Answer before you say CHEERS!

[sanju09]

Solution A is 30% alcohol by volume and Solution B is 20% alcohol by volume. In what ratio the two solutions should be mixed so as to obtain a mixture that is 22% alcohol by volume?
A. 3:2
B. 2:3
C. 1:2
D. 1:3
E. 1:4


Made Up!

[theCodeToGMAT]

M1 = 30%
M2 = 20%
M = 22%

using Weighted Average

N1/N2 = (20-22)/(22-30) = 2/8 = 1:4

[spoiler]{E}[/spoiler]?

CHEERS!!!

[ganeshrkamath]

Solution A is 30% alcohol by volume and Solution B is 20% alcohol by volume. In what ratio the two solutions should be mixed so as to obtain a mixture that is 22% alcohol by volume?
A. 3:2
B. 2:3
C. 1:2
D. 1:3
E. 1:4


Made Up!

Volume of solution A = a
Volume of alcohol in solution A = 0.3a

Volume of solution B = b
Volume of alcohol in solution B = 0.2b

Volume of mixture = (a+b)
Volume of alcohol in mixture = 0.22(a+b) = 0.3a + 0.2b
0.22a + 0.22b = 0.3a + 0.2b
0.02b = 0.08a
a/b = 1/4

Choose E

Cheers

[GMATGuruNY]

Solution A is 30% alcohol by volume and Solution B is 20% alcohol by volume. In what ratio the two solutions should be mixed so as to obtain a mixture that is 22% alcohol by volume?
A. 3:2
B. 2:3
C. 1:2
D. 1:3
E. 1:4


Made Up!

The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.

Step 1: Plot the 3 percentages on a number line, with the percentages for A and B on the ends and the percentage for the mixture in the middle.
A 30%-----------22%-----------20% B

Step 2: Calculate the distances between the percentages.
A 30%-----8-----22%-----2-----20% B

Step 3: Determine the ratio in the mixture.
The required ratio of A to B is equal to the RECIPROCAL of the distances in red.
A:B = 2:8 = 1:4

The correct answer is E.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html

Alternate approach.
We can PLUG IN THE ANSWERS, which represent how many parts 30% alcohol must be mixed with how many parts 20% alcohol to yield an AVERAGE alcohol percentage of 22%.

Answer choice C: 1:2
Here, the mixture is composed of 1 part 30% for every 2 parts 20%.
Average alcohol percentage for 3 every parts = (1*30 + 2*20)/3 = 70/3 ≈ 23.
Since the resulting alcohol percentage is TOO HIGH, we need more parts of the SMALLER percentage (20%).
Eliminate A, B and C.

Answer choice D: 1:3
Here, the mixture is composed of 1 part 30% for every 3 parts 20%.
Average alcohol percentage for every 4 parts = (1*30 + 3*20)/4 = 90/4 = 22.5.
Since the resulting alcohol percentage is TOO HIGH, we need more parts of the SMALLER percentage (20%).

The correct answer is E.

Answer choice E: 1:4
Here, the mixture is composed of 1 part 30% for every 4 parts 20%.
Average alcohol percentage for every 5 parts = (1*30 + 4*20)/5 = 110/5 = 22.
Success!