# 12men or 15women can do pce of work in 14 days.in how many days 3men&5women can complete same work.?

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12 men take 14 days, so 1 man takes 12*14=168 days

15 women take 14 days, so 1 woman takes 15*14=210days

In one day a man gets 1/168 of the job done, and a woman gets

1/210 of the job done.

Let X = the number of days

Sinre there are 3 men and 5 woman,

3*X/168 + 5*X/210 = 1

3*210*X + 5*168*X = 168*210=35380

630*X + 840*X = 35380

1470*X = 35380

X = 24days

Brian was close, but he had:

Thus they are equivalent to 7 men

That means 7*14/12 = 49/6 days = 8.16 days

The last line should have been

That means 7*12/14 = 24 days

Wil2Play said:

From your statement, A man can do the work of 15/12ths, or 5/4ths of a woman. so, 3 + 5*(5/4) men = (12 + 25)/4 men = 37/4 men = 9.25

12 men can do the job in 14 days means it takes 168 man-days of work. 168/9.25 = 18.16 days

He should have had 3*(5/4) + 5 = 35/4 women = 8.75 women.

15 women can do the job in 14 days means it takes 210 woman-days of work. 210 / 8.75 = 24 days

ok, Wil fixed it!

Source(s): Damn I'm good
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• [edit - oops, got the ratio reversed]

From your statement, A man can do the work of 15/12ths, or 5/4ths of a woman.

so,

3 + 5*(4/5) men

= (15 + 20)/5 men

= 7 men

12 men can do the job in 14 days means it takes 168 man-days of work.

168/7 = 24 days

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• 12 men can do 1 job in 14 days.

12 men can do 1/14 of the job in one day. (They're using 1/14 of the time.)

3 men can do 1/[(14)(4)] = 1/56 of the job in one day. (There are 1/4 of the men.)

15 women can do 1 job in 14 days.

15 women can do 1/14 of the job in one day. (They're using 1/14 of the time.)

5 women can do 1/[(14)(3)] = 1/42 of the job in one day. (There are 1/3 of the women.)

Together, 3 men and 5 women do (1/56 + 1/42) of the job in one day.

1/56 + 1/42 = 3/168 + 4/168 = 7/168 = 1/24

Together, they do 1/24 of the job in one day.

They'll take 24 days to complete the job.

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• 15 women = 12 men

So, 1 woman = 12/15 man

So 5 women = 5*12/15 men = 4 men

Thus they are equivalent to 7 men

That means 7*14/12 = 49/6 days = 8.16 days

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• 14*4 = 56

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• 24 days

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• That means 12men*14days/work = 1 and 15women*14days/work = 1

Thus, men = work/168days and women = work/210days

And (3men + 5 women)*x/work = 1

Substituting, (3work/168days + 5work/210days)*x/work = 1

=(work/56days + work/42days)*x/work

Since work/56days + work/42days

= 98work/2352days

= 49work/1176days

= work/24days

Then substituting, work*x/24days*work=1

And x/24days=1

Thus, x=24days

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