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Stereos

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by alex.gellatly » Mon May 21, 2012 7:06 pm
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company X last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?

A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2

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by Anurag@Gurome » Mon May 21, 2012 7:15 pm
alex.gellatly wrote:Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company X last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?

A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2

Thanks
Let us assume that total stereos = 15
Then number of basic stereos = 2/3 of total = (2/3) * 15 = 10
and Number of deluxe stereos = 1/3 of total = (1/3) * 15 = 5

If time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units.
Total time for Basic = 10 * 1 = 10
Total time for Deluxe = 5 * (7/5) = 7
So, total time for both = 10 + 7 = 17
Therefore, deluxe/total = [spoiler]7/17[/spoiler]

The correct answer is A.
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by sam2304 » Mon May 21, 2012 7:30 pm
Given 2/3 were basic and rest were deluxe stereos.

Consider the number as it is, 2 basic and 1 deluxe stereo.

it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo.

Time taken for basic be b, then d = 7b/5
= d/b => 7/5

Time for basic is 5 hours and deluxe is 7 hours. We considered 2 deluxe and 1 basic stereo.

Total time for basic = 10 hours
total time for deluxe = 7 hours
Deluxe stereo hours/total hours = 7/(10+7)

IMO A.
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by Scott@TargetTestPrep » Thu Jan 11, 2018 2:08 pm
alex.gellatly wrote:Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company X last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?

A. 7/17
B. 14/31
C. 7/15
D. 17/35
E. 1/2
We can let the total number of stereos = 12; thus, 8 are basic and 4 are deluxe.

We can let the number of hours to produce a basic stereo = 10, and thus it takes 7/5 x 10 = 14 hours to produce a deluxe stereo.

So the number of hours to produce the deluxe stereos last month was 14 x 4 = 56 hours, and the number of hours to produce the basic stereos was 8 x 10 = 80 hours.

Thus, the time to make the deluxe stereos was 56/(56 + 80) = 56/136 = 7/17 of the total time taken to produce all stereos.

Answer: A
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