2 men and 3 boys can do a piece of work in 10 days while 3 men and 2

Question

2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days . In how many days can 2 man and 1 boy do the work?

A. 15 
B. 18
C. 12.5 
D. 10 
E. 16

EgmatQuantExpert · Accepted Answer

• 2 men and 3 boys can do a piece of work in 10 days. o Thus, 20 men and 30 boys can do a piece of work in 1 day......(i) • 3 men and 2 boys can do the same work in 8 days. o Thus, 24 men and 16 boys can do the same work in 1 day....(ii) • Equating (i) and (ii) we get - o 20 men + 30 boys = 24 men + 16 boys o 4 men = 14 boys o 2 men = 7 boys • Substituting this in equation (i) we get o 10 boys can do a piece of work in 10 days. o But we need to find out in how many days 2 men and 1 boy can do the work, which is equivalent to 8 boys.  8 boys can do the same work in (10*10/8) = 12.5 days. Thanks, Saquib Quant Expert e-GMAT Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

https://e-gmat.com/blogs/wp-content/uploads/2016/12/NP-Free-Trial-e1481107541356.png

chetan2u · Answer

Two points before coming to the solution..
1) under no circumstances, it is sub-600 level.
2) the choices are always in ascending order, so may not be a very authentic source although the Q is ok.

Let m men can complete the job on their own and B boys can complete the work.
So  \frac{2}{m}+\frac{3}{b}=\frac{1}{10} ..
  \frac{2*3}{m}+\frac{3*3}{b}=\frac{3}{10} ..(i)

\frac{3}{m}+\frac{2}{b}=\frac{1}{8} ...
  \frac{2*3}{m}+\frac{2*2}{b}=\frac{2}{8} ...(ii)

Subtract i from ii..
  \frac{9}{b}-\frac{4}{b}=\frac{3}{10}-\frac{2}{8} ..
 \frac{5}{b}=\frac{1}{20} ...
Or b=20*5=100..
Substitute in i to get value of m..
  \frac{2}{m}+\frac{3}{100}=\frac{1}{10} ..
  \frac{2}{m}=\frac{1}{10}-\frac{3}{100} ..
 \frac{2}{m}=\frac{7}{100} ..

We are looking for  \frac{2}{m}+\frac{1}{b}=7/100+1/100=8/100 ..
So time taken=100/8=12.5..

jxav · Answer

Let x be men and y boys
(2y+3x)/xy=1/10 
(3y+2x)/xy=1/8
Through elimination you will get
X=2/7y
Therefore 10/y=1/10
Y rate=1/100
X rate=3.5/100
So rate of 2x+y=8/100 or 1/12.5 per day. Therefore it will be completed in 12.5 day

Sent from my SM-G935F using  GMAT Club Forum mobile app

gracie · Answer

2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days . In how many days can 2 man and 1 boy do the work?

A. 15 
B. 18
C. 12.5 
D. 10 
E. 16

let m and b=rates for 1 man and 1 boy respectively
multiplying,
6m+9b=3/10 and
6m+4b=1/4
subtracting,
b=1/100
m=3.5/100
let d=days
d(7/100+1/100)=1
d=12.5 days
C

Chemerical71 · Answer

thank you for reply..I have been preparing for gmat since few months.For quant, i am doing manhattan, veritas and some gmat club solution mainly you , Bunnel after completing official sources.. I think this problem is consistent with gmat quant that's why i have posted. :-D

Suryangshu · Answer

10*(2M+3B)=8*(2M+16B)

we get 2M=7B.

We have to find 2M+1B= 7B+1B

putting this in the first equation we get-- replacing 2M by 7B
10B takes 10 days

Therefore 1B takes 100 days .

hence 8B takes 100/8 = 12.5 days

ScottTargetTestPrep · Answer

Let m = the rate of 1 man and b = the rate of 1 boy. We can create the equations:

2m + 3b = 1/10

and

3m + 2b = 1/8

Multiplying the first equation by -2 and the second by 3, we have:

-4m - 6b = -2/10

and

9m + 6b = 3/8

Adding the equations together, we have:

5m = 3/8 - 2/10

5m = 3/8 - 1/5

5m = 15/40 - 8/40

5m = 7/40

m = 7/200

Substitute m = 7/200 into 2m + 3b = 1/10, we have

2(7/200) + 3b = 1/10

7/100 + 3b = 1/10

3b = 10/100 - 7/100

3b = 3/100

b = 1/100

Letting x = the number of days needed to complete the work by 2 men and 1 boy, we have:

x(2(7/200) + 1/100) = 1

x(8/100) = 1

x = 100/8 = 12.5

Answer: C

Mo2men · Answer

Dear EMPOWERgmatRichC I tried to use same concept that you used in the following but ended up choosing wrong answer: https://gmatclub.com/forum/if-12-men-an ... l#p2137361 3 men and 2 boys would take a total of 8 days to complete a task. If we HALVE the number of workers again, we would again DOUBLE the amount of time needed to complete the task: 1.5 men and 1 boys would take a total of 16 days to complete a task. The question ask for 2 men and 1 boy. With using extra 0.5 man , it should take little less than 16, which is 15 in answer choices. It is the close number to 16. However, the answer is (12.5) Can you help please? Thanks

EMPOWERgmatRichC · Answer

Hi Mo2men,

You CAN use that same logic here, but you have to be a bit more focused on the 'impact' that each man has on the overall calculation/rate. The prompt gives us two pieces of data to work with:

2 men and 3 boys can do a piece of work in 10 days 
3 men and 2 boys can do the same work in 8 days

Consider the second piece of information relative to the first piece. We remove 1 boy from the job, so we LOSE that boy's work output. Adding 1 extra man 'makes up' for that loss AND then cuts the total down from 10 days to 8 days. Thus, that 1 man clearly has a big impact on the total time; by himself, he clearly represents MORE than a 2 day decrease in time needed to complete the job (again, he's also making up for the lost productivity from losing that 1 boy). Thus, 1/2 of a man would account for MORE than a 1 day decrease in time needed to complete the job.

You are absolutely correct that it would take 1.5 men and 1 boy a total of 16 days to complete the task. Adding that extra 1/2 of a man would decrease that total by MORE than 1 day though, so the correct answer CANNOT be 15 days (it has to be something less than that). Logically, 12.5 days makes far more sense.

GMAT assassins aren't born, they're made,
Rich

fskilnik · Answer

Let´s repeat EXACTLY the same approach we used here: https://gmatclub.com/forum/if-12-men-an ... 11-20.html \begin{array}{*{20}{c}} {\left( { ext{I}} ight)} \ {\left( {{ ext{II}}} ight)} \end{array}\,\,\begin{array}{*{20}{c}} {\left \,\,\, - \,\,{ ext{1}}\,\,{ ext{work}}\,\,\, - \,\,\,10\,\,\,{ ext{days}}} \ {\left \,\,\, - \,\,{ ext{1}}\,\,{ ext{work}}\,\,\, - \,\,\,8\,\,\,{ ext{days}}} \end{array} { ext{?}}\,\,\,{ ext{:}}\,\,\,\left \,\,\, - \,\,{ ext{1}}\,\,{ ext{work}}\,\,\, - \,\,\,?\,\,{ ext{days}} Let "task" be the fraction of this work that one man can do in 1 day, hence: 1\,{ ext{man}}\,\,\, - \,\,\,1\,\,{ ext{day}}\,\,\, - \,\,\,1\,\,\,{ ext{task}} Let k (k>0) be the fraction of the "task" defined above that one boy can do in 1 day (where k may be between 0 and 1, or equal to 1, or greater), hence: 1\,{ ext{boy}}\,\,\, - \,\,\,1\,\,{ ext{day}}\,\,\, - \,\,\,k\,\,\,{ ext{task}} Now the long-lasting benefit of this "structure": everything else becomes easy and "automatic": \left( { ext{I}} ight)\,\,\,\,\, \Rightarrow \,\,\,\,\left \,\, - \,\,{ ext{10}}\,\,{ ext{days}}\,\,\, - \,\,\,2 \cdot 10 \cdot 1 + 3 \cdot 10 \cdot k\,\,\,{ ext{tasks}}\,\, = \,\,\,1\,\,{ ext{work}}\, \left( {{ ext{II}}} ight)\,\,\, \Rightarrow \,\,\,\,\left \,\, - \,\,{ ext{8}}\,\,{ ext{days}}\,\,\, - \,\,3 \cdot 8 \cdot 1 + 2 \cdot 8 \cdot k\,\,\,{ ext{tasks}}\,\, = \,\,\,1\,\,{ ext{work}} Therefore: 20 + 30 \cdot k = 24 + 16 \cdot k\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,k = \frac{2}{7}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,1\,{ ext{work}}\,\,{ ext{ = }}\,\,\,{ ext{28}}\frac{4}{7}\,\,\,{ ext{tasks}} ?\,\,\,\,:\,\,\,\,\left \,\,\,\, - \,\,\,{ ext{1}}\,\,{ ext{day}}\,\,\, - \,\,\,2 \cdot 1 + 1 \cdot \frac{2}{7} = 2\frac{2}{7}\,\,{ ext{tasks}} And we finish in "high style", using UNITS CONTROL, one of the most powerful tools of our method: ?\,\,\, = \,\,\,28\frac{4}{7}\,\,\,{ ext{tasks}}\,\,\,\left( {\frac{{1\,\,{ ext{day}}}}{{2\frac{2}{7}\,\,{ ext{tasks}}}}\begin{array}{*{20}{c}} earrow \ earrow \end{array}} ight)\,\,\,\, = \,\,\,\,\frac{{7 \cdot 28 + 4}}{{2 \cdot 7 + 2}} = \frac{{200}}{{16}} = \frac{{80 + 16 + 4}}{8} = 12\frac{1}{2}\,\,\,\,\,\left Obs.: arrows indicate licit converter . This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.

ajtmatch · Answer

setup the equation as : work done by team 1 = work done by team 2
i.e. 10 days ( 2 men + 3 boys ) = 8 days ( 3 men + 2 boys)

10 (2m + 3b) = 8 (3m + 2b)
solving this equation gives you : 7b = 2m

now substitute this in the above equation of work done by team 1 : 
so 10 boys do a certain work in 10 days

now we are asked work done by 2 men + 1 boy; this is equivalent to work done by 8 boys

so, if 10boys take 10 days, then 8boys take x days?
solving for x, we get x = 12.5 days

Mo2men · Answer

Hi  ajtmatch

I liked your solution a lot but I do not understand one issue. what does the following abbreviations b & m reflect? Does it mean rate of man & rate of boy?

Thanks in advance

ajtmatch · Answer

Mo2men  - It is just an abbreviation for boys and men - it means the number of boys and the number of men.

so red it as - in 10 days, 2 mens and 3 boys can do a set of work. the same set of work can be one by 3men and 2 boys in 8 days.
so in short we equate the same set of works together and find eithet m or b

hope that helps

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

2 men and 3 boys can do a piece of work in 10 days while 3 men and 2

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

2 men and 3 boys can do a piece of work in 10 days while 3 men and 2

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