The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they all change simultaneously at 8 a.m then at what time will they again change simultaneously?

Solution of question from book:

Secondary school Mathematics for Class 10 R S Aggarwal V Aggarwal

Unit 1: Number system

Chapter 1.1: Real numbers

Exercise 1B

Question :

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they all change simultaneously at 8 a.m then at what time will they again change simultaneously?

Solution:

There are three different road crossings and at each crossing there are traffic lights which changes after 48, 72 and 108 seconds respectively.

At first they all changed together at 8 a.m simultaneously.

To solve it we will find the LCM of the given time intervals.

Prime factors of:

48 = 2 x 2 x 2 x 2 x 3

72 = 2 x 2 x 2 x 3 x 3

108 = 2 x 2 x 3 x 3 x 3

LCM of 48, 72 and 108 = 2 x 2 x 2 x 2 x 3 x 3 x 3 = 432 seconds

Changing it into minutes = 7 min 12 sec

Since all the traffic lights changed simultaneously at 8 a.m then next will change simultaneously at 8:07:12 a.m.

Watch the video solution of the above question by clicking this link:

Question : The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they all change simultaneously at 8 a.m then at what time will they again change simultaneously?

Video solution:

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