Ex 3.7, 6 - Chapter 3 Class 6 Playing with Numbers

Transcript

Ex 3.7, 6 (Introduction) The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?Let the traffic lights change in 1 second, 2 second, 3 seconds At 6 seconds, all of them change again. Now, this 6 is actually the LCM of 1, 2, 3 So, Time when they change again = LCM of 1, 2, 3 Ex 3.7, 6 The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?Traffic Lights change every 48 seconds, 72 seconds, 108 seconds We need to find the time when they change simultaneously Now, time when they change again will be more than 48, 72, 108 So we find LCM Time when they change again = LCM of 48, 72, 108 LCM of 48, 72, 108 LCM = 2 2 2 2 3 3 3 = 16 27 = 432 Time when they change again = 432 seconds But We need to find time after 7 am So, first we convert 432 seconds into minutes Time = 432 seconds = 432/60 minutes Time = 7 Minutes 12 Seconds Thus Required Time = 7am + 7 minutes 12 Seconds = 7:07:12 am