Hard Solutions/Mixture Problem

(C) 37 1/2%

rtaha2412 wrote: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%

8 kg of solution y = 2.4 kg of X and 5.6 kg of water
2 kg of water evaporates
6 kg of liquid = 2.4 kg of X and 3.6 kg of water

2 kg of solution y = 0.6 kg of X and 1.4 kg of water

Final solution = 3 kg of X and 5 kg of water

Required percentage = 3/8 * 100 % = 37.5%

Choose C

Cheers

OA is C. 37.5%

8 liters of solution before
2 liters more solution added
Total solution = 10 liter (3 liter X , 7 liter Water)
Now remove 2 liter water from this 10 liter solution.
Total solution 8 liter (3 liters X ,5 liter water)
Hence percentage of X = 75/2 = 37.5

S1 = 8: x1 = 0.3 x 8 = 2.4, w1 = 0.7 x 8 = 5.6
S1/4 = 2: x1/4 = 0.6, w1/4 = 1.4
S2 = 6: x2 = 2.4, w2 = 5.6 - 2 = 3.6
S3 = S2 + S1/4 = 8: x3 = 3, w3 = 5

x3/S3 = 3/8 = 37.5%

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%

Didn't get it.

jaspreetsra wrote: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%

Didn't get it.

2 kilograms of water -- 1/4 of the original 8 liters of mixture -- evaporates and is replaced by Solution Y.
The correct answer will be obtained as long as 1/4 of the original volume evaporates and is replaced by Solution Y.
Thus, we can make the math easier by rephrasing the problem as follows:

Solution Y is 30 percent liquid X and 70 percent water. If 25 liters of water evaporates from 100 liters of Solution Y, and 25 liters of Solution Y is added to the remaining 75 liters 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%

Original mixture:
Total volume = 100 liters.
Amount of liquid X = 30% of 100 = 30 liters.
Amount of water = 70% of 100 = 70 liters.

New mixture:
Here, 25 liters of water is replaced by 25 liters of Solution Y.
Amount of liquid X remaining from the original mixture = 30 liters.
Amount of liquid X in the 25 liters of added Solution Y = 30% of 25 = 7.5 liters.
Resulting percentage:
(total amount of liquid X)/(total volume) = (30 + 7.5)/100 = 37.5%.

The correct answer is C.