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

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22 Nov 2017, 20:57

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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?

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?

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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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?

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 = \(\frac{320*2}{3*20}=\frac{32}{3} = 10.66\)

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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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

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?

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