A particular work can be completed by $6$ men and $6$ women in $24$ days; whereas the same work can be completed by $8$ men and $12$ women in $15$ days, according to the amount of work done , one man is equivalent to how many women?
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$ 2\dfrac{1 }{2 } $ women
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$ 5\dfrac{1 }{3 } $ women
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$ 5\dfrac{2 }{3 } $ women
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$ \dfrac{3}{2 } $ women
D
Correct answer
Explanation
Let M be men's rate and W be women's rate. 6M + 6W = 1/24. 8M + 12W = 1/15. Multiply first by 2: 12M + 12W = 2/24 = 1/12. Subtract second from this: 4M = 1/12 - 1/15 = (5-4)/60 = 1/60. So M = 1/240. Then 6(1/240) + 6W = 1/24 => 1/40 + 6W = 1/24 => 6W = 1/24 - 1/40 = (5-3)/120 = 2/120 = 1/60. So W = 1/360. M/W = (1/240) / (1/360) = 360/240 = 3/2.