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8 hours of work for a woman is equal to 6 hours of work for a man or 12 hours of work for a boy. If 9 men working 6 hours daily can complete a work in 6 days, then in how many days 12 men, 12 women and 12 boys working 8 hours daily will complete the same work?
  • a)
    5/2 days
  • b)
    3/2 days
  • c)
    7/2 days
  • d)
    3 days
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
8 hours of work for a woman is equal to 6 hours of work for a man or ...
1 man done work in 6×6×9 hours
Since 8W=6M=12B
therefore 12M+12W+12B=27M
therefore 27 men will do work in (6×6×9/27) = 12 hours
= 12/8=1.5 days
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Most Upvoted Answer
8 hours of work for a woman is equal to 6 hours of work for a man or ...
Understanding Work Rates
To solve the problem, we first need to establish the work rates of men, women, and boys based on the information given:
- Work Rate Relationships:
- 8 hours of a woman's work = 6 hours of a man's work
- 8 hours of a woman's work = 12 hours of a boy's work
From this, we can derive the following work rates:
- Man's work rate: 1 man's work in 6 hours = 1/6 work/hour
- Woman's work rate: 1 woman's work in 8 hours = 1/8 work/hour
- Boy's work rate: 1 boy's work in 12 hours = 1/12 work/hour
Calculating Total Work Done by 9 Men
Next, we find the total work done by 9 men working 6 hours daily for 6 days:
- Daily work by 9 men: 9 men * (1/6 work/hour) * 6 hours = 9 work units
- Total work in 6 days: 9 work units/day * 6 days = 54 work units
Calculating Work Done by 12 Men, 12 Women, and 12 Boys
Now, we calculate how much work 12 men, 12 women, and 12 boys can do in one day:
- Work by 12 men: 12 men * (1/6 work/hour) * 8 hours = 16 work units
- Work by 12 women: 12 women * (1/8 work/hour) * 8 hours = 12 work units
- Work by 12 boys: 12 boys * (1/12 work/hour) * 8 hours = 8 work units
Total Daily Work
- Total work by 12 men, 12 women, and 12 boys:
- 16 (men) + 12 (women) + 8 (boys) = 36 work units/day
Calculating Days to Complete the Work
Finally, we determine how many days it takes to complete the total work of 54 units:
- Days required: Total work / Daily work = 54 work units / 36 work units/day = 1.5 days
Hence, the answer is 3/2 days, which corresponds to option B.
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8 hours of work for a woman is equal to 6 hours of work for a man or 12 hours of work for a boy. If 9 men working 6 hours daily can complete a work in 6 days, then in how many days 12 men, 12 women and 12 boys working 8 hours daily will complete the same work?a)5/2 daysb)3/2 daysc)7/2 daysd)3 daysCorrect answer is option 'B'. Can you explain this answer?
Question Description
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