Final answer:
After calculating the least common multiple (LCM) of the intervals 48, 72, and 108, we find that the traffic lights will change simultaneously every 432 seconds. Adding this to the start time of 8:20:00 hrs results in the next simultaneous change occurring at 8:27:12 hrs. Option D is corrrect.
Step-by-step explanation:
The question is asking for the next time all three traffic lights, which change at intervals of 48 seconds, 72 seconds, and 108 seconds, will change simultaneously after a certain time.
To determine this time, we need to calculate the least common multiple (LCM) of the time intervals. The LCM of 48, 72, and 108 is 432 seconds, which is the smallest number that all three numbers divide evenly into. This means that the traffic lights will all change simultaneously every 432 seconds.
To find out when they will next change simultaneously after 8:20:00 hrs, we add 432 seconds to 8:20:00 hrs.
Convert 432 seconds to minutes and seconds: 432 seconds is 7 minutes and 12 seconds.
Add this to the initial time of 8:20:00 hrs.: 8:20:00 + 0:07:12 = 8:27:12 hrs.
Therefore, the traffic lights will again change simultaneously at 8:27:12 hrs. The correct answer is D. 8:27:12 hrs.