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# The traffic lights at three different road crossing change after every 48 seconds, 72 seconds and 108 seconds respectively.If they change simultaneously at 7 : 00 a.m, at what time will they change simultaneously again?

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This question is taken from real numbers chapter in which we have given that traffic lights at three different road crossing change after every 48 seconds, 72 seconds and 108 seconds respectively and we have to find at what time will they change simultaneously if they they change simultaneously at 7 : 00 a.m.

Kindly solve the above problem in detail

RS Aggarwal, Class 10, chapter 1B, question no 26

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1. ## Consider the problem

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

So,
48=2×2×2×2×3
72=2×2×2×3×3
108=2×2×3×3×3

Therefore, L.CM of 48,72,108 is
(2×2×2×2×3×3×3)=432

So, time when they change again =432seconds

But we need to find time after 7am So, first we convert 432seconds into minutes.

Time=432second=432/60minutesTime=7 minutes 12 seconds

Thus,
Required time =7am+7minutes 12seconds
=7:07:12am

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