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Answer :
Let's solve the problem step by step:
The company employs three security men, A, B, and C, who work on a rotational basis. Let's break down the schedule:
1. Rotation Cycle: Each security person works for one week. The cycle is:
- Week 1: A
- Week 2: B
- Week 3: C
2. Complete Cycle: After three weeks, the cycle repeats:
- Week 4: A
- Week 5: B
- Week 6: C
- And so on...
3. Goal: We need to find out after how many weeks they will repeat their duties starting from the first week of a month.
4. Understanding Monthly Cycles: Usually, a month may have 4 or 5 weeks. Since they are in a 3-week rotation cycle, we want to find a common point when their cycle aligns with the start of a month.
5. Common Period: To determine after how many weeks the rotation will start again on the first week of a month:
- A complete cycle of the security guards is every 3 weeks.
- If a month is considered as 4 weeks (a typical length for simplification), we look for when the weeks partially align with their cycle.
- We need the least common multiple (LCM) of 3 weeks (the cycle length) and 4 weeks (the simplified month length).
LCM Calculation:
- When you take the LCM of 3 and 4:
[tex]\[
\text{LCM}(3, 4) = 12
\][/tex]
This means that every 12 weeks, the complete cycle will align such that they will begin their rotation again at the start of the first week of a month.
Hence, the security men will start their duties from the first week of a month again after 12 weeks.
The company employs three security men, A, B, and C, who work on a rotational basis. Let's break down the schedule:
1. Rotation Cycle: Each security person works for one week. The cycle is:
- Week 1: A
- Week 2: B
- Week 3: C
2. Complete Cycle: After three weeks, the cycle repeats:
- Week 4: A
- Week 5: B
- Week 6: C
- And so on...
3. Goal: We need to find out after how many weeks they will repeat their duties starting from the first week of a month.
4. Understanding Monthly Cycles: Usually, a month may have 4 or 5 weeks. Since they are in a 3-week rotation cycle, we want to find a common point when their cycle aligns with the start of a month.
5. Common Period: To determine after how many weeks the rotation will start again on the first week of a month:
- A complete cycle of the security guards is every 3 weeks.
- If a month is considered as 4 weeks (a typical length for simplification), we look for when the weeks partially align with their cycle.
- We need the least common multiple (LCM) of 3 weeks (the cycle length) and 4 weeks (the simplified month length).
LCM Calculation:
- When you take the LCM of 3 and 4:
[tex]\[
\text{LCM}(3, 4) = 12
\][/tex]
This means that every 12 weeks, the complete cycle will align such that they will begin their rotation again at the start of the first week of a month.
Hence, the security men will start their duties from the first week of a month again after 12 weeks.
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