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Answer :
To solve this problem, we need to determine after how many weeks the security men A, B, and C will repeat their duties starting from the first week of a month. Here’s a step-by-step explanation:
1. Understand the Rotation Cycle:
- The security men A, B, and C rotate their duties every week in a cycle of three weeks.
- A works in the 1st week, B in the 2nd week, and C in the 3rd week.
2. Finding the Pattern Repetition:
- What we want to find is how many weeks it takes for their duty rotation pattern to align again with the start of a new month.
- Months typically start in any week, but they have a repeating property based on every 4 weeks.
3. Aligning the Week Pattern with the Month Start:
- Since the rotation repeats every 3 weeks, we look for when this 3-week pattern lines up again with the beginning of another month.
- The idea here is that this repetition coincides with a full alignment every cycle that smoothly covers complete months, considering the total weeks.
4. Calculating the Weeks Until Alignment:
- Given the rotation is three weeks, we find a scenario approximating a longer cycle that results in them restarting duties from the start of a new month.
- After careful consideration, we find that after 6 weeks (which is two cycles of their 3-week rotation), the pattern will start over again on the same day they began. This essentially tunes with month starts if considered on an average monthly day basis.
Therefore, the answer is that they will repeat their duties in alignment with the start of a month every 6 weeks. This is the number of weeks after which their rotational duties begin again from the first week of a new month.
1. Understand the Rotation Cycle:
- The security men A, B, and C rotate their duties every week in a cycle of three weeks.
- A works in the 1st week, B in the 2nd week, and C in the 3rd week.
2. Finding the Pattern Repetition:
- What we want to find is how many weeks it takes for their duty rotation pattern to align again with the start of a new month.
- Months typically start in any week, but they have a repeating property based on every 4 weeks.
3. Aligning the Week Pattern with the Month Start:
- Since the rotation repeats every 3 weeks, we look for when this 3-week pattern lines up again with the beginning of another month.
- The idea here is that this repetition coincides with a full alignment every cycle that smoothly covers complete months, considering the total weeks.
4. Calculating the Weeks Until Alignment:
- Given the rotation is three weeks, we find a scenario approximating a longer cycle that results in them restarting duties from the start of a new month.
- After careful consideration, we find that after 6 weeks (which is two cycles of their 3-week rotation), the pattern will start over again on the same day they began. This essentially tunes with month starts if considered on an average monthly day basis.
Therefore, the answer is that they will repeat their duties in alignment with the start of a month every 6 weeks. This is the number of weeks after which their rotational duties begin again from the first week of a new month.
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