Question

3.
Traffic lights at three different crossings on a road change after every 10 minutes,
15 minutes and 20 minutes, respectively. If they change
together at 9 a.m. first, when will they change together
again?

​

Answer 1

Answer:

The traffic light at three different road crossing 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 reminder

Hence, 432 seconds = 7 min 12 seconds

∴ The time = 7 a.m. + 7 minutes 12 seconds

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Answer 2

Explanation

Given

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

GivenThe traffic light at three different road crossing 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 secondshhu

⇒ 48 = 2 × 2 × 2 × 2 × 3

⇒ 48 = 2 × 2 × 2 × 2 × 3⇒ 72 = 2 × 2 × 2 × 3 × 3

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

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

⇒ 48 = 2 × 2 × 2 × 2 × 3⇒ 72 = 2 × 2 × 2 × 3 × 3⇒ 108 = 2 × 2 × 3 × 3 × 3Hence LCM of 48, 72 and 108 = (2 × 2 × 2 × 2 × 3 × 3 × 3)LCM of 48, 72 and 108 = 432

⇒ 48 = 2 × 2 × 2 × 2 × 3⇒ 72 = 2 × 2 × 2 × 3 × 3⇒ 108 = 2 × 2 × 3 × 3 × 3Hence LCM of 48, 72 and 108 = (2 × 2 × 2 × 2 × 3 × 3 × 3)LCM of 48, 72 and 108 = 432So after 432 seconds they will change simultaneously

⇒ 48 = 2 × 2 × 2 × 2 × 3⇒ 72 = 2 × 2 × 2 × 3 × 3⇒ 108 = 2 × 2 × 3 × 3 × 3Hence LCM of 48, 72 and 108 = (2 × 2 × 2 × 2 × 3 × 3 × 3)LCM of 48, 72 and 108 = 432So after 432 seconds they will change simultaneouslyWe know that

⇒ 48 = 2 × 2 × 2 × 2 × 3⇒ 72 = 2 × 2 × 2 × 3 × 3⇒ 108 = 2 × 2 × 3 × 3 × 3Hence LCM of 48, 72 and 108 = (2 × 2 × 2 × 2 × 3 × 3 × 3)LCM of 48, 72 and 108 = 432So after 432 seconds they will change simultaneouslyWe know that60 seconds = 1 minute

⇒ 48 = 2 × 2 × 2 × 2 × 3⇒ 72 = 2 × 2 × 2 × 3 × 3⇒ 108 = 2 × 2 × 3 × 3 × 3Hence LCM of 48, 72 and 108 = (2 × 2 × 2 × 2 × 3 × 3 × 3)LCM of 48, 72 and 108 = 432So after 432 seconds they will change simultaneouslyWe know that60 seconds = 1 minuteso on dividing 432 / 60 we get 7 as quotient and 12 as reminder

⇒ 48 = 2 × 2 × 2 × 2 × 3⇒ 72 = 2 × 2 × 2 × 3 × 3⇒ 108 = 2 × 2 × 3 × 3 × 3Hence LCM of 48, 72 and 108 = (2 × 2 × 2 × 2 × 3 × 3 × 3)LCM of 48, 72 and 108 = 432So after 432 seconds they will change simultaneouslyWe know that60 seconds = 1 minuteso on dividing 432 / 60 we get 7 as quotient and 12 as reminderHence, 432 seconds = 7 min 12 seconds

⇒ 48 = 2 × 2 × 2 × 2 × 3⇒ 72 = 2 × 2 × 2 × 3 × 3⇒ 108 = 2 × 2 × 3 × 3 × 3Hence LCM of 48, 72 and 108 = (2 × 2 × 2 × 2 × 3 × 3 × 3)LCM of 48, 72 and 108 = 432So after 432 seconds they will change simultaneouslyWe know that60 seconds = 1 minuteso on dividing 432 / 60 we get 7 as quotient and 12 as reminderHence, 432 seconds = 7 min 12 seconds∴ The time = 7 a.m. + 7 minutes 12 seconds

⇒ 48 = 2 × 2 × 2 × 2 × 3⇒ 72 = 2 × 2 × 2 × 3 × 3⇒ 108 = 2 × 2 × 3 × 3 × 3Hence LCM of 48, 72 and 108 = (2 × 2 × 2 × 2 × 3 × 3 × 3)LCM of 48, 72 and 108 = 432So after 432 seconds they will change simultaneouslyWe know that60 seconds = 1 minuteso on dividing 432 / 60 we get 7 as quotient and 12 as reminderHence, 432 seconds = 7 min 12 seconds∴ The time = 7 a.m. + 7 minutes 12 secondsHence the lights change simultaneously at 7:07:12 a.m