why the answer is (c)
• First, determine the length of the train using the initial scenario where the person travels in the same direction. The relative speed is 100 km/h - 4 km/h = 96 km/h. Convert this to m/s: 96 * (5/18) = 26.666... m/s. The length of the train is Relative Speed * Time = 26.666... m/s * 15 s = 400 meters. Next, calculate the relative speed when the person travels in the opposite direction. The relative speed is 100 km/h + 4 km/h = 104 km/h. Convert this to m/s: 104 * (5/18) = 28.888... m/s. Finally, calculate the time taken to cross the person: Time = Length / Relative Speed = 400 m / 28.888... m/s. This equals 400 / (104 * 5/18) = (400 * 18) / 520 = 7200 / 520 ≈ 13.846 seconds. Rounding to two decimal places gives 13.85 seconds, which matches option (c).
Why the other options are wrong
- (a) 13·51
- 13.51 seconds is incorrect because it does not correspond to the calculated relative speed of 104 km/h for the opposing direction scenario.
- (b) 13·65
- 13.65 seconds is incorrect as it is lower than the actual calculated time of approximately 13.85 seconds.
- (d) 14·05
- 14.05 seconds is incorrect as it is higher than the actual calculated time of approximately 13.85 seconds.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.