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Three machines operating independently, simultaneously, and

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CAMANISHPARMAR
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Re: Three machines operating independently, simultaneously, and [#permalink] New post   08 Jul 2019, 00:01
kiseki wrote:
Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?

A. 6
B. 9
C. 12
D. 27
E. 48


Read carefully: We need to find out "in how many fewer hours of simultaneous operation could the production order be fulfilled?"

The Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours.

Four machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 27 hours.

Hence 36-27=9 fewer hours (option B is the correct ans)
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Re: Three machines operating independently, simultaneously, and [#permalink] New post   13 Jul 2019, 06:59
3 machines will do it in 36 hours. So 4 machines will do it in 36/4 = 9 hours less
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Re: Three machines operating independently, simultaneously, and [#permalink] New post   05 Oct 2019, 17:06
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kiseki wrote:
Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?

A. 6
B. 9
C. 12
D. 27
E. 48


If 3 machines working together take 36 hours to complete a job, then 1 machine by itself will take 3 times as long, or 3 x 36 = 108 hours to complete the same job. However, 4 machines working together will take ¼ as long, or ¼ x 108 = 27 hours to complete the job. Therefore, 1 additional machine (added to 3 machines) will save 36 - 27 = 9 hours.

Answer: B
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Re: Three machines operating independently, simultaneously, and [#permalink] New post   26 Aug 2021, 00:23
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There are multiple approaches to solve this Question. Let’s try a simple approach.
Since it is given that each machine work at the same constant rate, we can assume that each machine will do 1 order in 1 hour.
No of orders done by 1 machine in 36 hours = 36 orders
Total no of orders done by 3 machines in 36 hours = 36* 3 orders
If we add one more machine, then there is a total of 4 machines
Time taken by 4 machines to do the same no of orders = 36*3/4 = 9* 3 = 27 hours.

So four machines working together can fulfill the orders in 9 hours less time.

Option B is the answer.

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Re: Three machines operating independently, simultaneously, and [#permalink] New post   12 Oct 2021, 07:26
1/x + 1/x + 1/x= 1/36

x= 36*3

new time (36*3)/4 = 27

Difference = 36-24= 9.

Option B
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Re: Three machines operating independently, simultaneously, and [#permalink] New post   11 Dec 2023, 19:05
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Re: Three machines operating independently, simultaneously, and [#permalink]
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