The traffic lights at three different road crossings change after every 48 sec, 72 sec and 108 sec, respectively. They all change simultaneously at 08:20:00 hours, when will they again change simultaneously?

According to question, it is given that,

The traffic lights change after every 48 sec, 72 sec and 108 sec.

So, all three lights will again change simultaneously after a time interval = lcm(48,72,108)

Now, $$48=2^4\times\ 3$$

$$72=2^3\times\ 3^2$$

$$108=2^2\times\ 3^3$$

So, lcm(48,72,108)=$$2^4\times\ 3^3$$ = $$432$$ sec

Also, 432 sec = 7 min and 12 sec

So, they will again change simultaneously after 7 min and 12 sec

Initial time was 08:20:00 hours

So, final time = 08:27:12 hours

Option B is the correct answer