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GMAT - Problem Solving - Percentage

Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 % fescue. If a mixture of X and Y contains 30% ryegrass, what percent of the weight of the mixture is X?

Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 % fescue. If a mixture of X and Y contains 30% ryegrass, what percent of the weight of the mixture is X?

A. 10%
B. 33 1/3%
C. 40%
D. 50%
E. 66 2/3%

Let's assume that the weight of X in the mixture of X and Y be x and that of Y be y

Total weight of the mixture = x + y

Amount of rye grass in the mixture = 40% of x + 25% of y = 0.4x + 0.25y

% of ryegrass in the mixture = (0.4x + 0.25y) / (x + y)

0.3 = (0.4x + 0.25y) / (x + y)

0.3x + 0.3y = 0.4x + 0.25y

0.05y = 0.1x

y = 2x

Percentage of X in the mixture = 100*x / (x + y) = 100*x / (x + 2x) = 100*1/3 = 33.33%

B is correct.