guerrero wrote:Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 20% respectively. If the vodkas are mixed in equal ratio and the individual profit percents on them are increased by 1/3 and 2/3, respectively, then the mixture will fetch the profit of
A. 18%
B. 20%
C. 21%
D. 23%
E. 25%
OAB
The values in red reflect the intent of the problem.
Let x = the profit on the first vodka and y = the profit on the second vodka.
When x:y = 1:2, profit = 10%.
Thus, when 1 unit of x% profit is combined with 2 units of y% profit, the average profit for the 3 units is 10%:
(x + 2y)/3 = 10
x + 2y = 30.
When x:y = 2:1, profit = 20%.
Thus, when 2 units of x% profit are combined with 1 unit of y% profit, the average profit for the 3 units is 20%:
(2x + y)/3 = 20
2x + y = 60.
Doubling the second equation, we get:
4x+2y = 120.
Subtracting the first equation from the doubled second equation, we get:
(4x+2y) - (x+2y) = 120-30
3x = 90
x = 30.
Substituting x = 30 into 2x + y = 60, we get:
2(30) + y = 60
y = 0.
Thus:
Every liter of x = 30% profit, while every liter of y = 0% profit.
New profits:
x's profit increased by 1/3 = 30 + (1/3)30 = 40.
y's profit increased by 2/3 = 0 + (2/3)0 = 0.
When equal amounts of the two new profits are combined, the average profit = (40+0)/2 = 20%.
The correct answer is
B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
