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

Question

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

CrackverbalGMAT · Accepted Answer

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

stne · Answer

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

culpavoluptatum · Answer

Thank you for sharing the solution. But I think we can get the answer once we get 1M=11W.
As we need to find the share of income for 2 Women from $11791.

And the final equation states that there were 1M + 2W = 11791
1M + 2W = 11791
=> 11W + 2W = 11791
=> 13W = 11791
=> W = 907
Share for 2W will be 2 x 907= 1814

Answer A.

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