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Y is 30 percent liquid X

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by sanju09 » Thu Jan 14, 2010 4:56 am
Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X?
(A) 27 ½%
(B) 30%
(C) 100/3%
(D) 37 ½%
(E) 40%
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by chrsrook » Thu Jan 14, 2010 7:42 am
Given: Y= 0.3X+0.7W

In 8Kgs of Y, there are 8*0.3=2.4 Kgs of X and 8*0.7=5.6 Kgs of water.

When 2Kgs of water evaporate, there are 3.6Kgs of water left along with the original 2.4Kgs of X.

Now, 2Kgs of Y are added to the existing 6Kgs of Y.

The 2 Kgs of Y will also contain X and W in the same ration (0.3 and 0.7).

So X in 2Kgs of Y= 2*0.3=0.6 and W in 2 Kgs of Y=2*0.7=1.4

Total Y= 6+2=8
Total X= 2.4+0.6= 3
Total W=3.6+1.4= 5

% of X in Y= 3/8*100= 37.5%

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by singhsa » Sun Sep 12, 2010 4:31 am
The solution seems manageable. I was wondering if there is a way of solving this using Allegation Method.
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by gmatt14 » Fri Oct 15, 2010 7:42 am
Most importantly, we have to concentrate on what is being asked! If you concentrate solely on X, you can solve this question fast.

Consider the attached table, which helped me out a lot to grasp this concept.

From the table we gain the equation:

0.3 (8) + 0.3 (2) = 0.3 (8+2) = 0.3 (10) = 3

8 kg of solution Y contains 3 kg of solution X:

3/8 = 37.5 %

Hope this helps! ;-)
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by GMATGuruNY » Fri Oct 15, 2010 8:30 am
sanju09 wrote:Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X?
(A) 27 ½%
(B) 30%
(C) 100/3%
(D) 37 ½%
(E) 40%
The water that is being replaced is 2/8 = 25% of the total solution. We are replacing this 25% with solution Y. Thus, the percentage of liquid X in the total solution is going to increase by 25%:

1.25*30 = 37.5.

The correct answer is D.

Similarly, if the water being replaced were 4/8 = 50% of the total solution, the percentage of liquid X in the total solution would increase by 50%. The resulting solution would be 1.5*30 = 45% X and 55% water.
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