Word Trans (Fractions): Company S produces two kinds of ster

For me, I would approach it by first translating english into math, then picking smart numbers.

First, we know
2/3 basic in a month
1/3 deluxe in a month

Then we know it takes 7/5 to make a deluxe than a basic
Pick smart numbers
Assume Basic = 5
Then Deluxe = (7/5) * 5 = 7

Then we want deluxe hours over total hours in a month
Pick smart numbers
Assume Basic = 2
Then Deluxe = 1

Basic hours in a month = 2*5 = 10
Deluxe hours in a month = 1*7 = 7
Total hours = 10 + 7 = 17

Deluxe / Total = 7/17

Please let me know if the answer is the correct and if the approach makes sense.

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 think sometimes its better to have a generalised solution, coz there might be questions where substituting values might not help..so here is the solotion

Let the total no. pieces manufactured be X
Basic Deluxe
No. of pieces (2/3)X (1/3)X
Time taken Y (7/5)Y

Total time taken to manufacture Basic ones (2/3)XY
Total time taken to manufacture Deluxe ones (7/15)XY
Total time taken to manufacture Both = (2/3)XY + (7/15)XY = (17/15)XY

Time for Deluxe:Time for both = {(7/15)XY}/{(17/15)XY} = 7/17

Best approach in such question is assume numbers:

lets say total 3 stereos were produced

2 = basic 1=delux

Time to produce delux = (7/5)T
Time to produce basic = 2 x T

total time = (7/5)T+2T = (17/5)T

delux/total = (7/5)T / (17/5)T = 7/17

7/17 is the correct answer. Thanks.

I agree... best approach on these types of questions is to plug smart numbers.

Thanks for your input folks.
II

I am not clear on this one?

Is there a better approach to handle this toughie?

Please help

Let the total stereos be 60.
So Basic: 40, Delux: 20..
Let the Basic one takes 25 hours to produce..
So the delux one wud take 35 hours..
So total time for Basic : 40 * 25
Total time for Delux : 20 * 35
Answer you are looking for: 20 * 35/(20 * 35 40 * 25 )

= 700/1700 = 7 /17 and answer is D..

II 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

Whats the best approach to tackle this one ?
Thanks.
II

Plug in SMALL numbers.

Let the number of stereos = 3.
Since 2/3 were basic:
Basic stereos = 2.
Deluxe stereos = 1.

Let the number of hours to produce a basic stereo = 5.
Then the number of hours to produce a deluxe stereo = (7/5)*5 = 7.

Total number of hours to produce the 2 basic stereos = 5*2 = 10.
Total number of hours to produce the 1 deluxe stereo = 7.

Deluxe stereo hours/Total hours = 7/(10+7) = 7/17.

The correct answer is A.