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.
- (a) 4:59:00 PM
- (b) 4:59:02 PM
- (c) 4:58:42 PM ✓ UPSC's answer
- (d) 4:56:32 PM
Why the answer is (c)
• Let $d$ be the distance from the camp to the explosion site. The time taken for sound to travel this distance is $t_s = d/300$ seconds.
• The time taken for a drone to travel this distance is $t_d = d/30$ seconds. Note that $t_d = 10 t_s$.
• Let $T$ be the time of the explosion. The first drone starts at $T + t_s$. It reaches the spot at $T + t_s + t_d$ and sends the picture instantly. The picture is received at 5:02 PM. Thus, $5:02 \text{ PM} = T + t_s + t_d$.
• The second drone starts immediately after the first picture is received, i.e., at 5:02 PM. It reaches the spot at $5:02 \text{ PM} + t_d$ and sends the picture. The picture is received at 5:05 PM. Thus, $5:05 \text{ PM} = 5:02 \text{ PM} + t_d$.
• From the second equation, $t_d = 3$ minutes = 180 seconds.
• Since $t_d = 180$ s, then $t_s = t_d / 10 = 18$ seconds.
• Substituting back into the first equation: $5:02 \text{ PM} = T + 18 \text{ s} + 180 \text{ s} = T + 198 \text{ s}$. Therefore, $T = 5:02 \text{ PM} - 198 \text{ s}$. 198 seconds is 3 minutes and 18 seconds. 5:02:00 PM minus 3 minutes 18 seconds is 4:58:42 PM.
Why the other options are wrong
- (a) 4:59:00 PM
- This option incorrectly assumes the drone travel time is negligible or miscalculates the total delay, resulting in a time only 2 minutes before the first receipt.
- (b) 4:59:02 PM
- This option fails to account for the sound travel time ($t_s$) in the first drone's total journey, leading to an incorrect subtraction of only the drone travel time.
- (d) 4:56:32 PM
- This option likely results from a significant arithmetic error in converting the drone travel time or incorrectly summing the sound and drone travel times.
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.