carcass wrote:
Joseph bought two varieties of rice, costing 5 cents per ounce and 6 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 7 cents per ounce,making a profit of 20 percent. What was the ratio of the mixture?
A. 1:10
B. 1:5
C. 2:7
D. 3:8
E. 5:7
What is the level of this one ??? I have problems to set up an equation. Thanks.
Source: GMAT Bible, an excerpt.
Actually, the question is not very tricky. Perhaps 650 or so. A couple of things here - If you understand the theory of mixtures, you don't have to set up equations. In most GMAT equations, if you know your theory well, much algebra is not required. Also, the numbers will be a little better. e.g.
"Joseph bought two varieties of rice, costing 4 cents per ounce and 5.5 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 6 cents per ounce,making a profit of 20 percent. What was the ratio of the mixture?"
Since a profit of 20% was made, the cost price of the mixture must have been 5. (20% of 5 will be 1 which when added to 5 will give 6)
w1/w2 = (A2 - Aavg)/(Aavg - A1) = (5.5 - 5)/(5 - 4) = 1/2
They were mixed in the ratio 1:2.
For the detailed theory, check out this post:
http://www.veritasprep.com/blog/2011/04 ... -mixtures/Mind you, better numbers doesn't mean no decimals or fractions. It means that the numbers make sense in that scenario. If it is a 20% increase (i.e. 1/5 more), chances are the original number is divisible by 5. If you are dealing with circles, chances are the radius is a multiple of 7 (to cancel off the 7 in \({\pi}\)) etc.
The method I have used above is the same as allegation. You can either draw the cross diagram, the scale diagram or use this formula. Everything is just a slightly different presentation of the same concept.