Problem Solving

A cask contains 3 parts wine and one part water. What part of the mixture must be drawn off and substituted by water so that the resulting mixture may be half wine and half water.

1/2
5/2
1/3
3/2

please help me understand the approach

thanks!

guerrero wrote:A cask contains 3 parts wine and one part water. What part of the mixture must be drawn off and substituted by water so that the resulting mixture may be half wine and half water.

1/2
5/2
1/3
3/2

please help me understand the approach

thanks!

A solution that is 25% water is to be combined with 100% water so that the resulting solution is 50% water.
Use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.

Step 1: Plot the 3 percentages on a number line, with the two percentages in the two ingredients (25% and 100%) on the ends and the percentage in the mixture (50%) in the middle.
25%----------50%-------------------100%

Step 2: Calculate the distances between the percentages.
25%-----25----50%---------50---------100%

Step 3: Determine the ratio in the mixture.
The required ratio of solution to water is the RECIPROCAL of the distances in red.
S:W = 50:25 = 2:1.

In the resulting ratio:
Total mixture = S+W = 2+1 = 3.
W=1.
W/total = 1/3.

For two similar problems, check here:

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

An alternate approach is to plug in the answers.
B and D make no sense: it is not possible to draw off more than 100% of the original solution.

Answer choice C: 1/3
Since the denominator here is 3 and the original solution is 1/4 water, let the total = 3*4 = 12 units.
Amount of solution to be replaced with pure water = (1/3)12 = 4.
Amount of water in the remaining 8 units of solution = (1/4)8 = 2.
Water/total = (4+2)/12 = 1/2.
Success!