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Mixtures and Alligation - February 17, 2004
The GMAT Sample Math question for the day is from the topic Mixtures and Alligation.
Question
In what ratio should a 20% methyl alcohol solution be mixed with a 50% methyl alcohol solution so that the resultant solution has 40% methyl alcohol in it?
A. 1 : 2
B. 2 : 1
C. 1 : 3
D. 3 : 1
E. 2 : 3
The correct choice is (A) and the correct answer is 1 : 2.
Explanatory Answer
Let there be 1 litre of the solution after mixing 20% methyl alcohol and 50% methyl alcohol..
If the concentration of methyl alcohol in it is 40%, then 0.4 litres of the resultant mixture is methyl alcohol.
Let x litres of the solution containing 20% methyl alcohol be mixed with (1 - x) litres of the solution containing 50% methyl alcohol to get 1 litre of the solution containing 40% methyl alcohol.
X litres of 20% methyl alcohol solution will contain 20% of x = 0.2x litres of methyl alcohol in it.
(1 - x) litres of 50% methyl alcohol solution will contain 50% of (1- x) = 0.5(1 - x) litres of methyl alcohol.
The sum of these quantities of methyl alcohols added up to the total of 0.4 litres in the resultant mixture.
Therefore, 0.2x + 0.5(1 - x) = 0.4 litres
0.2x + 0.5 - 0.5x = 0.4
0.5 - 0.4 = 0.5x - 0.2x
x =  litres
And 1 - x = 1 -  litres.
So, the two solutions are mixed in the ratio of 1 : 2.
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