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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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