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Working alone, printers X, Y, and Z can do a certain [#permalink]
27 Jan 2007, 15:12

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Difficulty:

55% (hard)

Question Stats:

62% (02:22) correct
38% (01:26) wrong based on 141 sessions

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 ?

This mean that Machine Y and Z can finish 11/90 job in one hour

So how long will will take for Machine X to finish 11/90 job? Rate(X) = 12 hour/job
Time(x) to do 11/90 job = 11/90 job x 12 hour/job = 11 x 12 /90 = 44/30 = 22/15 hours

Re: Working alone, printers X, Y, and Z can do a certain [#permalink]
24 Jan 2013, 03:23

Thanks for your fast reply Karishma,

As this was still difficult for me to understand, I have created an easy example for better understanding. Let’s assume all printers take 12 hours. So printer Y and Z are doing the same job as printer X twice as fast.

X = 1/12 (job/hours) Y = 1/12 (job/hours) Z = 1/12 (job/hours) Y+Z = 2/12 = 1/6 (job/hours)

X : (Y+Z) = 1 : 2 => This ratio refers to the output.

Regarding Time Taken, X makes in 12 hours 1 job and Y+Z are doing in 6 hours 1 job. So what you are saying is that we are comparing the hours and not the jobs right? And therefore the ratio of X : Y is 12 : 6, which is 2 : 1.

Summarizing both steps: X : (Y+Z) = (1/12) : (2/12) = 1 : 2 => This ratio refers to the output. X : (Y+Z) = (1/12) : (1/6) = 12: 6 = 2 : 1 => This ratio refers to the time

Referring to my example again: X = 12 hours Y+Z = 6 hours Ratio is not 12 : 6 or 2 : 1 because time taken is inverse to rate? Instead the Ratio is (1/12) : (1/6) = (6/12) = 1 : 2

Actually this TIME-IS-INVERSE-APPROACH is quite difficult to understand. I can apply it but still it is difficult to understand. May be it is just easier to divide 2 fractions. (Divide Y+Z by X).

Last edited by leventg on 24 Jan 2013, 05:04, edited 1 time in total.

Re: Working alone, printers X, Y, and Z can do a certain [#permalink]
24 Jan 2013, 03:40

Expert's post

leventg wrote:

Thanks for your fast reply Karishma,

As this was still difficult for me to understand, I have created an easy example for better understanding. Let’s assume all printers take 12 hours. So printer Y and Z are doing the same job as printer X twice as fast.

X = 1/12 (job/hours) Y = 1/12 (job/hours) Z = 1/12 (job/hours) Y+Z = 2/12 = 1/6 (job/hours)

X : (Y+Z) = 1 : 2 => This ratio refers to the output.

Regarding Time Taken, X makes in 12 hours 1 job and Y+Z are doing in 6 hours 1 job. So what you are saying is that we are comparing the hours and not the jobs right? And therefore the ratio of X : Y is 12 : 6, which is 2 : 1.

Summarizing both steps: X : (Y+Z) = (1/12) : (2/12) = 1 : 2 => This ratio refers to the output. X : (Y+Z) = (1/12) : (1/6) = 2 : 1 => This ratio refers to the time.

Referring to my example again: X = 12 hours Y+Z = 6 hours Ratio is not 12 : 6 or 2 : 1 because time taken is inverse to rate? Instead the Ratio is (1/12) : (1/6) = (6/12) = 1 : 2

Actually this TIME-IS-INVERSE-APPROACH is quite difficult to understand. I can apply it but still it is difficult to understand. May be it is just easier to divide 2 fractions. (Divide Y+Z by X).