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40 employees take 30 days,working at 8 hrs per day,to complete a task.

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Posts: 54

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Location: India
Concentration: Technology, General Management
WE: Information Technology (Computer Software)
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40 employees take 30 days,working at 8 hrs per day,to complete a task. [#permalink]

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New post 22 Nov 2017, 20:57
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A
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Difficulty:

  75% (hard)

Question Stats:

53% (02:00) correct 48% (02:34) wrong based on 40 sessions

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40 employees take 30 days,working at 8 hrs per day,to complete a task. 40 employees start the work but after 10 days,20 leave and are replaced by employees who are 1/2 as productive.How many hours per day should the new team work if the work has to be completed in the scheduled timeline?

1. 12
2. 20
3. 10.6
4. 6
5. 30

Source: Experts' Global
[Reveal] Spoiler: OA

Kudos [?]: 23 [0], given: 69

Expert Post
Math Expert
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D
Joined: 02 Aug 2009
Posts: 5352

Kudos [?]: 6132 [0], given: 121

Re: 40 employees take 30 days,working at 8 hrs per day,to complete a task. [#permalink]

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New post 23 Nov 2017, 01:16
Sangeeta2018 wrote:
40 employees take 30 days,working at 8 hrs per day,to complete a task. 40 employees start the work but after 10 days,20 leave and are replaced by employees who are 1/2 as productive.How many hours per day should the new team work if the work has to be completed in the scheduled timeline?

1. 12
2. 20
3. 10.6
4. 6
5. 30

Source: Experts' Global



Hi...

the TIMER shows all have gone wrong, so here is something which may help ..

two ways..
1) LOGICAL...
for the remaining days 20 are working for 8 hrs and other 20 will require to work for 16hrs..
so all 40 work for entire 8 hrs and then share the remaining work of 16-8=8 hrs..
these 8 hrs are of the speed of 1/2 productive and if we add full productive person, it is SAME as adding 2 half-productive persons..

so these 8 hrs is being shared by 1+2=3 person, MEANING each person requires to do \(\frac{8}{3}=2.66\) hrs
so the hours required is \(8+2.66=10.66\)
C
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6132 [0], given: 121

Expert Post
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Math Expert
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Joined: 02 Aug 2009
Posts: 5352

Kudos [?]: 6132 [1], given: 121

Re: 40 employees take 30 days,working at 8 hrs per day,to complete a task. [#permalink]

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New post 23 Nov 2017, 01:29
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Expert's post
Sangeeta2018 wrote:
40 employees take 30 days,working at 8 hrs per day,to complete a task. 40 employees start the work but after 10 days,20 leave and are replaced by employees who are 1/2 as productive.How many hours per day should the new team work if the work has to be completed in the scheduled timeline?

1. 12
2. 20
3. 10.6
4. 6
5. 30

Source: Experts' Global


PROPER method..
40 require \(30*8=240\) hrs, so 1 full productive will require \(240*40\)h.....1hr work = \(\frac{1}{240*40}\), so
1 hr work of half productive = \(\frac{1}{2}*\frac{1}{240*40}= \frac{1}{480*40}\)..
combined work of these two - set of productive+half productive = \(\frac{1}{240*40}+\frac{1}{480*40} = \frac{3}{480*40}\)
now there are 20 sets so 1 hr work of all 40 = \(20*\frac{3}{480*40}=\frac{1}{320}\)
so they require to work for 320 h for complete work but remaining work is \(\frac{30-10}{30}=\frac{2}{3}\), this will be completed in \(\frac{320*2}{3}\)
and these hours are equally spread across 20 days, so per day = \(\frac{320*2}{3*20}=\frac{32}{3} = 10.66\)

C
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6132 [1], given: 121

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Affiliations: CIPS
Joined: 01 Apr 2012
Posts: 66

Kudos [?]: 38 [0], given: 14

Location: United Arab Emirates
Concentration: General Management, Strategy
GMAT 1: 720 Q50 V38
WE: Supply Chain Management (Energy and Utilities)
Re: 40 employees take 30 days,working at 8 hrs per day,to complete a task. [#permalink]

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New post 23 Nov 2017, 02:33
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Total man hour required to complete the task = 40*30*8 = 9,600 man hours

Situation 1:
40 employees works 8 hour each for 10 days = 40*10*8 = 3,200 man hours completed

Situation 2:
20 employees (Set 1) replaced by another set of 20 employees (Set 2) who are half productive as Set 1

Here, the new group has been asked to complete the task within 30 days by working additional hours in a day. Remaining no. of days is 20.

Hence, the new group has to complete 6,400 man hours in 20 days. 20 employees in set 1 is twice productive as 20 employees in set 2. All employees will work for same no. of hours in the day.

20 employees in set 1 * 20 days * x days + 1/2 (20 employees in set 2 * 20 days * x days) = 6,400
400 x + 200 x = 6,400
600 x = 6,400
x = 10.66

So the answer is C

Kudos [?]: 38 [0], given: 14

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Re: 40 employees take 30 days,working at 8 hrs per day,to complete a task. [#permalink]

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New post 23 Nov 2017, 06:07
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Sangeeta2018 wrote:
40 employees take 30 days,working at 8 hrs per day,to complete a task. 40 employees start the work but after 10 days,20 leave and are replaced by employees who are 1/2 as productive.How many hours per day should the new team work if the work has to be completed in the scheduled timeline?

1. 12
2. 20
3. 10.6
4. 6
5. 30

Source: Experts' Global


Using Ratios:

When half the employees are exchanged for 1/2 as productive employees, the total rate of work becomes 3/4 of original.

Time taken = 4/3 of original for same work

Original time taken for remaining work would have been = 20*8 = 160 hrs
New time taken for remaining work = 160 * 4/3 hrs = 640/3 hrs
In 20 days, this implies 640/3*20 = 10.6 hrs per day

Answer (C)
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Kudos [?]: 18130 [4], given: 236

Re: 40 employees take 30 days,working at 8 hrs per day,to complete a task.   [#permalink] 23 Nov 2017, 06:07
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40 employees take 30 days,working at 8 hrs per day,to complete a task.

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