Question

On a G.T. road three consecutive traffic lights change after 36,42,and 72 s. If the lights are first switched on at 9:00 am, then at what time will they change simultaneously?

Answer 1

hello friend here is your answer

lights change first light = 36 sec

second light = 42 sec

third light = 72 sec

so the time while they remain same

third light - second light

second light- first light

72 sec - 42 sec = 30 sec

42 sec - 36 sec = 6 sec

now as we know first light switched on at = 9:00 am

so it will change at = 9:00:36 (hh:mm:ss)

second light = 9:00:36+0:00:06= 9:00:42

third light = 9:00:42 + 0:00:30 = 9:01:12

so the sequence will follow the same producer

first light will change after 36 s
second will change after 6 s of first
third will change after 30 sec of second light

hope it helps !

Answer 2

Here, the question asks us 'at what time will they change simultaneously', which means that we need to find LCM.

36 = 2×2×3×3

42 = 2×3×7

72 = 2×2×2×3×3

So, LCM = 2×2×2×3×3×7

So, LCM = 504

Thus, the lights change after every 504 seconds.

And 504 s = 8 min 24 sec

So, the traffic lights will change again at 09:08:24 am