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?
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.