Confused with this sum

[Architj]

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

[GMATGuruNY]

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

Let the job = 180 units.
Rate for X= w/t = 180/12 = 15 units per hour.
Rate for Y = w/t = 180/15 = 12 units per hour.
Rate for Z = w/t = 180/18 = 10 units per hour.
Combined rate for Y and Z = 12+10 = 22 units per hour.

Rate and time are RECIPROCALS.
Since (rate for X)/(rate for Y and X) = 15:22, (time for X)/(time for Y and Z) = 22:15.

The correct answer is D.

[coolhabhi]

[quote="Architj"]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[/quote]

Since Printer X completes a job in 12 hours, it means it would complete 1/12th part in 1 hour
Similarly if Printer Y & Z work together then they will complete [(1/15) + (1/18)]th part in 1 hour i.e 11/90th part in 1 hour
so ratio of rates is (1/12) : (11/90) => 15/22
=> ratio of the time is 22/15
Answer [spoiler]D[/spoiler]

[Brent@GMATPrepNow]

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

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)
= [spoiler]22/15[/spoiler]
= D

Cheers,
Brent

[[email protected]]

Hi Architj,

This question can be solved by using the Work Formula:

Work = (A)(B)/(A+B) where A and B are the individual times required to complete a job.

We're given the respective times that it takes 3 machines to complete a print job:

Machine X = 12 hours
Machine Y = 15 hours
Machine Z = 18 hours

We're then asked for the ratio of X (working alone) to Y and Z (working together).

Using the Work Formula, we can figure out how long it takes Y and Z working together....

(15)(18)/(15+18) = 270/33 = 90/11 hours to complete the job

Since Machine X can do the job in 12 hours, the final ratio is....

12/(90/11)

This becomes....
(12)(11)/90 = 44/30 = 22/15

Final Answer: D

GMAT assassins aren't born, they're made,
Rich