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Rates Question

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Rates Question

by Nisha1218 » Sun Sep 09, 2007 6:51 pm
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 tme it takes printer X to do the job working alone at its raste, 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

The OA is D, but I don't understand how. When I solved the problem I set up my equation as:

1/12 / [1/15 + 1/18] = 15/22...so why wouldn't the answer be C???

please help!
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by Neo2000 » Sun Sep 09, 2007 8:12 pm
You've found out for 1 hour's work and you need to find out for the full work.

Note that Yand Z together should take less time than X. Therefore their ratio should be smaller.
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by samirpandeyit62 » Sun Sep 09, 2007 8:18 pm
Hi Nisha,
The Q asks us to find ratio of time take and not rate, in your explanation you have taken ratios of their rates thats why u got the reciprocal of the ans

now time for machine x is 12 hrs

y & z combined i.e combine their rates so we have 1/15 +1/18

i.e 33/15X18
i.e 11/90
we know that R X t =w
hence combined time of y & z is 1/(11/90) i.e 90/11

so our ratio is 12/90/11 i.e 12X11/90

i.e 22/15

In such q's you can always double check the numerator & denominator of the fraction you get as the answer& ask your self a question that which one should be bigger.
Regards
Samir
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