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# Hard Solutions /Mixture problem 600-700 level

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Hard Solutions /Mixture problem 600-700 level [#permalink]  08 Nov 2010, 13:02
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Question Stats:

77% (02:41) correct 23% (01:42) wrong based on 108 sessions
Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid X?

a 30%
b 33 1/3%
c 37 1/2%
d 40%
e 50%
[Reveal] Spoiler: OA
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Re: Hard Solutions /Mixture problem 600-700 level [#permalink]  08 Nov 2010, 13:16
At the beggining, you have 8KG of solution Y, i.e.

70% * 8KG = 5,6 KG of Water
30% * 8KG = 2,4 KG of X

2KG of water evaporate:

5,6KG - 2KG = 3,6KG of Water
2,4KG of X

3,6KG + 2*0,70 = 5KG of Water
2,4KG + 2*0,30 = 3 KG of X

So you have 3KG of X in 8KG (3 + 5) solution.
Therefore X concentration is 3/8 = 37,5%
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Re: Hard Solutions /Mixture problem 600-700 level [#permalink]  08 Nov 2010, 23:01
Took time to solve this one, the statement 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid was confusing to me. After thinking more deeply, it was clear to me that new 2 kg of solution Y will also be 30% liquid X and 70% water, and then I was able to get the answer. That was a bit tricky and nice question.
Kudos +1 for posting the question
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Re: Hard Solutions /Mixture problem 600-700 level [#permalink]  08 Nov 2010, 23:25
Initially you start with 8kg of solution which has 2.4kg of X and 5.6kg of water
Post evaporation : 2.4kg of X and 3.6kg of water
Now we add back 2kg of Y --> 1.4Kg water + 0.6Kg X
So we have left 5Kg Water & 3Kg X

Percentage concentration is (3/5)*100 or 37.5%
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Re: Hard Solutions /Mixture problem 600-700 level [#permalink]  08 Nov 2010, 23:43
shrouded1 wrote:
Initially you start with 8kg of solution which has 2.4kg of X and 5.6kg of water
Post evaporation : 2.4kg of X and 3.6kg of water
Now we add back 2kg of Y --> 1.4Kg water + 0.6Kg X
So we have left 5Kg Water & 3Kg X

Percentage concentration is (3/5)*100 or 37.5%

Yea, that's exactly how I solved but you know at first I was kinda adding 2 to 6 kg without considering liquid X and water's concentration within 2 kg being added.
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Re: Hard Solutions /Mixture problem 600-700 level [#permalink]  10 Dec 2011, 12:51
Liquid x in 8 kg = 8*30%=12/5
Liquid x in next 2 kg = 2*30% = 3/5
Total x = 12/5 + 3/5 = 15/5 = 3
so, (3/8)*100= 37.5%
Ans. C
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Re: Hard Solutions /Mixture problem 600-700 level [#permalink]  11 Dec 2011, 22:43
Initially we have 8kg of solution which has 3/10 0f 8= 2.4kg of X and 7/10 of 8 = 5.6kg of water after evaporation : 2.4kg of X and 3.6kg of water
Now we added 2kg of solution Y --> 7/10 of 2=1.4Kg water + 3/10 0f 2 =0.6Kg X
So we have left 5Kg Water & 3Kg X

Percentage concentration is (3/5)*100 or 37.5%
Re: Hard Solutions /Mixture problem 600-700 level   [#permalink] 11 Dec 2011, 22:43
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