Two different solutions of alcohol with respective proportions of

SOL:
Lets assume that 40L of sol1 was mixed with 10L of sol2.

Alcohol in Sol1: 40*3/4 = 30L
Alcohol in Sol2: 10*2/5 = 4L

Total Alcohol in the mixed solution of 50L = 30 + 4 = 34L

Alcohol concentration in the new sol: (34/50)*100 = 68%

Good strategy by samrus. A slightly different way using variables:

Let sol1 have x liters, and sol2 have y liters.
The ratio of alcohol to water in the final solution will be :
[ (3/4)*x + (2/5)*y ] / [ (1/4)*x + (3/5)*y ]

Now, x=4y, substituting x in the above ratio, we get 17/8 as the ratio of alcohol to water in the final solution.
Hence, concentration of alcohol is (17/25)*100 % = 68%

I have one more way of doing this with the grid

Assume 40 Liters for sol 1 and 10 Liters for sol 2


Liters.....%.......Totals
40........75%....40(.75)
10........40%......10(.40)
50.........X........

So you have 50X=40(.75)+10(.40)
50x=30+4
50x=34
x=.68 or 68%

Solution B Let it be X
Ratio - 2:3
2y+3Y=X
5y=X
so y=X/5
Now ratio converted to amount becomes 2X/5 and 3X/5

Solution A will be 4X
Ratio - 3:1
3y+1y=4X
y=X
Ratio converted to amount = 3X and 1X

Mixture (A+B) Amount = 3x+1x = 4x
Alcohol amount = 3X+ 2X/5 -----------------------FROM ABOVE
= 17X/5

Concentration = individual amount /total amount *100 = 17x/5 * 1/5x *100 = 17/25*100 = 68%

A different approach:
Alcohol in soln1 = 3/4 and in soln2 = 2/5
Using Alligation:
3/4--------?--2/5
4 : 1
So the resultant ratio (the ?) is at a 1/5th distance from 3/4 (or conversely at a 4/5th distance from 2/5.
3/4 - 2/5 = 7/20
Now, calculating 1/5th of 7/20 and subtracting it from 3/4
(3/4) - (1*5)/(7*20)
= 75/100 - 7/100
= 68/100
= 68%

This approach is not quite advisable in this particular problem unless one is instinctive wrt alligation, but definitely awfully handy in other scenarios. This is just to enlighten people towards proper understanding of Alligation
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Second solution = 20
Thus first solution = 80
New solution (20+80) = 100

Alcohol in first solution = 80*3/4 = 60
Alcohol in second solution = 20*2/5 = 8
Total Alcohol = 68
Concentration of Alcohol 68/100*100= 68% Ans.
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(x-(2/5))/((3/4)-x) = 4/1

5x=2/5+3

x=17/25

%= 68%

Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 4 times the amount of the second solution?

A. 17%
B. 25%
C. 34%
D. 50%
E. 68%

let x=amount of second solution
let a=% of alcohol in combined solution
3/4*4x+2/5*x=a*5x
→3/4*4+2/5=5a
→a=.68=68%
E

Can someone help to explain why solving the question as below didnt give OA?
x: the proportion of alcohol to water of new solution
(x-2/3)/(3-x)=4
15x=38
x=38/15
=>> the concentration of alcohol in the new solution is 38/(38+15)=38/53??

Thank you in advance!!!

Track on alcohol; use water only to determine the percentage of alcohol in each solution.

Mixture A = .75 alcohol
\(\frac{3A}{1W}\): 4 parts total
Alcohol is 3 parts of 4, or
\(\frac{3}{4}\) = .75 of Mixture A

Mixture B = .40 alcohol
\(\frac{2A}{3W}\): 5 parts total
Alcohol is 2 parts of 5, or
\(\frac{2}{5}\) = .40 of Mixture B

Percent alcohol = concentration

\((Concen_{A})(Vol_{A}) + (Concen_{B})(Vol_{B})=\)

\((Concen_{A+B})(Vol_{A+B})\)

Mixture A has 4 times the volume of Mixture B. Let volume of A = 4 and volume of B = 1, where x = percentage of alcohol in final mixture

(.75)(4) + (.40)(1) = (x)(4+1)
3 + .4 = 5x
3.4 = 5x

x = \(\frac{3.4}{5} = \frac{34}{50} = \frac{68}{100} = x\)

x = 68 percent
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simplest approach


(3/4 (4) + 2/5(1) ) / (1/4 (4) + 3/5 (1)) = 17/ 8
so conc of alcohol is 17/25

Hi generis,

can you help me to understand why in the picture above (alligation method) instead of 4/1 is "x" isnt 4/1 combined ratio ?

i am trying to understand alligation method and drum this concept into my head

is there difference between weighted average method and alligation ?

many thanks for your contribution to my understanding

D.

Hi dave13

In allegation method, the center point (which is \(x\) here) usually refers to the quantity of the mixture.

So if you have two solutions A & B whose alcohol content is \(\frac{3}{4}\) & \(\frac{2}{5}\) respectively, then alcohol content of mixture will be represented by \(x\) here.

the ratio of difference of individual content with the content of the mixture gives you the ratio of quantities in the mixture.

\(=>(x-2/5)/(3/4-x)=\frac{4}{1}\) (this is similar to weighted average method)

The important thing to note in allegation method is the center point refers to the quantity of the mixture and not ratio of elements of the mixture.

Many thanks niks18 for clear explanation!:) I bookmarked your post what do you think of this idea https://gmatclub.com/forum/bookmarks-25 ... l#p2005645

Hi,

Can someone please explain me why are we considering Sol1 40L and Sol2 10L?. Question says Sol1 was 4 times Sol2.
So it should be Sol1 = 4 * Sol2 right?

Thanks

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