The traffic lights at three different road crossing change after every 48 seconds, 72 seconds and 108 seconds respectively. If they all change simultaneously at 8 a.m., then at what time will they again change simultaneously?

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08:07:12

08:06:12

09:06:12

08:07:00

answer is A.

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Detailed Solution

It is given that the traffic lights at three different road crossing individually change after every 48 seconds, 72 seconds and 108 seconds
We have to determine the time at which the three traffic lights will change after they simultaneously changes at 8 am.
The time at which the lights generally change simultaneously will be the LCM of the given individual times.
So, we will proceed with the prime factorization of the numbers 48, 72 and 108 to get their LCM as follows,

48 = 2 × 2 × 2 × 2 × 3 72 = 2 × 2 × 2 × 3 × 3 108 = 2 × 2 × 3 × 3 × 3

LCM of 48, 72, 108 =

2 × 2 × 2 × 2 × 3 × 3 × 3

= 432
This means that the three traffic lights change simultaneously after every 432 seconds.
Now, we know that 1 minute = 60 seconds and so, 432 seconds in minutes will be,

43260 = 7.2 7.2 = 7 + 0.2 × 60

That is 7 minutes 12 seconds or 00:07:12 in the standard time notation.
So, adding this time to 08:00:00, we get the time after which the traffic lights change simultaneously as 08:07:12 hours.
Hence, the correct option is (1).

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