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Solution Y is 30 percent liquid X and 70 percent water. If 2 [#permalink]

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18 Jul 2004, 23:13

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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?

Y has 30% X and 70% of water
therefore 8kg of Y wd hv 2.4kg X and 5.6 of Water
if 2 kg of water evaporates, then water left is 3.6
2 kg of solution Y is added so it wd add 0.6 kg of X and 1.4 kg of water.
thus we have 3(2.4+0.6) kg of X in 8 kg(6+2 added) of solution Y which is 3/8 fraction or (3/8)*100% of solution X in the new mixture which comes to 37.5%
i cant think of any faster solution..if there is,please let me know friends _________________

Re: Solution Y is 30 percent liquid X and 70 percent water. If 2 [#permalink]

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25 Nov 2013, 08:47

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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. 30% B. 33 1/3% C. 37 1/2% D. 40% E. 50%

In 8 kilograms of solution Y there are 0.3*8=2.4 kilograms of solution X;

After 2 kilograms of water are replaced by 2 kilograms of solution Y, to the existing 2.4 kilograms of solution X, 0.3*2=0.6 kilograms of solution X are added, so in the new solution of 8 kilograms there are 2.4+0.6=3 kilograms of solution X, which is 3/8*100=37.5% of this new solution.

I agree with viveksah and I might have done the same thing. But in general with mixture problems, I always make a quick chart that's designed to line everything up properly. In this case, the chart looked like this:

Note: The zero in the percent of water after the water evaporated is just a place holder, not a zero. I just didn't bother calculating it since it's not important.

From here, I can see that 5/8 of the new mixture are water, so 3/8 are liquid x. I chose to do the whole chart in water because water is what evaporated from the original.

whenever there's a mixture problem, there's always the whole, the percentage, and then the part. If you line it all up properly, and add down, the chart takes care of the rest.

The question is: what percent of this new solution is liquid X? That is the ratio of liquid x to solution y. So you only need to find out the eventual kilograms of liquid x and kilograms of solution y.
liquid x is consisted of two parts:
part 1: the original part ---- 30% x 8 kg
part 2: the added liquid x part ---- 30% x 2 kg
So the total of liquid x is 30% x 8 + 30% x 2 = 30% (8 + 2) = 3
The eventual solution y is 8 kg, which is very obvious, so you can write it this way:

Re: Solution Y is 30 percent liquid X and 70 percent water. If 2 [#permalink]

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25 Nov 2013, 08:40

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Re: Solution Y is 30 percent liquid X and 70 percent water. If 2 [#permalink]

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18 Apr 2014, 21:37

30%X | 70%W

Step 1: 2.4 X | 5.6 W

Step 2: 2.4 X | 3.6 W

Step 3: +0.6 X | + 1.4 W

Final: 3 X | 5 W

Proportion

3/8 * 100 = 75/2 _________________

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Re: Solution Y is 30 percent liquid X and 70 percent water. If 2
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18 Apr 2014, 21:37

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