The work done by a man is double the work done by a woman in the same

Question

The work done by a man is double the work done by a woman in the same time. If 10 men can do a piece of work in 8 days, then in how many days that work can be done by 3 men and 4 women?

(A) 4
(B) 80/11
(C) 8
(D) 16
(E) 18

SangamJena · Answer

Rate of Men =1/80
Rate of Women = 1/160

3 men & 4 women combined rate is (3/80+4/160)

Hence days required is
(6+4/160) * Days = 1 (Work Done)

In 16 days they will complete the work.

Answers is D.

darunp · Answer

Assuming workdone by men = 2 units/day and so workdone by women = 1 unit/day

workdone by 10 men = 10*2*8

workdone by 3 men and 4 women = 3*2*d + 4*1*d

equation then becomes 10*2*8 = 6d+4d
d=16

azamatboden · Answer

Super easy. Convert 4 women into 2 men. 10 * 8 = 5 * x --> X= 16

ThatDudeKnows · Answer

There is no variable in the question, but there is some piece of information that would make our lives much easier. 
The work done by a man is solving 2 GMAT questions in a day.
The work done by a woman is solving 1 GMAT question in a day.
10 men can solve 20 GMAT questions in a day.
10 men can solve 160 GMAT questions in a day. That's the job.
3 men can solve 6 GMAT questions in a day. 4 women can solve 4 GMAT questions in a day. 
Together, 3 men and 4 women can solve 10 GMAT questions in a day.
It will take them 16 days to solve 160 GMAT questions.

Answer choice D.

ThatDudeKnowsHiddenPlugIn

ScottTargetTestPrep · Answer

Since a man can do double the work of a woman, one man is equivalent to two women. Thus, a group of 3 men and 4 women is equivalent to a group of 5 men. We are told that 10 men can do the work in 8 days and we need to find the number of days that 5 men can do the same work. Since the number of men is halved, the number of days will be doubled, which means that 5 men can do the work in 2 * 8 = 16 days.

Alternate Solution:

The rate of 10 men is  \frac{1}{8}\frac{	ext{job}}{	ext{day}} , which means the rate of one man is  \frac{1}{80}\frac{	ext{job}}{	ext{day}} .

We are told that one man can do double the work of a woman, which means that the rate of one man is double the rate of one woman. Thus, the rate of one woman is  \frac{1}{160}\frac{	ext{job}}{	ext{day}} . Then, the rate of 3 men and 4 women is:

\Rightarrow 3	imes\frac{1}{80} + 4	imes\frac{1}{160} 
 \Rightarrow \frac{3}{80} + \frac{2}{80} 
 \Rightarrow \frac{5}{80} 
 \Rightarrow \frac{1}{16}

Thus, the rate of 3 men and 4 women is  \frac{1}{16}\frac{	ext{job}}{	ext{day}} . This means that 3 men and 4 women can do  \frac{1}{16}  of the job in one day, so it will take 16 days to complete the whole job.

Answer: D

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