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.

Correct Option: (c) 4:58:42 PM

Let d be the distance from the camp to the explosion site. Speed of sound = 300 m/s. Time taken by sound to reach the sensor = d / 300. At this instant (t1 = d / 300 after explosion), the first drone starts flying at 30 m/s. Time taken by the first drone to reach the spot = d / 30. Total time elapsed from explosion to receipt of first picture = (d / 300) + (d / 30) = 11d / 300. This first picture was received at 5:02 PM. Immediately (at 5:02 PM), a second drone starts flying to the spot. Its travel time is also d / 30. The second picture is received at 5:05 PM, which means the second drone's travel time (d / 30) equals 3 minutes = 180 seconds. So d / 30 = 180 => d = 5400 meters. Now, total time from explosion to the first picture = 11d / 300 = (11 x 5400) / 300 = 198 seconds = 3 minutes 18 seconds. Since the first picture was received at 5:02 PM, the explosion took place 3 minutes 18 seconds before 5:02 PM, which is 4:58:42 PM. Hence, option (c) is correct.