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A work crew of 4 Men takes 5 days to complete one-half of a

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A work crew of 4 Men takes 5 days to complete one-half of a [#permalink] New post 13 Mar 2010, 08:24
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70% (01:53) correct 30% (01:08) wrong based on 76 sessions
A work crew of 4 Men takes 5 days to complete one-half of a job. If 6 men are then added to the crew and the men continue to work at the same rate, how many days will it take the enlarged crew to do the rest of the job?

A. 2
B. 3
C. 3 1/3
D. 4
E. 4 4/5
[Reveal] Spoiler: OA

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Last edited by Bunuel on 29 Sep 2013, 08:05, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Multiple persons doing a job [#permalink] New post 13 Mar 2010, 09:45
I think Answer is 2 days..

Suppose 1 man can do work in X days..

so 4 men will do in ..

4/X=1/5*1/2 as half job is done

X=40

now 6 more are added then

10/40=1/2*1/d for remaining half job

d=2 Number of days
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Re: Multiple persons doing a job [#permalink] New post 13 Mar 2010, 11:08
Hussain15 wrote:
A work crew of 4 Men takes 5 days to complete one-half of a job. If 6 men are then added to the crew and the men continue to work at the same rate, how many days will it take the enlarged crew to do the rest of the job?

A) 2
B) 3
C) 3 1/3
D) 4
E) 4 4/5

Well, I have problems in solving a work problem involving multiple persons doing a same job, like this one.

Kindly share your answers with explanations.


Total work in men-days unit = 4*5*2
Now work done by 4 men = 4*5
6 people added and let say they take d days to complete the rest half = 10d
4*5*2 = 4*5 + 10d
=> d = 2
So a is the answer
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Re: Multiple persons doing a job [#permalink] New post 15 Mar 2010, 07:18
Hussain15 wrote:
Correct both of you. Thanks.


I probably missed something here...here is my logic

=>In one day the 4 guys do 10% of the job (half div by 5 days )

=>each of the 4 men does 2,5% of the job per day
=>if they are 10 that makes 25% of the job per day
=>so I come to 4 days needed

can someone help track the issue in my approach?

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Re: Multiple persons doing a job [#permalink] New post 13 Apr 2010, 21:35
defoue wrote:
Hussain15 wrote:
Correct both of you. Thanks.


I probably missed something here...here is my logic

=>In one day the 4 guys do 10% of the job (half div by 5 days )

=>each of the 4 men does 2,5% of the job per day
=>if they are 10 that makes 25% of the job per day
=>so I come to 4 days needed

can someone help track the issue in my approach?

Rgds


You almost got it. What you missed is the fact that half the job is already done, and that the question asks you to find how much time it will take 10 men to do the remaining half of the job.
Your answer of 4 days is for the complete job.
Therefore 10 men will take 2 days to complete half of the job.

Please let me know if you need further explanation.
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Re: Multiple persons doing a job [#permalink] New post 16 Apr 2010, 12:23
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4 men <==> 10 days to complete the job as they have completed 1/2 in 5 days.
1 man <==> 40 days
i.e. 1 day work of a man = 1/40

now 6 more are added so total men = 10

since 1 day work of man = 1/40
=> 1 day work of 10 men = 1/40 * 10 = 1/4

so number of days = (1/2)/(1/4) = 2
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Re: Multiple persons doing a job [#permalink] New post 16 Apr 2010, 13:49
4men...5 days....0.5 work
10 men...x days....0.5 work

x (less days) = (4/10) * 5 days = 2 days.
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Re: Multiple persons doing a job [#permalink] New post 19 Apr 2010, 06:07
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Sortcut Formula is :

W1 W2
--------- = --------
D1 * N1 D2 * N2

W1 = W/2
N1 = 4
D1 = 5

W2 = W/2
N2 = 10 (4 Men + 6 Men)
D2 = ?

Substituting them will give you the answer.

ALSO : This question does not need a calculation as half of the work is done in 5 days by 4 men so rest half of the work will be done by 10 men will be less than half of 5 days and there is only one option in answers the is less than 2.5 days which is 2.
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Re: Multiple persons doing a job [#permalink] New post 28 Sep 2013, 09:30
Rate(4) =1/10
Rate(1) =1/40
Rate(10)=1/4

Work Done =1/2
Work Left = 1/2

Rate * Time = Work

1/4 * Time = 1/2

Time =2 days !
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Re: A work crew of 4 Men takes 5 days to complete one-half of a [#permalink] New post 29 Sep 2013, 08:13
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Hussain15 wrote:
A work crew of 4 Men takes 5 days to complete one-half of a job. If 6 men are then added to the crew and the men continue to work at the same rate, how many days will it take the enlarged crew to do the rest of the job?

A. 2
B. 3
C. 3 1/3
D. 4
E. 4 4/5


4 Men takes 5 days to complete one-half of a job --> 1/2 of the job consists of 4*5=20 units (1 man does 1 unit of work in 1 day).

To complete the remaining 20 units of work 4 + 6 = 10 men will need 20/10 = 2 days.

Answer: A.
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Re: A work crew of 4 Men takes 5 days to complete one-half of a   [#permalink] 29 Sep 2013, 08:13
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