If two different solutions of alcohol with a respective prop

Question

If two different solutions of alcohol with a respective proportion of water to alcohol of 3:1 and 2:3 were combined, what is the concentration of alcohol in the new solution if the original solutions were mixed in equal amounts?

A. 30.0%
B. 36.6%
C. 42.5%
D. 44.4%
E. 60.0%

This is how i did it:
propn of alcohol in first solution : 1:4
propn of alcohol in second solution: 3:5
so, propn of alcohol in the new solution = 4:9 = 44.4%

EMPOWERgmatRichC · Accepted Answer

Hi Anupamt,

As alexau has pointed out, this question can be solved as a straight "average" of two percents. Most questions in this category are "weighted averages" though, so you have to adjust your approach (and your "math") to whatever information you're given to work with.

If you're not great at dealing with ratios yet, then you can TEST VALUES and get the solution that way. Here's how....

We're given two solutions of alcohol:
1) The first is 3 parts water to 1 part alcohol
2) The second is 2 parts water to 3 parts alcohol

We're asked to mix EQUAL AMOUNTS of each alcohol. Since the first alcohol has "4 parts" and the second alcohol has "5 parts", we want to use a common multiple of both. The least would be 20....

So let's say that we have....
20 ounces of the first solution: 15 ounces of water and 5 ounces of alcohol
20 ounces of the second solution: 8 ounces of water and 12 ounces of alcohol

Mixing those 40 ounces together, we have (17 ounces of alcohol)/(40 ounces total)

17/40 = 42.5% alcohol

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

ezhilkumarank · Answer

Alcohol: Water

First mixture -- 3:1 -- 15:5
Second mixture -- 2:3 -- 8:12

Equal amounts of the mixture were combined, hence the final mixture will be in the ratio -- (15+8): (5+12) -- 23:17

% of alcohol -- 17/(23+17) * 100

= (17/40) * 100

= 42.5

mainhoon · Answer

If you mix 1:4 and 3:5 in equal amounts, the result is not 4/9 but 17/40 which should be 42.5%

uwezo · Answer

In this case you are adding fractions to generate a new total. 
Common denominator of the to 2 fractions is 20 (1/4=5/20 and 3/5=12/20). 
Combining the mixtures mean you will be adding the numerators and denominators separately yielding 17/40.

Then to get the percentage 40 x 2.5=100 17x2.5=42.5.

There may be a quicker way of getting to this.

soumanag · Answer

picking numbers:

let 20 l of each is mixed.  
in solution 1 amount of alcohol = 20X(1/4) = 5 L
in solution 2 amount of alcohol = 20X(3/4)=12 L

total 17 L alcohol in 40 L of solution => (17/40)X100 = 42.5%

gmatpapa · Answer

I think this is an averages question.

%ge of alcohol in solution 1:  \frac{1}{4}= 25% 
%ge of alcohol in second solution=  \frac{3}{5}= 60%

Since they are mixed in equal quantities, Average alcohol %=  \frac{(60%+25%)}{2}= 42.5%

fluke · Answer

1st solution
3:1::Water:Alcohol
Percent of alcohol in the 1st solution= 1/(3+1) = 1/4 = 0.25

2nd Solution
2:3::Water:Alcohol
Percent of alcohol in the 2nd solution = 3/(2+3)=3/5=0.6

Lets say we mix 1 liter from each of the two solutions and form a new solution.

Alcohol in the new solution from the first solution: 0.25 litres
Alcohol in the new solution from the second solution: 0.6 litres

Total alcohol in the new solution: 0.25+0.6 = 0.85 litres
Total weight of the new solution: 1+1=2 litres

Let x be the percent of alcohol in the new solution.

0.85 = 2 * x
x = 0.85/2 = 0.425 = 42.5%

Ans: "C"

ccooley · Answer

This is a lot easier if you just  pick numbers ! The problem itself only gives you ratios and percents, so you're free to pick any values you like.

You want the same amount of each solution, so come up with a quantity that will be easy to split into either of the ratios. The first ratio has four total parts, and the second ratio has five total parts, so an easy quantity to work with would be something that's divisible by both 4 and 5, such as  20 liters . Let's say that there are 20 liters of each solution.

Therefore, the first solution contains 20*(3/4) = 15 liters of water and 20*(1/4) = 5 liters of alcohol.

The second solution contains 20*(2/5) = 8 liters of water and 20*(3/5) = 12 liters of alcohol.

So, in total, there are 5+12 = 17 liters of alcohol. The total amount of the solution is 20 + 20 = 40 liters. So, the question is just: what percent is 17 out of 40?

17/40 = 170/400 = (170/4)/100 = 42.5/100 or 42.5%.

sayan640 · Answer

The problem can be solved either using the alligation or conventional way.   KarishmaB 
 egmat 
Let X be the conc. of alocohol in the new solution. 
Find the alligation diagrams attached herewith.
Solving ,
x - 25 - 60 -x
x = 42.5%

OR

solving , 3/5 - x = x - 1/4
2*x = 17/20
x = 170/4 = 42.5%

sayan640 · Answer

The question can also be solved using conventional way.
Let, With x gm of first solution , y gm of second solution is mixed.

The conc. of alcohol in the new solution = (x/4 + 3*y / 5 ) / x + y = (5*x + 12*y) / 20 (x+y) = 17/40 * 100 = 42.5%
(since x and y are equal as both the solutions were mixed in equal amount ) = 42.5% Ans.

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If two different solutions of alcohol with a respective prop

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