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8 hours work of a woman is equal to 6 hours work of a man or 12 hours work of 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?
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Verified Answer
8 hours work of a woman is equal to 6 hours work of a man or 12 hours...
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
Most Upvoted Answer
8 hours work of a woman is equal to 6 hours work of a man or 12 hours...
Understanding Work Equivalence
To solve the problem, we first need to establish the work equivalence between men, women, and boys.
Work Equivalence
- 1 woman's work for 8 hours = 6 hours of a man's work
- 1 woman's work for 8 hours = 12 hours of a boy's work
From this, we can derive:
- In 1 hour, 1 woman does 3/4 of a man's work (since 8 hours = 6 hours of a man).
- In 1 hour, 1 boy does 2/3 of a woman's work (since 12 hours = 8 hours of a woman).
Calculating Work Done by 9 Men
- 9 men working 6 hours daily for 6 days complete the work.
- Total man-hours = 9 men * 6 hours/day * 6 days = 324 man-hours.
Finding Total Work in Woman and Boy's Terms
- Since 1 man's work for 1 hour = 4/3 of a woman's work for 1 hour:
- Total work in terms of women's hours = 324 * (4/3) = 432 woman-hours.
- Since 1 boy's work for 1 hour = 3/2 of a woman's work for 1 hour:
- Total work in terms of boy's hours = 432 * (3/2) = 648 boy-hours.
Work Done by 12 Men, 12 Women, and 12 Boys
- Each can work for 8 hours a day:
- Work done by 12 men in one day = 12 * 8 = 96 man-hours.
- Work done by 12 women in one day = 12 * 8 * (4/3) = 128 woman-hours.
- Work done by 12 boys in one day = 12 * 8 * (3/2) = 144 boy-hours.
Total Daily Work
- Total work per day = 96 + 128 + 144 = 368 hours.
Calculating Days to Complete the Work
- Total work required = 648 boy-hours / 368 hours/day ≈ 1.76 days.
Therefore, the answer is approximately 3/2 days, or option 'B'.
To solve the problem, we first need to establish the work equivalence between men, women, and boys.
Work Equivalence
- 1 woman's work for 8 hours = 6 hours of a man's work
- 1 woman's work for 8 hours = 12 hours of a boy's work
From this, we can derive:
- In 1 hour, 1 woman does 3/4 of a man's work (since 8 hours = 6 hours of a man).
- In 1 hour, 1 boy does 2/3 of a woman's work (since 12 hours = 8 hours of a woman).
Calculating Work Done by 9 Men
- 9 men working 6 hours daily for 6 days complete the work.
- Total man-hours = 9 men * 6 hours/day * 6 days = 324 man-hours.
Finding Total Work in Woman and Boy's Terms
- Since 1 man's work for 1 hour = 4/3 of a woman's work for 1 hour:
- Total work in terms of women's hours = 324 * (4/3) = 432 woman-hours.
- Since 1 boy's work for 1 hour = 3/2 of a woman's work for 1 hour:
- Total work in terms of boy's hours = 432 * (3/2) = 648 boy-hours.
Work Done by 12 Men, 12 Women, and 12 Boys
- Each can work for 8 hours a day:
- Work done by 12 men in one day = 12 * 8 = 96 man-hours.
- Work done by 12 women in one day = 12 * 8 * (4/3) = 128 woman-hours.
- Work done by 12 boys in one day = 12 * 8 * (3/2) = 144 boy-hours.
Total Daily Work
- Total work per day = 96 + 128 + 144 = 368 hours.
Calculating Days to Complete the Work
- Total work required = 648 boy-hours / 368 hours/day ≈ 1.76 days.
Therefore, the answer is approximately 3/2 days, or option 'B'.
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8 hours work of a woman is equal to 6 hours work of a man or 12 hours work of 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?
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