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.

x = vodka 1
y = vodka 2

The method above is terrific. You can also use substitution instead of elimination.

1: x:y = 1:2 for a 10% profit
(x + 2y)/3 = 10%
x + 2y = 30
x=30-2y

2: x:y = 2:1 for 20% profit
(2x + y)/3 = 20%
2x + y = 60


Substitute 1 into 2
2(30-2y) + y = 60
60 - 4y + y = 60
-3y=0
y=0 (Substitute that back into 1): x = 30-2y = 30-2(0) = 30

Increased profits:
x: 30 + 1/3 * 30 = 40
y: 0 + 2/3 * 0 = 0

Combination of new profit vodkas. The ratio is 1:1 (equal amounts).
(40+0)/2 = 20%

Answer B