25 men reap a field in 20 days

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nhai2003: Senior | Next Rank: 100 Posts; Posts: 75; Joined: Tue Feb 10, 2009 11:30 pm

by nhai2003 » Fri Jul 10, 2009 10:55 pm

25 men reap a field in 20 days. when should 15 men leave the work if the whole field is to be reaped in 37-1/2 days after they leave the work?

I dont know where to start????

Thanks guys

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Source: Beat The GMAT — Problem Solving | Fri Jul 10, 2009 10:55 pm

scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

by scoobydooby » Fri Jul 10, 2009 11:08 pm

25 men take 20 days to complete a piece of work
=> 1 man takes 500 days to complete the piece of work.
=> 1 mans 1 day work=1/500 of the total work
=>10 mens 1 day work=1/500*10 of total work
=>10 mens 37.5 days work= 1/500*10*75/2=3/4 work

so 1/4 of the work must have been done by all 25 men before 15 of them left.

to do full work 25 men take 20 days
=>to do 1/4 work, 25 men will take 20/4=5 days.

so 15 men should leave after 5 days

(it looks clumsy, am sure theres a shorter/smarter solution somewhere)

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adam15: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Mon May 12, 2008 12:26 pm; Thanked: 3 times

by adam15 » Sun May 09, 2010 3:07 pm

I used this method to solve the problem.
but the result is different with the previous post could anyone tell me what is wrong?
let "t" be the time required by the first 25 men .
we know that 25 do the job in 20 days. their total production is 20*25
in the same way for the first part of job where 25 men were involved
25*t+(25-15)*((75/2)-t)=25*20
solving this equation yields
t=25/3.

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clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Sun May 09, 2010 3:24 pm

agree with answer 5-days
let it be total job-500,and rate of given worker=1, x-number of days they worked all together
25*1*x+(25-15)*1*37 1/2=500
x=5

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harshavardhanc: Legendary Member; Posts: 526; Joined: Sat Feb 21, 2009 11:47 pm; Location: India; Thanked: 68 times; GMAT Score:680

by harshavardhanc » Mon May 10, 2010 12:13 am

clock60 wrote:agree with answer 5-days
let it be total job-500,and rate of given worker=1, x-number of days they worked all together
25*1*x+(25-15)*1*37 1/2=500
x=5

it should be 5 days.

per person per day of work is 1/(25*20) = 1/500

see that the question says : 37.5 days after they leave the work. That means, for these 37.5 days, 10 workers are on the job who will do (37.5 *10)/500 = 3/4th of the total work. That means, 1/4th is already done by 25 people.

1/4 of the work will be done in 20/4 = 5 days.

HTH

in these

Regards,
Harsha

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rbansal: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Tue Jul 20, 2010 7:42 pmFollowed by: 1 member; Thanked: 1 times

by rbansal » Mon May 16, 2011 4:28 pm

Hello,

When you got that 1 man takes 500 days to complete the task. I understand you just did 25 x 20 but can you please explain the rational behind it. I am getting very stuck on why 1 man would take 500 days to complete the task .

Thank you,

RB

scoobydooby wrote:25 men take 20 days to complete a piece of work
=> 1 man takes 500 days to complete the piece of work.
=> 1 mans 1 day work=1/500 of the total work
=>10 mens 1 day work=1/500*10 of total work
=>10 mens 37.5 days work= 1/500*10*75/2=3/4 work

so 1/4 of the work must have been done by all 25 men before 15 of them left.

to do full work 25 men take 20 days
=>to do 1/4 work, 25 men will take 20/4=5 days.

so 15 men should leave after 5 days

(it looks clumsy, am sure theres a shorter/smarter solution somewhere)

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon May 16, 2011 4:57 pm

nhai2003 wrote:25 men reap a field in 20 days. when should 15 men leave the work if the whole field is to be reaped in 37-1/2 days after they leave the work?

I dont know where to start????

Thanks guys

Let rate per man = 1 unit per day.
Work completed by the 25 men each day = 25*1 = 25 units.
Over 20 days, total work = 20*25 = 500 units.

After the 15 men leave, rate for the 10 remaining men = 10 units per day.
Work completed by these 10 men over the last 37.5 days = 10 * 37.5 = 375 units.

Thus, work to be completed before the 15 men leave = 500-375 = 125 units.
Time for all 25 men to complete 125 units = w/r = 125/25 = 5 days.

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Sat Aug 20, 2011 6:04 am

GMATGuruNY wrote:
nhai2003 wrote:25 men reap a field in 20 days. when should 15 men leave the work if the whole field is to be reaped in 37-1/2 days after they leave the work?

I dont know where to start????

Thanks guys
Let rate per man = 1 unit per day.
Work completed by the 25 men each day = 25*1 = 25 units.
Over 20 days, total work = 20*25 = 500 units.

After the 15 men leave, rate for the 10 remaining men = 10 units per day.
Work completed by these 10 men over the last 37.5 days = 10 * 37.5 = 375 units.

Thus, work to be completed before the 15 men leave = 500-375 = 125 units.
Time for all 25 men to complete 125 units = w/r = 125/25 = 5 days.

Thanks GMATGuru, u made the simplest amd the effective solution!!

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