Vedadots
Q7980/80—
Q80·CSAT · Prelims 2026

Quantitative — Relative Moving Object Passing Speeds

NumericalTime-Speed-DistanceArithmetic Problem● Medium

Question

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?

Options

a

13.51

b

13.65

Answer
c

13.85

d

14.05

Explanation

Let L be the physical length of train T. We evaluate both directional travel scenarios using relative speed principles [cite: 5357, 5358].

Scenario 1 Analysis (Same Direction): When moving in the same direction, subtract the speeds to find the relative speed [cite: 5357, 5358]:

S₍rel1₎ = 100 - 4 = 96 km/h = 96 × 5/18 = 80/3 m/s

Use the travel time (15 seconds) to calculate the train's length :

L = S₍rel1₎ × t_1 = 80/3 × 15 = 400 meters

Scenario 2 Analysis (Opposite Direction): When moving in opposite directions, add the speeds to find the relative speed:

S₍rel2₎ = 100 + 4 = 104 km/h = 104 × 5/18 = 260/9 m/s

Calculate the new passing time (t_2) using the train length:

t_2 = L/S₍rel2₎ = 400/(260/9) = 400 × 9/260 = 360/26 = 180/13 ≈ 13.846 seconds

Let us round to two decimal places, which gives approximately 13.85 seconds, matching choice (c). Let us re-verify the division steps: 180 \div 13 = 13.84615\dots, which rounds up cleanly to 13.85.

For relative speed problems involving moving objects, moving in the same direction reduces relative speed (S_1 - S_2), while moving in opposite directions increases it (S_1 + S_2).

Answer: (c).

Question details

Year

2026

Paper

CSAT

Question

Q80

Section

Quantitative Aptitude

Sub-topic

Time-Speed-Distance

Type

Arithmetic Problem

Difficulty

Medium

Source hint

Relative motion — direction variations and speed ratios

See all questions on Time-Speed-Distance

Browse every tagged question across all years

Explore →
Back to CSAT 2026