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# 50 equally efficient people were employed to complete a work in 90 day

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Math Expert
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50 equally efficient people were employed to complete a work in 90 day  [#permalink]

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05 Jul 2017, 00:40
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71% (01:39) correct 29% (01:31) wrong based on 151 sessions

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50 equally efficient people were employed to complete a work in 90 days. How long did it actually take to complete the work?

(1) After 30 days, the 50 people had completed only 25 percent of the work and worked at the same rate thereafter.
(2) Had 25 additional people, each having an efficiency equal to each of the initial 50 people, been employed after 30 days, the work would have been completed on time.

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Re: 50 equally efficient people were employed to complete a work in 90 day  [#permalink]

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05 Jul 2017, 02:22
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Bunuel wrote:
50 equally efficient people were employed to complete a work in 90 days. How long did it actually take to complete the work?

(1) After 30 days, the 50 people had completed only 25 percent of the work and worked at the same rate thereafter.
(2) Had 25 additional people, each having an efficiency equal to each of the initial 50 people, been employed after 30 days, the work would have been completed on time.

Hi...
Basically we require the working efficiency of each...

Let's see the statements..
I...
50 of them complete 25% in 30 days..
So 50 of them will complete 25*4% in 30*4=120days..
Sufficient

II...
Working days.. 50*90+(25)(90-30)...
So for 50 of them, $$\frac{50*90+25*60}{50}=\frac{50*(90+30)}{50}=120$$
Suff

D
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Re: 50 equally efficient people were employed to complete a work in 90 day  [#permalink]

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05 Jul 2017, 03:52
50 equally efficient people were employed to complete a work in 90 days. How long did it actually take to complete the work?

(1) After 30 days, the 50 people had completed only 25 percent of the work and worked at the same rate thereafter.
(2) Had 25 additional people, each having an efficiency equal to each of the initial 50 people, been employed after 30 days, the work would have been completed on time.

Solution:

Statement 1: This statement clearly says that the entire work will be completed by 120 days. Sufficient.

Statement 2: This statement says, 50 people worked for 30 days. And 75 people worked for 60 days to complete the work on time. So if 50 people had worked instead of 75,the work would have been completed after 120 days. Sufficient.

Therefore the answer is Option D.
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Joined: 03 Jun 2017
Posts: 7
Re: 50 equally efficient people were employed to complete a work in 90 day  [#permalink]

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15 Jul 2017, 20:30
It is obviously D, but I am getting 135 for (b) when doing the calculation the following way:
Initial rate per worker 1/(90*50), so by 25 workers working for 60 days at that rate, they would complete 1/3 of the job: 60 * (25/4500) = 1/3
therefore 50 workers working for 90 days would work at the rate of 135 to complete 2/3 of the job. 90 * X = 2/3 ---> X =135.
What am I doing wrong?
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Joined: 02 Aug 2009
Posts: 7558
Re: 50 equally efficient people were employed to complete a work in 90 day  [#permalink]

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15 Jul 2017, 21:05
1
Milano2017 wrote:
It is obviously D, but I am getting 135 for (b) when doing the calculation the following way:
Initial rate per worker 1/(90*50), so by 25 workers working for 60 days at that rate, they would complete 1/3 of the job: 60 * (25/4500) = 1/3
therefore 50 workers working for 90 days would work at the rate of 135 to complete 2/3 of the job. 90 * X = 2/3 ---> X =135.
What am I doing wrong?

hi..

You are goi wrong in THAT you are taking initial rate as $$\frac{1}{90*50}$$, which is not the case
If that was the case, Q is not required as then answer would be 90.
They were employed to complete in 90 days but their efficiency was less.

Another simpler way to look at the Q apart from the way I had mentioned in above post
ONLY extra work is 25 for 60 days.. SAME as 25*2 for 60/2 days that is 50 men doing for 30 days.
so in a way those 50 have to work for 30 days more if no extra strength is there, thus answer is 90+30=120

hope it helps
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Re: 50 equally efficient people were employed to complete a work in 90 day  [#permalink]

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16 Jul 2017, 00:25
chetan2u wrote:
Bunuel wrote:
50 equally efficient people were employed to complete a work in 90 days. How long did it actually take to complete the work?

(1) After 30 days, the 50 people had completed only 25 percent of the work and worked at the same rate thereafter.
(2) Had 25 additional people, each having an efficiency equal to each of the initial 50 people, been employed after 30 days, the work would have been completed on time.

II...
Working days.. 50*90+(25)(90-30)...
So for 50 of them, $$\frac{50*90+25*60}{50}=\frac{50*(90+30)}{50}=120$$

why have you divided it by 50? but total people were 75
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Re: 50 equally efficient people were employed to complete a work in 90 day  [#permalink]

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16 Jul 2017, 06:31
rocko911 wrote:
chetan2u wrote:
Bunuel wrote:
50 equally efficient people were employed to complete a work in 90 days. How long did it actually take to complete the work?

(1) After 30 days, the 50 people had completed only 25 percent of the work and worked at the same rate thereafter.
(2) Had 25 additional people, each having an efficiency equal to each of the initial 50 people, been employed after 30 days, the work would have been completed on time.

II...
Working days.. 50*90+(25)(90-30)...
So for 50 of them, $$\frac{50*90+25*60}{50}=\frac{50*(90+30)}{50}=120$$

why have you divided it by 50? but total people were 75

Because the question is asking you how long would it take 50 workers to finish the job by themselves. So the formula is total job/total people. If you divide by 75, then you get number of days it would take 75 people to finish the job, which is not the question asked. Hope this helps.
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Posts: 7
Re: 50 equally efficient people were employed to complete a work in 90 day  [#permalink]

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16 Jul 2017, 06:33
chetan2u wrote:
Milano2017 wrote:
It is obviously D, but I am getting 135 for (b) when doing the calculation the following way:
Initial rate per worker 1/(90*50), so by 25 workers working for 60 days at that rate, they would complete 1/3 of the job: 60 * (25/4500) = 1/3
therefore 50 workers working for 90 days would work at the rate of 135 to complete 2/3 of the job. 90 * X = 2/3 ---> X =135.
What am I doing wrong?

hi..

You are goi wrong in THAT you are taking initial rate as $$\frac{1}{90*50}$$, which is not the case
If that was the case, Q is not required as then answer would be 90.
They were employed to complete in 90 days but their efficiency was less.

Another simpler way to look at the Q apart from the way I had mentioned in above post
ONLY extra work is 25 for 60 days.. SAME as 25*2 for 60/2 days that is 50 men doing for 30 days.
so in a way those 50 have to work for 30 days more if no extra strength is there, thus answer is 90+30=120

hope it helps

Ok now it makes sense. I misread the question. I understood that (b) is telling me that 25 workers worked the initial rate of 50 workers (the rate they were supposed to work to be able to finish the job in 90 days), and not the actual rate of 50 workers. Thanks for your help. Kudos to you.
Re: 50 equally efficient people were employed to complete a work in 90 day   [#permalink] 16 Jul 2017, 06:33
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