UPSC Prelims 2026 · CSAT
Question 20: Basic Numeracy
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?
AnswerUPSC’s answer is (c).
Same direction: relative speed 100 − 4 = 96 km/h = 80/3 m/s. In 15 seconds the train covers its own length: (80/3) × 15 = 400 m. Opposite direction: relative speed 104 km/h = 260/9 m/s, so the time is 400 ÷ (260/9) = 3600/260, which is about 13.85 seconds. The same result comes from 15 × 96/104.
Why each option is right or wrong
- (a) Wrong: 400 m at 104 km/h takes 13.85 s, not 13.51 s.
- (b) Wrong: slightly low; the time is 13.85 s.
- (c) Right: 400 m ÷ 104 km/h is about 13.85 s.
- (d) Wrong: 14.05 s is too high; the time is 13.85 s.
Only the provisional key (27 May 2026) was found; the final key replaces it when found.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2026, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.