Question

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 8 a.m., after how much time will they change simultaneously again?
1. 7 min 12 sec
2. 7 min 7 sec
3. 8 min 12 sec
4. 8 min 10 sec

Answer 1

Correct Answer - Option 1 : 7 min 12 sec

The traffic light at three different road crossings change after every 48 seconds,72 seconds, and 108 seconds respectively. 

So let us take the LCM of the given time that is 48 seconds, 72 seconds, 108 seconds

⇒ 48 = 2 × 2 × 2 × 2 × 3

⇒ 72 = 2 × 2 × 2 × 3 × 3

⇒ 108 = 2 × 2 × 3 × 3 × 3

Hence LCM of 48, 72 and 108 = (2 × 2 × 2 × 2 × 3 × 3 × 3)

LCM of 48, 72 and 108 = 432

So  after 432 seconds, they will change simultaneously

We know that

60 seconds = 1 minute

so on dividing 432/60 we get 7 as quotient and 12 as a reminder

∴ 432 seconds = 7 min 12 seconds