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25 Nov 2019, 01:39
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
56% (03:19) correct
44%
(03:05)
wrong
based on 130
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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
(A) $1,814
(B) $1,876
(C) $2,012
(D) $2,216
(D) $2,543
25 Nov 2019, 06:41
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CaptainLevi
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
24 Aug 2020, 20:18
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The objective is to find the work done by 1 man and 1 woman
Equation 1: \(6M + 14W = \frac{1}{5}\) (work done in 1 day) or 30M + 70W = 1
Equation 2: \(2M + 3W = \frac{1}{16}\) (\(\frac{1}{4}\)th work takes 4 days, work done in 1 day is \(\frac{1}{16}\)) or 32M + 48W = 1
Equating and solving: 30M + 70W = 32M + 48W
2M = 22W
Therefore 1M = 11W
Putting in equation 2: 2*11W + 3W = \(\frac{1}{16}\)
Therefore 1W = \(\frac{1}{16 * 25}\) = \(\frac{1}{400}\)
Therefore 1 M = 11W = 11 * \(\frac{1}{400}\) = \(\frac{11}{400}\)
Work don by 1 Man and 2 Women are in the ratio \(\frac{11}{400}\) : \(\frac{2}{400}\) = 11 : 2
Share of the 2 women = \(\frac{2}{13} * 11791 = $1814\)
Option A
Arun Kumar
Equation 1: \(6M + 14W = \frac{1}{5}\) (work done in 1 day) or 30M + 70W = 1
Equation 2: \(2M + 3W = \frac{1}{16}\) (\(\frac{1}{4}\)th work takes 4 days, work done in 1 day is \(\frac{1}{16}\)) or 32M + 48W = 1
Equating and solving: 30M + 70W = 32M + 48W
2M = 22W
Therefore 1M = 11W
Putting in equation 2: 2*11W + 3W = \(\frac{1}{16}\)
Therefore 1W = \(\frac{1}{16 * 25}\) = \(\frac{1}{400}\)
Therefore 1 M = 11W = 11 * \(\frac{1}{400}\) = \(\frac{11}{400}\)
Work don by 1 Man and 2 Women are in the ratio \(\frac{11}{400}\) : \(\frac{2}{400}\) = 11 : 2
Share of the 2 women = \(\frac{2}{13} * 11791 = $1814\)
Option A
Arun Kumar
