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

Question

1 man and 2 women can complete a work in 10 days. 2 men and 3 women can complete the work in 6 days. Find the number of days needed by 4 men and 4 women to complete the work.

A. 5
B. 15/4
C. 3
D. 5/2
E. 15/7

CareerGeek · Answer

Given, 1/m + 2/w = 1/10 ....... (1) & 
2/m + 3/w = 1/6 ....... (2)

2*(1) - (2) --> 2(1/m + 2/w) - (2/m + 3/w) = 2/10 - 1/6
--> 4/w - 3/w = 1/5 - 1/6 = (6 - 5)/30
--> 1/w = 1/30
--> w = 30 days

From (1), 1/m + 2/30 = 1/10
--> 1/m = 1/10 - 1/15 = (3 - 2)/30 = 1/30
--> m = 30 days

--> For 4 men & 4 women = 4/m + 4/w = 4/30 + 4/30 = 8/30
Number of days needed = 30/8 = 15/4

IMO Option B

CrackverbalGMAT · Answer

The problem given is a typical Time and Work problem. The steps involved is to form equations and solve them.

We need to remember to convert Time into work while creating the equations.

1 days work of 1 man and 2 women =  \frac{1}{10}

So M + 2W =  \frac{1}{10}

10M + 20W = 1 Equation (1)

1 days work of 2 men and 3 women =  \frac{1}{6}

So 2M + 3W =  \frac{1}{6}

12M + 18W = 1 Equation (2)

Equating (1) and (2) 10M + 20W = 12M + 18W

2M = 2W or M = W. i.e the number of days taken by 1 man is equal to the number of days taken by 1 Women

Putting W = M in Equation (1), we get 10M + 20M = 1 or 30M = 1

Therefore work done by 1 man in 1 day =  \frac{1}{30}  = work done by 1 woman in 1 day

For 4 men and 4 women, work done in 1 day =  \frac{4}{30}  +  \frac{4}{30}  =  \frac{1}{10}  =  \frac{4}{15}

The number of day is =  \frac{15}{4}  (converting work into days)

Option B

Arun Kumar

IanStewart · Answer

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.

GMATWhizTeam · Answer

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.

ScottTargetTestPrep · Answer

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

muhammaddk92 · Answer

MMWWW = 1/6 days
MWW = 1/10 days

MMWWW - MWW = M+W
1/6 - 1/10 = 1/15

So 1M+1W take 15 days to do 1 job. 
4M+4W will take  15/4

ManifestDreamMBA · Answer

That's an interesting solution, looks really cool. Do you mind sharing the logic behind this?

muhammaddk92 · Answer

I just subtracted to get a pair of 1M and 1W. So if one pair of MW can do a job in 15 hours, 4 pairs i.e. MMMMWWWW will take 15/4.

ManifestDreamMBA · Answer

Thanks for the response. I am thinking it is same as the sum of rates of the 2 groups to get the combined rate. Given the total and one set is given, the other set(i.e. M+W) has been identified by the difference. Kudos to the new method

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards