GMAT Challenge Series (700+): Q11

Vodka Tonic.jpg

Question:

Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching a profit of 10% and 20% respectively. If the vodkas are mixed in and equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of

A. 18%

B. 20%

C. 21%

D. 23%

E. Cannot be determined

MBA Wisdom's Answer:

$$\text{Let the profit on vodka 1 = x%}$$ $$\text{Let the profit on vodka 2 = y%}$$ $$$$ $$\text{When the vodkas are mixed in the ratio 1:2 (total of 3 parts) the average profit is 10%:}$$ $${\left( \text{x} + \text{2y}\right) \over {3}} = {10}$$ $$\text{When the vodkas are mixed in the ratio 2:1 (total of 3 parts) the average profit is 20%:}$$ $${\left( \text{2x} + \text{y}\right) \over {3}} = {20}$$ $$$$ $$\text{Solve for x and y:}$$ $$\text{(1): } \text{x} + \text{2y} = {30}$$ $$\text{(2): } \text{2x} + \text{y} = {60}$$ $$$$ $${\text{x} + {2}\left({60}-\text{2x}\right)} = {30}$$ $$\text{x} + {120} - \text{4x} = {30}$$ $$\text{-3x} = {-90}$$ $$\text{x} = {30}$$ $$$$ $${30} + \text{2y} = {30}$$ $$\text{2y} = {0}$$ $$\text{y} = {0}$$ $$$$ $$\text{Solving gives: x = 30% and y = 0%}$$ $$$$ $$\text{After the profit of vodka 1 is increased by 4/3 the profit becomes 40%}$$ $$\text{After the profit of vodka 2 is increased by 5/3 the profit becomes 0%}$$ $$\text{If the vodkas are mixed in an equal ratio of 1:1, then the mixture will fetch a profit of: } {\left({40} + {0}\right) \over {2}} = \text{20%}$$

B. 20%