Quantitative — Relative Speed & Sound Telemetry

NumericalTime-Speed-DistanceArithmetic Problem● Hard

Question

An explosion takes place at a certain distance from an army camp. As soon as the sensor in the camp receives the sound of the explosion, a drone starts flying towards the spot of explosion. The drone clicks a picture from the spot and the camp receives it at the same time. Immediately another drone starts flying to the spot and it also sends a picture as soon as it reaches the spot. The two pictures were received at 5:02 PM and 5:05 PM, respectively. If the speed of the drones is 30~m/s, at what time did the explosion take place? Assume that the speed of sound is 300~m/s.

Options

4:59:00 PM

4:59:02 PM

4:58:42 PM

Answer

4:56:32 PM

Explanation

Let d be the fixed distance between the military camp and the site of the explosion [cite: 3847, 3848].

Analyze the first drone's timeline: The sound travels distance d at a speed of 300~m/s, taking a time of t₍sound₎ = d/300 seconds to reach the camp sensor[cite: 3848, 3904]. As soon as the sensor triggers, the first drone flies back to the spot at a speed of 30~m/s, taking a flight time of t₍flight1₎ = d/30 seconds[cite: 3848, 3849, 3903]. The picture telemetry returns instantly, so the first arrival timestamp is recorded at 5:02 PM [cite: 3849, 3851].

T_1 = T₍explosion₎ + d/300 + d/30 = T₍explosion₎ + 11d/300 = 5:02 PM

Analyze the second drone's timeline: The second drone launches immediately from the camp at 5:02 PM and travels the same distance d at 30~m/s, taking a flight time of t₍flight2₎ = d/30 seconds[cite: 3850, 3851, 3903]. Its picture arrives at 5:05 PM, creating a clean 3-minute (180 seconds) travel window between the two timestamps .

t₍flight2₎ = d/30 = 3 minutes = 180 seconds \implies d = 180 × 30 = 5400 meters

Calculate the Explosion Time (⟨MATH⟩T₍explosion₎⟨/MATH⟩): Substitute d = 5400 meters back into the first equation:

Total delay from explosion to image 1 = 5400/300 + 5400/30 = 18s + 180s = 198 seconds 198 seconds = 3 minutes and 18 seconds

Subtract this delay from the 5:02:00 PM timestamp :

T₍explosion₎ = 5:02:00 PM - 3 min 18 s = 4:58:42 PM

Breaking down sequential travel intervals allows tracking multi-agent telemetry timelines back to a single source event.

Answer: (c).

Question details

Year

2026

Paper

CSAT

Question

Q21

Section

Quantitative Aptitude

Sub-topic

Time-Speed-Distance

Type

Arithmetic Problem

Difficulty

Hard

Source hint

Relative tracking — multi-agent sound and drone intervals

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