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

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Manager
Joined: 18 Jul 2019
Posts: 54
Six men and fourteen women can complete a work in five days, whereas  [#permalink]

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25 Nov 2019, 01:39
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Difficulty:

75% (hard)

Question Stats:

38% (03:26) correct 62% (02:37) wrong based on 13 sessions

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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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Joined: 27 May 2012
Posts: 947
Six men and fourteen women can complete a work in five days, whereas  [#permalink]

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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

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