The traffic lights at three different road crossings change after every 48 seconds, 72 seconds, and 108 seconds. If they start changing simultaneously at 8 a.m, after how much time will they change again simultaneously?

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8:07:12 AM

8:08:12 AM

8:07:12 PM

8:07:21 AM

answer is A.

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Detailed Solution

The given data is as follows;
The traffic lights at three different road crossings change after every 48 seconds, 72 seconds, and 108 seconds.
We are required to find after how much time they will change again simultaneously when they start changing simultaneously at 8 a.m.
We shall find the LCM of 48, 72, and 108 by dividing these numbers by least common. multiples until no further division is possible and then multiplying all the divisors which are prime numbers.

2 48, 72, 108 2 24, 36, 54 2 12, 18, 27 3 6, 9, 27 3 2, 3, 9 2, 1, 3

That is,

⇒ L C M = 2 × 2 × 2 × 2 × 3 × 3 × 3 ⇒ L C M = 24 × 33 ⇒ L C M = 432

The required time for simultaneous change is,

⇒ 8 hour + 108 second ⇒ 8 hour + 10860 minute ⇒ 8 hour + 7 minute +12 second

Therefore, the traffic lights starting their change simultaneously at 8 a.m. will change again simultaneously at 8:07:12 AM.
Hence option (1) is correct.

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