15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would take 21 women if 3 women do as much work as 2 men, keeping the hours constant?
- 30
- 19
- 20
- None of these
Explanation
Given that 3 women = 2 men in terms of work:
Work done by 15 men in 1 hour = 1 / (21 * 8)
Work done by 1 man in 1 hour = 1 / (15 * 21 * 8)
Work done by 1 woman in 1 hour = (2/3) * (1 / (15 * 21 * 8))
Work done by 21 women in 1 hour = 21 * (2/3) * (1 / (15 * 21 * 8))
= 14 / (15 * 21 * 8)
= 1 / (15 * 9 * 8) (simplified for 21 women working)
If 21 women work for 6 hours a day:
Work done by 21 women in 1 day = 6 * (1 / (15 * 9 * 8)) * (15 * 9)
= 6 / 8
To complete the work:
Number of days = 8 / 6 * 21
= 28
None of the given options directly match the calculation approach provided, but recalculating properly considering the work equivalence and hours:
15 men * 21 days * 8 hours = 2520 man-hours
Given 3 women = 2 men, 21 women = 14 men equivalent
Let x be the number of days for 21 women working 6 hours/day:
14 men * x days * 6 hours = 2520 man-hours
84x = 2520
x = 30
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