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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 simmultaneously at 7 : 00 a.m , at what time will they change simmultaneously again
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the traffic lights at three different road crossing change after every...
Given that traffic light at three different road crossing change after every 48 seconds,72 seconds and 108 seconds respectively.
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
Hence LCM of 48, 72 and 108 is (2 x 2 x 2 x 2 x 3 x 3 x 3)
= 432
That is after 432 seconds they will change simultaneously
432 seconds = 7 min 12 seconds
Thus the traffic lights change simultaneously at 7:7:12 am
This question is part of UPSC exam. View all Class 10 courses
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the traffic lights at three different road crossing change after every...
The given problem requires finding the time at which the traffic lights at three different road crossings will change simultaneously again. To solve this problem, we need to determine the least common multiple (LCM) of the given time intervals.
Finding the LCM:
The time intervals between the changes of the traffic lights are 48 seconds, 72 seconds, and 108 seconds. To find the LCM, we can list the multiples of each interval until we find a common multiple.
Multiples of 48: 48, 96, 144, 192, 240, ...
Multiples of 72: 72, 144, 216, 288, 360, ...
Multiples of 108: 108, 216, 324, 432, 540, ...
From the lists above, we can see that the first common multiple is 216, which means the traffic lights will change simultaneously after 216 seconds.
Converting the time interval to hours and minutes:
Now, we convert the time interval of 216 seconds to hours and minutes to determine when the traffic lights will change simultaneously again.
216 seconds can be divided into 60 seconds (1 minute) and 156 seconds. Therefore, we have:
216 seconds = 3 minutes and 36 seconds.
Since the traffic lights change simultaneously at 7:00 a.m., we add 3 minutes and 36 seconds to this time.
7:00 a.m. + 3 minutes and 36 seconds = 7:03:36 a.m.
Therefore, the traffic lights will change simultaneously again at 7:03:36 a.m.
Summary:
- The least common multiple (LCM) of the time intervals 48 seconds, 72 seconds, and 108 seconds is 216 seconds.
- Converting 216 seconds to hours and minutes gives us a time interval of 3 minutes and 36 seconds.
- Adding this time interval to the initial time of 7:00 a.m. gives us the time of 7:03:36 a.m. when the traffic lights will change simultaneously again.
Finding the LCM:
The time intervals between the changes of the traffic lights are 48 seconds, 72 seconds, and 108 seconds. To find the LCM, we can list the multiples of each interval until we find a common multiple.
Multiples of 48: 48, 96, 144, 192, 240, ...
Multiples of 72: 72, 144, 216, 288, 360, ...
Multiples of 108: 108, 216, 324, 432, 540, ...
From the lists above, we can see that the first common multiple is 216, which means the traffic lights will change simultaneously after 216 seconds.
Converting the time interval to hours and minutes:
Now, we convert the time interval of 216 seconds to hours and minutes to determine when the traffic lights will change simultaneously again.
216 seconds can be divided into 60 seconds (1 minute) and 156 seconds. Therefore, we have:
216 seconds = 3 minutes and 36 seconds.
Since the traffic lights change simultaneously at 7:00 a.m., we add 3 minutes and 36 seconds to this time.
7:00 a.m. + 3 minutes and 36 seconds = 7:03:36 a.m.
Therefore, the traffic lights will change simultaneously again at 7:03:36 a.m.
Summary:
- The least common multiple (LCM) of the time intervals 48 seconds, 72 seconds, and 108 seconds is 216 seconds.
- Converting 216 seconds to hours and minutes gives us a time interval of 3 minutes and 36 seconds.
- Adding this time interval to the initial time of 7:00 a.m. gives us the time of 7:03:36 a.m. when the traffic lights will change simultaneously again.
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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 simmultaneously at 7 : 00 a.m , at what time will they change simmultaneously again Related: CBSE Sample Question Paper Mathematics (2017-18)
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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 simmultaneously at 7 : 00 a.m , at what time will they change simmultaneously again Related: CBSE Sample Question Paper Mathematics (2017-18) for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about the traffic lights at three different road crossing change after every 48 seconds, 72 seconds and 108 seconds respectively . If they change simmultaneously at 7 : 00 a.m , at what time will they change simmultaneously again Related: CBSE Sample Question Paper Mathematics (2017-18) covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for the traffic lights at three different road crossing change after every 48 seconds, 72 seconds and 108 seconds respectively . If they change simmultaneously at 7 : 00 a.m , at what time will they change simmultaneously again Related: CBSE Sample Question Paper Mathematics (2017-18).
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