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Six men and fourteen women can complete a work in five days, whereas

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Six men and fourteen women can complete a work in five days, whereas  [#permalink]

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New post 25 Nov 2019, 01:39
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Six men and fourteen women can complete a work in five days, whereas two men and three women can complete one-fourth of the same work in four days. If one man and two women take up and complete the same work, earning a total wage of $11 ,791 for the same, what is the total share of the two women in this amount?

(A) $1,814
(B) $1,876
(C) $2,012
(D) $2,216
(D) $2,543
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Six men and fourteen women can complete a work in five days, whereas  [#permalink]

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New post 25 Nov 2019, 06:41
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CaptainLevi wrote:
Six men and fourteen women can complete a work in five days, whereas two men and three women can complete one-fourth of the same work in four days. If one man and two women take up and complete the same work, earning a total wage of $11 ,791 for the same, what is the total share of the two women in this amount?

(A) $1,814
(B) $1,876
(C) $2,012
(D) $2,216
(D) $2,543


Let \(r_m \)be the rate of Man and \(r_w\) be the rate of Women

\(r_m*16+r_w*14= .2\)
\(r_m*2 + r_w*3 =.0625\) ( if 2 men and 3 women can do\( \frac{1}{4} \)of the work in 4 days then they can do the whole work in 16 days hence rate together \(\frac{1}{16}=.0625\))

Solving the above two equations we get \(r_m\)=.0275 and \(r_w=.0025 \) or 1 women can do the whole work in\(\frac{1}{.0025}= 400\hspace{1mm}\) days and 1 man can do the whole work in \(\frac{1}{.0275}= \frac{400}{11}\hspace{1mm}\) days
So the rate of 1 man and 2 women is: 1* .0275 + 2*.0025= .0325 or 1 Man and 2 women can do the whole work in \(\frac{1}{.0325}=\frac{400}{13}\) days

We know 1 women can do the whole work in 400 days therefore in \(\frac{400}{13} \)days 1 women can do \(\frac{1}{13}\) of the work and 2 women can do \(\frac{2}{13}\)of the work

Now they are paid in proportion to the amount of work done, so for \(\frac{2}{13}\) of work, women are paid \(\frac{2}{13}\) of the money.
\(\frac{2}{13}\)*11 ,791 = 1814

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Six men and fourteen women can complete a work in five days, whereas   [#permalink] 25 Nov 2019, 06:41
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