1 man and 2 women can complete a work in 10 days. 2 men and 3 women ca

2 men and 3 women do 5 "works" in 30 days
1 man and 2 women do 3 "works" in 30 days

so the extra 1 man and 1 woman in the first line above must be doing 2 "works" in 30 days, and thus do 1 "work" every 15 days. If we use 4 times as many workers, it will take 1/4 the time, so 4 men and 4 women will do 1 "work" in 15/4 days.

Solution

• Let us assume that the rate of working of a man \(= r_m\) units/ day
• And the rate of working a woman \(= r_w\) units/ day
• Now, we know that work = rate *time.

o So, \(total \space work = (r_m + 2*r_w)*10 = (2*r_m + 3*r_w)*6 ….Eq.(i) \)
o \(⟹ 5*r_m + 10*r_w = 6*r_m + 9*r_w \)
o \(⟹ r_w = r_m…..Eq.(ii)\)
o It means the rate of working of a man and a woman is same.
• Now, the time taken by 4 men and 4 women to complete the work \(= \frac{total \space Work}{rate \space of \space 4 \space men \space and \space 4 \space women} \)
• Now, substituting the value of total work from Eq.(i) into the above Equation, and using Eq.(ii), we get,

o The time taken by 4 men and 4 women to complete the work \(= \frac{(r_m + 2*r_w)*10 }{4*r_m + 4*r_w} = \frac{10*3*r_m}{8*r_m} = \frac{15}{4}\) days

Thus, the correct answer is Option B.

Solution:

We can let x = the rate of a man and y = the rate of a woman. We can create the equations:

x + 2y = 1/10

and

2x + 3y = 1/6

Subtracting the second equation from twice the first, we have:

2(x + 2y) - (2x + 3y) = 2(1/10) - 1/6

2x + 4y - 2x - 3y = 1/5 - 1/6

y = 1/30

Substituting 1/30 for y in the first equation, we have:

x + 2(1/30) = 1/10

x + 2/30 = 3/30

x = 1/30

Therefore, the rate of 4 men and 4 women is 4(1/30) + 4(1/30) = 8/30 = 4/15. Since rate is the inverse of time, it takes 1/(4/15) = 15/4 days for 4 men and 4 women to complete the work.

Alternate Solution:

Let m be the number of days for one man to complete the work and let w be the number of days for one woman to complete the work.

One man completes 1/m of the work in one day and one woman completes 1/w of the work in one day. Thus, when one man and two women work together, 1/m + 1/w + 1/w = 1/m + 2/w of the work is completed. On the other hand, we know the whole job is completed in 10 days when one man and two women work together, so in one day, 1/10 of the job is completed. Setting the two expressions equal, we obtain:

1/m + 2/w = 1/10

Similarly, when two men and three women work together, 2/m + 3/w of the job is completed. Since the job is completed in 6 days, 1/6 of the job is completed in one day; thus:

2/m + 3/w = 1/6

Subtracting the first equation from the second, we obtain:

1/m + 1/w = 1/6 - 1/10 = 1/15

This means that when one man and one woman work together, 1/15 of the job is completed in one day. Since 1/15 of the job is completed in one day, the whole job is completed in 15 days. Finally, four men and four women can complete the job four times faster compared to one man and one woman; thus, it will take 1/4 of the time to complete the job, i.e. 1/4 * 15 = 15/4 days.

Answer: B

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.