PGMAT 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
Can someone explain the best approach to solve these kind of problems?
Thanks.
We can plug in the answers, which represent the ratio of 5-cent rice to 6-cent rice.
Answer choice C: 2:7
Total cost of 2 ounces of 5-cent rice and 7 ounces of 6-cent rice = 2*5 + 7*6 = 52.
Revenue from 9 ounces of rice with a selling price of 7 cents per ounce = 9*7 = 63.
Percent profit = (63-52)/52 * 100 = 21.1%.
Too much profit.
Eliminate C.
To decrease the profit, the cost must include a greater proportion of 6-cent rice, the more expensive rice.
Answer choice B: 1:5
Total cost of 1 ounce of 5-cent rice and 5 ounces of 6-cent rice = 1*5 + 5*6 = 35.
Revenue from 6 ounces of rice with a selling price of 7 cents per ounce = 6*7 = 42.
Percent profit = (42-35)/35 * 100 = 20%.
Success!
The correct answer is
B.
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