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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 08 Sep 2010, 10:20
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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
[Reveal] Spoiler: OA
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Re: Stereo problem [#permalink] New post 08 Sep 2010, 11:25
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udaymathapati wrote:
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 32 were basic and the rest were deluxe. If it takes 57 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


udaymathapati please do check the questions when posting. Correct question is as follows:

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

# of basic stereos was 2/3 of total and # of deluxe stereos was 1/3 of total, let's assume total=15, then Basic=10 and Deluxe=5.

Now, 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 would be 10*1=10 and total time for Deluxe would be 5*7/5=7 --> total time for both of them would be 10+7=17 --> deluxe/total=7/17.

Answer: A.
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Re: Stereo problem [#permalink] New post 08 Sep 2010, 11:29
Bunuel wrote:
udaymathapati wrote:
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 32 were basic and the rest were deluxe. If it takes 57 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


udaymathapati please do check the questions when posting. Correct question is as follows:

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

# of basic stereos was 2/3 of total and # of deluxe stereos was 1/3 of total, let's assume total=15, then Basic=10 and Deluxe=5.

Now, 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 would be 10*1=10 and total time for Deluxe would be 5*7/5=7 --> total time for both of them would be 10+7=17 --> deluxe/total=7/17.

Answer: A.


OHHHHHHHHHH Goshhhhhhhhhhhhhhhhhh Thanx a lot bunuel u were a savior..I would have spent my whole night solving this question i tried every possible way to find out solution...trust me the only last thing i was trying to find out how can i make this question correct from the answer choices.. :((

where did u find this question BTW?
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Re: Stereo problem [#permalink] New post 08 Sep 2010, 12:05
wow thanks! i tried to answer before but i couldnt because of unknowns. Bunnel beat me to it yet again :(
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Re: Stereo problem [#permalink] New post 08 Sep 2010, 14:45
Or if you prefer variables:

Let B be # of basic units and D be # of deluxe units and T(B) and T(D) be the respective production time.

B = 2D => D = B/2
T(D) = 7/5 x T(B)

D x T(D)/[(B x T(B) + D x T(D)]
= (B/2 x 7/5 x T(B))/[(B x T(B)) + B/2 x 7/5 x T(B))
= B x T(B) x (7/10)/[B x T(B) x (7/10 + 1)]
= 7/17
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Re: please help (company problem) [#permalink] New post 15 Nov 2010, 07:44
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SoniaSaini 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

I'm not getting how to solve it?
Please help.
Thanks a lot in advance.


The easiest way would be to assume values:
2/3 were basic, 1/3 were deluxe.
So assume 2 basic and 1 deluxe were produced.
If 5 hrs are needed to make a basic one, 7 hrs are needed to make a deluxe stereo.
Total hrs needed = 2 x 5 + 1 x 7 = 17 out of which 7 were used for deluxe stereo.
So 7/17 is the fraction of time spent in making the deluxe stereo.

Since everything is in fraction terms, i.e. one related to the other, it is pretty easy to assume values and solve. Same should be done when everything is in percentage terms.
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Re: Stereo problem [#permalink] New post 15 Nov 2010, 08:16
Thanks a lot for replying.

Bunuel,
appreciate your help.
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Re: Stereo problem [#permalink] New post 15 Jan 2011, 05:41
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we have the following ratios:
basic (b) : deluxe (d)
2 units : 1 unit
5 hrs : 7 hrs

total time taken to produce basic units = 2*5= 10hrs
total time taken to produce deluxe units = 1*7= 7hrs
total time taken = 10+7= 17hrs

so, 7/17

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Re: Stereo problem [#permalink] New post 18 Jul 2011, 05:37
Hai Karishma,

I have a trouble in calculating the time to produce one deluxe stereo. How did you get value 7. I try to calculate in the following manner. (5+5*7/5) . I know it is wrong. Please explain. where i went wrong
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Re: Stereo problem [#permalink] New post 18 Jul 2011, 20:19
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Hai Karishma,

I have a trouble in calculating the time to produce one deluxe stereo. How did you get value 7. I try to calculate in the following manner. (5+5*7/5) . I know it is wrong. Please explain. where i went wrong


I have assumed values here. Let's look at the question again.


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.

Ok so if a total of 3 stereos were produced, 2 were basic (because 2/3 are basic) and 1 was deluxe

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

It takes 7/5 as many hours.. So if it takes 5 hrs to produce a basic one, a deluxe one takes 7/5 * 5 = 7 hrs. The question says 7/5 as many hours so you just multiply the hours it takes to produce a basic one with 7/5. Think of it this way - if the question said, "it takes twice as many hours as it takes to produce a basic one..." would you just multiply by 2 or would you follow your method?

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?


Hours taken for 2 basic stereos = 2*5
Hours taken for 1 deluxe = 1*7
Total hours = 17
Required fraction = 7/17
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Re: Stereo problem [#permalink] New post 20 Jul 2011, 11:58
Thanks a lot for your explanation
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Re: Stereo problem [#permalink] New post 05 Aug 2011, 10:29
B/D = 2/1

lets say time required to produce 1 Basic stereo = 5 hours
=> time required to produced 1 deluxe stereo = 7 hours


total time required to produce B basic stereo's = 5B hours

total time required to produce D deluxe stereo's = 7D hours

ratio of total time required to produce all deluxe stereo's to total time for all stereo's = 7D/(5B+7D) = 7/((5B/D)+7)

=7/17

Answer is A.
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Re: Stereo problem [#permalink] New post 05 Aug 2011, 10:58
assuming total stereo's manufactured=210(7*5*3*2)
deluxe stereo's= 70 and basic=140
7hrs/deluxe stereo and 5 per basic gives 490 hrs to manufacture deluxe and 700 hrs for basic stereo's
therefore 490/(490+700)=7/17
Answer is A
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Re: Stereo problem [#permalink] New post 21 Aug 2011, 09:51
let total stereos = 15

basic:deluxe = 10:5

time taken by deluxe = 7/5*5 = 7 hrs
time taken by basic = 1*10 = 10 hrs

ANS ............ 7/17
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Re: Company S produces two kinds of stereos: basic and deluxe. [#permalink] New post 24 Jun 2013, 03:04
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Re: Company S produces two kinds of stereos: basic and deluxe. [#permalink] New post 24 Jun 2013, 07:19
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1.Since the denominator in the fraction representing the number of units is 3 , assume a multiple of 3 as the number of units. Let us say 3 units were produced. So 1 was delux and 2 were basic
2. Since the denominator in the fraction representing the time taken to produce a unit is 5, assume a multiple of 5 as the time taken to produce a unit. Let it be 5. So if it takes 5 units of time to produce a basic set, it takes 7/5 * 5 units of time to produce a deluxe set. That is 7 units of time.
3. From (1) and (2) total time spent on basic and deluxe are 2*5 and 1*7 resp which are 10 and 7 units resp
4. Total time spent on both the basic and deluxe sets is 10+ 7 = 17
5. The fraction of time spent on deluxe = 7/17
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Re: Company S produces two kinds of stereos: basic and deluxe. [#permalink] New post 25 Jun 2013, 10:53
udaymathapati 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


In the above Questions, we have fractions 2/3, 7/5 and 1/3. We can assume some values and try solving the questions.
Since in fraction we have 3 and 5, LCM is 15, Let us assume total production to be multiple of 15 ( say 90)
As per question stem, Total production for 90 stereos will be as follows
Basic : 60
Deluxe: 30

Let us take time taken to produce 1 Basic stereo to be 5 hours
For deluxe stereo, it will be 7/5*7= 7 hours

Total time take to produce deluxe stereo as percentage of total production can now be calculated as follows

(30*7)/ (30*7+ 60*5) -----> 210/510 ----> 21/51 i.e 7/17

Ans should be A
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Re: Company S produces two kinds of stereos: basic and deluxe.   [#permalink] 25 Jun 2013, 10:53
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