# Time & Work Problem

12 men do a work in 36 days.In how many days can 18 men do the same work? Sol:This can be solved as 1 man's can do work in 12*36 days So,1 man's 1 day work (1/12*36) days Hence 18 men's 1 day work is (18/12*36) So Days taken for 18 men is (12*36)/18 days.

Similarly Here is another question where i applied the same concept but i'm not getting the answer. Q)4 men or 8 women can do a work in 24 days.How many days will 12 men and 8 women work to do same work. My Soln: 4 men or 8 women do a work in 24 days. so 1 man can do work in (24*4) days. So 1 man's 1 day work is 1/(24*4) Hence 12 men and 8 women or 16 mens can do work in 16/(24*4) So days taken for 16 men to do work us (24*4)/16 days. But the actual answer is 3/2 days.

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I think the "actual answer" is wrong. – Gerry Myerson Oct 3 '12 at 6:21
Your answer is correct. – Patrick Li Oct 3 '12 at 6:25

Let's divide the work into 192 ($=8\times24$) pieces.

A woman can do a piece a day (so 8 women can do the work in 24 days).

A man can do 2 pieces a day.

So 12 men and 8 women can do $12\times2+8\times1=32$ pieces a day.

So it will take them $192/32=6$ days, which is the answer you got.

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4 men need 24 days

8 women need 24 days

one man needs 96 days [4*24]

one woman needs 192 days [8*24]

so 12 men and 8 women need 6 days [192 / (96 / 12 + 192 / 8)]

==> 192 / ((4 * 24) / 12 + (8 * 24) / 8) = 6

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