# 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 FIND 1) according to the amount of work done one man is equivalent to how many women 2) the time taken by 4 men and 6 women to complete the same work

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by rutvianand
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2015-12-27T07:52:39+05:30
Let the work done by man and woman per day be x and y respectively . (6x + 6y ) 24 = 1 => x + y = 1/144 => y = 1/144 - x & (8x + 12y ) 15 = 1 => ( 2x + 3y) = 1/60 => ( 2x + 3/144 - 3x ) = 1/60 => -x + 1/48 = 1/60 => x = 1/48 - 1/60 = 1/240 y = 1/144 - 1/240 = 1/360 x/y = 360/240 = 36/24 = 3/2 So the amount of work done by man = 3/2 of woman . 2) Time taken by 4 men and 6 women = (4 * 1/240 + 6 * 1/360 ) t = 1 => 1/60 + 1/60 = 1/t => 1/30 = 1/t => t = 30 days
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2015-12-27T10:12:18+05:30

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Given,
6men + 6 women = 24 days
⇒ 6M + 6W = 24
and, 8M + 12W =15
1)Applying, M×D = M'×D'
(6M + 6W )×24= (8M + 12W)×15
⇒( M + W) ×6×24 = (2M +3W) ×4×15
⇒( M+ W)12 = (2M +3W)5
⇒12M + 12W = 10M +15W
2M = 3 W
hence, 2 men is equal to 3 women
2)now, 4M +6 W = ??
Applying M×D =M'×D'
(6M + 6W )×24 = (4M +6W ) ×D'
⇒(9W + 6W) ×24 = (6W +6W)×D'   ∵2M = 3 W
⇒15W ×24 = 12W ×D'
⇒D' = 30 days
It will takes 30 days to complete the same work by 4 men and 6 women