Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 19 Jul 2019, 16:00

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
G
Joined: 09 Jan 2016
Posts: 103
GPA: 3.4
WE: General Management (Human Resources)
2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

Show Tags

New post Updated on: 13 Mar 2019, 04:09
3
1
27
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

69% (03:08) correct 31% (03:09) wrong based on 161 sessions

HideShow timer Statistics


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

Originally posted by Chemerical71 on 16 Apr 2017, 06:20.
Last edited by Bunuel on 13 Mar 2019, 04:09, edited 1 time in total.
Updated.
Most Helpful Expert Reply
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 2943
Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

Show Tags

New post 16 Apr 2017, 21:49
6
8
Chemerical71 wrote:
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


    • 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 :)

Image
_________________
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7764
Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

Show Tags

New post 16 Apr 2017, 09:53
2
2
Chemerical71 wrote:
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



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..
_________________
General Discussion
Current Student
avatar
S
Joined: 09 Mar 2017
Posts: 91
Location: Netherlands
Concentration: General Management, Finance
GMAT 1: 690 Q45 V40
Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

Show Tags

New post 16 Apr 2017, 12:45
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
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1206
Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

Show Tags

New post 16 Apr 2017, 14:10
1
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
Manager
Manager
User avatar
G
Joined: 09 Jan 2016
Posts: 103
GPA: 3.4
WE: General Management (Human Resources)
Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

Show Tags

New post 16 Apr 2017, 23:58
chetan2u wrote:
Chemerical71 wrote:
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



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..
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
Manager
Manager
avatar
B
Joined: 20 Jun 2016
Posts: 59
Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

Show Tags

New post 11 Sep 2018, 07:52
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
_________________
Life is a challenge face it.
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6937
Location: United States (CA)
Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

Show Tags

New post 14 Sep 2018, 17:47
Chemerical71 wrote:
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 = 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
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

SVP
SVP
User avatar
V
Joined: 26 Mar 2013
Posts: 2284
Reviews Badge CAT Tests
Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

Show Tags

New post 24 Sep 2018, 04:05
Chemerical71 wrote:
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


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
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14590
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

Show Tags

New post 24 Sep 2018, 11:25
1
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
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 937
Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

Show Tags

New post 24 Sep 2018, 12:33
Chemerical71 wrote:
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´s repeat EXACTLY the same approach we used here: https://gmatclub.com/forum/if-12-men-an ... 11-20.html

\(\begin{array}{*{20}{c}}
{\left( {\text{I}} \right)} \\
{\left( {{\text{II}}} \right)}
\end{array}\,\,\begin{array}{*{20}{c}}
{\left[ {2\,\,{\text{men}}\,\,\, \cup \,\,\,{\text{3}}\,\,{\text{boys}}} \right]\,\,\, - \,\,{\text{1}}\,\,{\text{work}}\,\,\, - \,\,\,10\,\,\,{\text{days}}} \\
{\left[ {3\,\,{\text{men}}\,\,\, \cup \,\,\,{\text{2}}\,\,{\text{boys}}} \right]\,\,\, - \,\,{\text{1}}\,\,{\text{work}}\,\,\, - \,\,\,8\,\,\,{\text{days}}}
\end{array}\)

\({\text{?}}\,\,\,{\text{:}}\,\,\,\left[ {2\,\,{\text{men}}\,\,\, \cup \,\,\,1\,\,{\text{boy}}} \right]\,\,\, - \,\,{\text{1}}\,\,{\text{work}}\,\,\, - \,\,\,?\,\,{\text{days}}\)


Let "task" be the fraction of this work that one man can do in 1 day, hence:

\(1\,{\text{man}}\,\,\, - \,\,\,1\,\,{\text{day}}\,\,\, - \,\,\,1\,\,\,{\text{task}}\)

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:

\(1\,{\text{boy}}\,\,\, - \,\,\,1\,\,{\text{day}}\,\,\, - \,\,\,k\,\,\,{\text{task}}\)


Now the long-lasting benefit of this "structure": everything else becomes easy and "automatic":

\(\left( {\text{I}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\left[ {2\,\,{\text{men}}\,\,\, \cup \,\,\,{\text{3}}\,\,{\text{boys}}} \right]\,\, - \,\,{\text{10}}\,\,{\text{days}}\,\,\, - \,\,\,2 \cdot 10 \cdot 1 + 3 \cdot 10 \cdot k\,\,\,{\text{tasks}}\,\, = \,\,\,1\,\,{\text{work}}\,\)

\(\left( {{\text{II}}} \right)\,\,\, \Rightarrow \,\,\,\,\left[ {3\,\,{\text{men}}\,\,\, \cup \,\,\,{\text{2}}\,\,{\text{boys}}} \right]\,\, - \,\,{\text{8}}\,\,{\text{days}}\,\,\, - \,\,3 \cdot 8 \cdot 1 + 2 \cdot 8 \cdot k\,\,\,{\text{tasks}}\,\, = \,\,\,1\,\,{\text{work}}\)

Therefore: \(20 + 30 \cdot k = 24 + 16 \cdot k\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,k = \frac{2}{7}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,1\,{\text{work}}\,\,{\text{ = }}\,\,\,{\text{28}}\frac{4}{7}\,\,\,{\text{tasks}}\)


\(?\,\,\,\,:\,\,\,\,\left[ {2\,\,{\text{men}}\,\,\, \cup \,\,\,1\,\,{\text{boy}}} \right]\,\,\,\, - \,\,\,{\text{1}}\,\,{\text{day}}\,\,\, - \,\,\,2 \cdot 1 + 1 \cdot \frac{2}{7} = 2\frac{2}{7}\,\,{\text{tasks}}\)

And we finish in "high style", using UNITS CONTROL, one of the most powerful tools of our method:

\(?\,\,\, = \,\,\,28\frac{4}{7}\,\,\,{\text{tasks}}\,\,\,\left( {\frac{{1\,\,{\text{day}}}}{{2\frac{2}{7}\,\,{\text{tasks}}}}\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\, = \,\,\,\,\frac{{7 \cdot 28 + 4}}{{2 \cdot 7 + 2}} = \frac{{200}}{{16}} = \frac{{80 + 16 + 4}}{8} = 12\frac{1}{2}\,\,\,\,\,\left[ {{\text{days}}} \right]\)
Obs.: arrows indicate licit converter.


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Intern
Intern
avatar
B
Joined: 04 May 2018
Posts: 35
Location: India
GMAT 1: 650 Q46 V34
GMAT 2: 680 Q49 V34
GPA: 3.3
Premium Member
Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

Show Tags

New post 13 Feb 2019, 03:20
1
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
SVP
SVP
User avatar
V
Joined: 26 Mar 2013
Posts: 2284
Reviews Badge CAT Tests
Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

Show Tags

New post 13 Feb 2019, 05:47
ajtmatch wrote:
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


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
Intern
Intern
avatar
B
Joined: 04 May 2018
Posts: 35
Location: India
GMAT 1: 650 Q46 V34
GMAT 2: 680 Q49 V34
GPA: 3.3
Premium Member
Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

Show Tags

New post 13 Feb 2019, 19:15
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

Mo2men wrote:
ajtmatch wrote:
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


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
GMAT Club Bot
Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2   [#permalink] 13 Feb 2019, 19:15
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne