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If 12 men and 16 women can do a piece of work in 5 days and

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Re: If 12 men and 16 women can do a piece of work in 5 days and [#permalink]

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New post 20 Feb 2018, 23:49
Suppose 1 man takes m days and 1 woman takes w days to complete the work.

So, in 1 day, a man would do 1/m and a woman would do 1/w work

In 5 days, 12 men and 16 women would do 5*(12/m + 16/m) work

Similarly, in 4 days, 13 men and 24 women would do 4*(13/m + 24/w) work

But this is the total work. So,

5*(12/m + 16/m) = 4*(13/m + 24/w)
Solving, we get w=2m

Since 12 men and 16 women can do a piece of work in 5 days

So, from this we can find out that the total amount of work = 60 man-days + 80 women-days = 200 women-days.

7 men and 10 women = 14 women + 10 women= 24 women

So, number of days = 200/24 = 8.3 days.
Re: If 12 men and 16 women can do a piece of work in 5 days and   [#permalink] 20 Feb 2018, 23:49

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