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.

Answer: C.
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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

2KG of liquid are added:

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%

Answer:C
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

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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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.

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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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%

Solution Y total = 8
Liq x = 30% (8) = 2.4

Added 2 kg of Solution Y
Liq x = 30% (2) = 0.6

Final Solution wil have = (2.4 + 0.6) = 3 kg of Liq x

3/8 = 37.5%

1. The net effect of 2 kg of water evaporating and adding 2 kg of the solution is removing (-2 + 1.4 = -0.6) 0.6 kg of water and adding 0.6 kg of liquid
2 Therefore the changed solution contains, 2.4 + 0.6 = 3 kg of liquid and 5.6-0.6==5 kg of water.
3. Percentage of liquid is 3/8 * 100 % = 37 1/2 %
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The best way to solve these problems is to take one step at a time

Initial:
8 kg Solution Y
This means Solution X = 2.4 kg, Water = 5.6 kg

Step 2:
2 kg of water is evaporated.
Left over: Solution X = 2.4 kg and Water = 3.6 kg

Step 3:
2 kg of Solutoin Y is added
Or, 0.6 kg of Solution X and 1.4 kg of water is added

Final:
Solution X = 3, Water = 5
% of solution X = 3/8 * 100 = 37.5%

Option C

Hi,

I like using a table for mixture problems. This is what I came up with (see attachement):

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%

let x=% of liquid X in new solution
.3*8+.3*2=x(6+2)
x=3/8=37.5%
C

I also used the similar approach.
To Sum up:
Initial 8 kilograms of Y consist of 2.4 kg X and 5.6 kg water.
We then lose 2 kg water to evaporation, so we are down to 3.6 kg water.
The final step adds 2 kg Y, which consists of .6 kg X and 1.4 kg water.
Therefore, the final mixture contains 3 kg X and 5 kg water. 3/8 = 37.5%.

30% of 8 + 30% of 2 = 3 = X
X/T= 3/8 = 0.375 =37.5%

Posted from my mobile device

8 kg of the solution contains (8*0.3) kg = 2.4 kg of X

again,

2 kg of the add solution which is added will have 2*0.3 = 0.6 kg of X

Total final volume of the solution = 8 kg

Hence, % of X = (2.4+0.6)/8*100 = 3/8 * 100 =3* 12.5 = 37.5 %

Hence C)

Hello!

Tricky question, these topics is very challenging for me.

Is it possible to solve it with weighted averages?

Kind regards!

My reasoning:

8kg original solution is 30% X and 70% water or \(\frac{24}{10}kg liquid X and \frac{56}{10}kg water\)

Since we are looking for the percent of liquid X in our mixture we don't really care about the water in our solution.

We know that the total weight is 8kg and we are adding 2kg of solution Y, which has \(\frac{6}{10}kg liquid X\).

\(\frac{24}{10} + \frac{6}{10} = 3kg\) liquid X in the total solution.

\(\frac{3}{8} = 37.5%\)

Solution Y is 30 percent liquid X and 70 percent water


Total 8 litres

8 *0.3 = 2.4 kg liquid

5.6 kg = water

2 kilograms of water evaporate from 8 kilograms of solutions Y

so 5.6 -2 = 3.6 water is left

afterwards 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid

Since, solution Y cosists of 30 percent is liquid X and 70 percent is water

hence 2 *0.3 = 0.6 kg is liquid and 2-0.4 = 1.4 is water

2.4 +0.6 = 3 kg liquid

3.6+1.4 = 5 kg water

what percent of this new liquid solution is liquid X?

\(\frac{3}{8} = 0.37\)

Originally, solution Y has 0.3 x 8 = 2.4 kg of liquid X and 0.7 x 8 = 5.6 kg of water. After 2 kg of water evaporate, solution Y has 2.4 kg of liquid X and 3.6 kg of water. However, since 2 kg of solution Y (of which, 0.3 x 2 = 0.6 kg is liquid X and 0.7 x 2 = 1.4 kg is water) are added back to the remaining 6 kilograms of solution Y, solution Y now has 2.4 + 0.6 = 3 kg of liquid X and 3.6 + 1.4 = 5 kg of water). Therefore, the percent of the new solution is liquid X is 3/(3 + 5) = 3/8 = 37.5%.

Answer: C
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