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The traffic signals at four road crossing change every 30 second, 1 minute, 45 seconds and 75 seconds respectively. If they change simultaneously at 9 AM, at what time will they change simultaneously again.
- a)9:12 AM
- b)9.15 AM
- c)9.20 AM
- d)9.30 AM
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The traffic signals at four road crossing change every 30 second, 1 mi...
LCM of 30 sec, 1 min , 45 sec and 75 sec
= 15 min
∴ At 9:15 AM, they will simultaneously change again.
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Community Answer
The traffic signals at four road crossing change every 30 second, 1 mi...
Given:
- The traffic signals at four road crossings change every 30 seconds, 1 minute, 45 seconds, and 75 seconds respectively.
- They change simultaneously at 9 AM.
To find:
At what time will they change simultaneously again?
Solution:
To determine the time at which all four traffic signals will change simultaneously again, we need to find the time at which the signals will have a common multiple.
Let's find the least common multiple (LCM) of the times at which the signals change.
Step 1: Convert all time intervals to seconds:
- 30 seconds = 30 seconds
- 1 minute = 60 seconds
- 45 seconds = 45 seconds
- 75 seconds = 75 seconds
Step 2: Find the LCM of the time intervals:
To find the LCM, we can list the multiples of each time interval and find the smallest number that is common to all of them.
Multiples of 30 seconds: 30, 60, 90, 120, 150, 180, ...
Multiples of 60 seconds: 60, 120, 180, 240, 300, ...
Multiples of 45 seconds: 45, 90, 135, 180, 225, 270, ...
Multiples of 75 seconds: 75, 150, 225, 300, ...
The LCM of 30, 60, 45, and 75 seconds is 300 seconds.
Step 3: Convert the LCM back to minutes and seconds:
300 seconds = 5 minutes
Therefore, the traffic signals will change simultaneously again after 5 minutes.
Step 4: Add the time to the initial time:
9:00 AM + 5 minutes = 9:05 AM
So, the traffic signals will change simultaneously again at 9:05 AM.
Final Answer:
The traffic signals will change simultaneously again at 9:05 AM. Therefore, the correct answer is option 'B'.
- The traffic signals at four road crossings change every 30 seconds, 1 minute, 45 seconds, and 75 seconds respectively.
- They change simultaneously at 9 AM.
To find:
At what time will they change simultaneously again?
Solution:
To determine the time at which all four traffic signals will change simultaneously again, we need to find the time at which the signals will have a common multiple.
Let's find the least common multiple (LCM) of the times at which the signals change.
Step 1: Convert all time intervals to seconds:
- 30 seconds = 30 seconds
- 1 minute = 60 seconds
- 45 seconds = 45 seconds
- 75 seconds = 75 seconds
Step 2: Find the LCM of the time intervals:
To find the LCM, we can list the multiples of each time interval and find the smallest number that is common to all of them.
Multiples of 30 seconds: 30, 60, 90, 120, 150, 180, ...
Multiples of 60 seconds: 60, 120, 180, 240, 300, ...
Multiples of 45 seconds: 45, 90, 135, 180, 225, 270, ...
Multiples of 75 seconds: 75, 150, 225, 300, ...
The LCM of 30, 60, 45, and 75 seconds is 300 seconds.
Step 3: Convert the LCM back to minutes and seconds:
300 seconds = 5 minutes
Therefore, the traffic signals will change simultaneously again after 5 minutes.
Step 4: Add the time to the initial time:
9:00 AM + 5 minutes = 9:05 AM
So, the traffic signals will change simultaneously again at 9:05 AM.
Final Answer:
The traffic signals will change simultaneously again at 9:05 AM. Therefore, the correct answer is option 'B'.
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The traffic signals at four road crossing change every 30 second, 1 minute, 45 seconds and 75 seconds respectively. If they change simultaneously at 9 AM, at what time will they change simultaneously again.a)9:12 AMb)9.15 AMc)9.20 AMd)9.30 AMCorrect answer is option 'B'. Can you explain this answer?
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The traffic signals at four road crossing change every 30 second, 1 minute, 45 seconds and 75 seconds respectively. If they change simultaneously at 9 AM, at what time will they change simultaneously again.a)9:12 AMb)9.15 AMc)9.20 AMd)9.30 AMCorrect answer is option 'B'. Can you explain this answer? 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 signals at four road crossing change every 30 second, 1 minute, 45 seconds and 75 seconds respectively. If they change simultaneously at 9 AM, at what time will they change simultaneously again.a)9:12 AMb)9.15 AMc)9.20 AMd)9.30 AMCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The traffic signals at four road crossing change every 30 second, 1 minute, 45 seconds and 75 seconds respectively. If they change simultaneously at 9 AM, at what time will they change simultaneously again.a)9:12 AMb)9.15 AMc)9.20 AMd)9.30 AMCorrect answer is option 'B'. Can you explain this answer?.
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