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Working alone, Printers X, Y, and Z can do a certain printin

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Working alone, Printers X, Y, and Z can do a certain printin [#permalink] New post   25 Jun 2020, 10:55
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Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?

(A) 4/11
(B) 1/2
(C) 15/22
(D) 22/15
(E) 11/4
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink] New post   25 Jun 2020, 10:55
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink] New post   25 Jun 2020, 19:18
Isn't the answer should be C?
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink] New post   26 Jun 2020, 05:18
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Carcass wrote:
Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?

(A) 4/11
(B) 1/2
(C) 15/22
(D) 22/15
(E) 11/4


----ASIDE-----------------------------------
For work questions, there are two useful rules:
Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job
Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job
Example: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.
---------------------------------------------------------

Let’s use these rules to solve the question. . . .

Printer Y takes 15 hours to complete a job. So, by rule #1, printer Y’s rate is 1/15 of the job per hour
Printer Z takes 18 hours to complete a job. So, by rule #1, printer Z’s rate is 1/18 of the job per hour
So, their combined rate per hour = 1/15 + 1/18
= 6/90 + 5/90
= 11/90
So, working together, printers Y and Z can complete the 11/90 of the job in one hour.
When we apply rule #2, we can conclude that, working together, printers Y and Z will complete the entire job in 90/11 hours.


What is the ratio of the time it takes printer X to do the job, working at its rate, to time it takes printers y and z to do the job?
So, (time for X to complete)/ (time for Y & Z to complete) = 12/(90/11)
= (12)(11/90)
= 22/15

Answer: D
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink] New post   26 Jun 2020, 05:18
esaktasynov wrote:
Isn't the answer should be C?


The answer is D.
See my post above.

Cheers,
Brent
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink] New post   26 Jun 2020, 19:01
Yeah, you're right, my mistake
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink] New post   21 Jul 2022, 00:47
Solution -

Work Formula = (A*B)/(A+B)

X = 12 hours to do a job
Y = 15 hours to do a job
Z = 18 hours to do a job


Together, Y and Z take => (15*18)/(15+18) hours to do the job.


=> 270/33 = 90/11 hours

The ratio of X to (Y and Z) = 12/(90/11) = 12(11)/90 = 132/90 = 22/15

Answer (D)
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