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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 everyÂ 48seconds,72secondsÂ andÂ 108secondsÂ respectively

So,
48=2Ã—2Ã—2Ã—2Ã—3
72=2Ã—2Ã—2Ã—3Ã—3
108=2Ã—2Ã—3Ã—3Ã—3â€‹

Therefore, L.CM ofÂ 48,72,108Â is
(2Ã—2Ã—2Ã—2Ã—3Ã—3Ã—3)=432â€‹

So, time when they change againÂ =432seconds

But we need to find time afterÂ 7amÂ So, first we convertÂ 432secondsÂ into minutes.

Time=432second=432/60â€‹minutesâˆ´Time=7Â minutes 12Â secondsâ€‹

Thus,
Required timeÂ =7am+7minutesÂ 12seconds
=7:07:12am

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