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Company S produces two kinds of stereos: basic and deluxe.

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Company S produces two kinds of stereos: basic and deluxe. [#permalink] New post 14 Aug 2007, 01:49
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Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S 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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Re: PS - Deluxe [#permalink] New post 14 Aug 2007, 03:51
robinantony wrote:
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S 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


The answer is A i.e 7/17

Here is how I went.

Let the total # of Stereos : X
Basic Stereos = 2/3 X
Deluxe = 1/3 X

Time taken to make 1 Basic Stereo : T Hrs.
Time taken to make 1 Deluxe Stereo : 7/5T Hrs.


We are asked the fraction of time taken for Deluxe Stereo / Total # of stereos.
This is a common trap found in PS problems. In hurry we calculate the ration of time for Basic stereo to Deluxe stereo which I did.

Total Time taken for deluxe stereo : = 1/3X * 7/5 T
= 7/15 XT

Total time taken for all the stereos : ( 2/3XT) + (1/3X* 7/5T)
= ( 2/3XT) + (7/15 XT)
= (51/45) XT

Ratio : (7/15)/(17/15) = 7/17.
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 [#permalink] New post 14 Aug 2007, 04:52
i tried to pick #s for this, but didnt end up with the right answer. Can anyone see the flaw in my logic below:

let a total of 15 stereos be made --> therefore 10 are deluxe (2/3 of 15) and 5 are basic

Let a basic stereo take 1 hour to make --> therefore, a deluxe takes 7/5 hours, or 1.4 hours.

Total time for all 10 deluxe stereos are 10x(7/5) = 14 hours

Total time for all 5 basic stereos is 5x1 = 5 hours

The final ratio is 14/(14+5) = 14/19
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 [#permalink] New post 14 Aug 2007, 05:41
pmenon wrote:
i tried to pick #s for this, but didnt end up with the right answer. Can anyone see the flaw in my logic below:

let a total of 15 stereos be made --> therefore 10 are deluxe (2/3 of 15) and 5 are basic

Let a basic stereo take 1 hour to make --> therefore, a deluxe takes 7/5 hours, or 1.4 hours.

Total time for all 10 deluxe stereos are 10x(7/5) = 14 hours

Total time for all 5 basic stereos is 5x1 = 5 hours

The final ratio is 14/(14+5) = 14/19


The question says that 2/3 are basic NOT deluxe. :-D
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 [#permalink] New post 14 Aug 2007, 06:18
Assume # of Basic - 200
Assume # of Deluxe - 100

Now Time Assume Basic = 1 hour
Deluxe = 1.4 (or 7/5) of Basic = 1.4 hours

Time taken for Basic = 1 hr * 200 = 200
Time taken for Deluxe = 1.4 hr * 100 = 140

Ratio = 140/340 = 7/17 (A)

What is the OA?
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Re: PS - Deluxe [#permalink] New post 14 Aug 2007, 08:50
robinantony wrote:
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S 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


A.

Pick some numbers. Say Total produced = 9, Time to produce basic = 5.
We have 6 basic stereo and 3 deluxe stereo.
Time for each deluxe = (7/5)*5 = 7
Total time for deluxe = 7*3 = 21
Total time for both = 21+6*5 = 51.
Ans = 21/51 = 7/17
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 [#permalink] New post 14 Aug 2007, 19:05
Good going guys .. OA is A
  [#permalink] 14 Aug 2007, 19:05
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