UPSC Prelims 2026 CSAT, question 20

Topic: Arithmetic

Q20

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) $13.85$ Correct answer
(d) $14.05$

Solution.

Answer: (c) $13.85$

When $P$ moves in the same direction as train $T$ , their relative speed is $100 - 4 = 96$ km/h; when $P$ moves in the opposite direction, their relative speed is $100 + 4 = 104$ km/h.
Since the length of the train is constant, the crossing time in the opposite direction is $15 \times \frac{96}{104} = \frac{180}{13} \approx 13.85$ seconds.