If Amberly wants to create a 40% saline solution combining solution A,

Question

If Amberly wants to create a 40% saline solution combining solution A, which is an 18% saline solution and solution B, which is a 72% saline solution, what must the ratio of the volumes of solution A to solution B be to create a 40% saline solution?

a. 1/2
b. 11/16
c. 3/4
d. 1
e. 16/11

a. 1/2
b. 11/16
c. 3/4
d. 1
e. 16/11

Leo8 · Answer

0.40 ( x + y) = 0.18x + 0.72y

40x + 40y = 18x + 72y

22x = 32y

\frac{x}{y}  =  \frac{16}{11}  = E

generis · Answer

Expanding just a bit on  Leo8  's good post above.

When asked for a ratio of two solutions in a resultant mixture, you can use two variables and simply find their amounts in relation to one another.

One iteration of a weighted average equation here is 
(Concentration of A)(Vol A) + (Concen of B)(Vol B) = (Desired Concen)(Total vol = A+B)

"Concentration" here = percent saline

A = the 18% saline solution
B = the 72% saline solution
A + B = total volume of resultant solution
Desired concentration of saline in resultant solution is 40%

.18(A) + .72(B) = .40(A + B)
18A + 72B = 40A + 40B
32B = 22A

Ratio of A to B?
 \frac{A}{B} = \frac{32}{22}=\frac{16}{11} , or

16 : 11

Answer E

Turkish · Answer

The best way to do this is by alligation method.

We have A=18 and B=72
 combine=40
 72-40=32 and 40-18=22

32:22= 16/11. Answer E

ccooley · Answer

If you mix the two solutions equally, you'll end up with a solution that's exactly halfway between them. The halfway point between 18% and 72% is 45%.

https://i.imgur.com/WM0M5KX.png

(By the way, I figured that out by averaging 18 and 72. (18 + 72)/2 = 90/2 = 45.)

So, we don't want a 1:1 ratio. (D) is out.

In order to make a solution with  less  than 45% saline, you'd need  more  of the 18% solution. Since a 1:1 ratio of the solutions will have too much saline, then there must be more 18% solution than 72% solution.

The only answer with this property is (E).

EgmatQuantExpert · Answer

Method : Using Alligation

Final Solution Saline Concentration : 40 %

Initial Solution A Saline Concentration : 18%

Initial Solution B Saline Concentration : 72%

Ratio of A : B = (72 - 40) : ( 40 - 18) = 32 : 22 = 16 : 11

Thus, the correct answer is    Option E   .

Regards,
Saquib
e-GMAT
Quant Expert

luisdicampo · Answer

Deconstructing the Question

Solution A is   18\%  , solution B is   72\%  , and the target is   40\%  .

We need the ratio of A to B using weighted average.

Step-by-step

Difference between B and the mean is

72 - 40 = 32

Difference between the mean and A is

40 - 18 = 22

So the ratio of A to B is

32:22

Simplify:

\frac{32}{22} = \frac{16}{11}

Answer: E

If Amberly wants to create a 40% saline solution combining solution A,

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If Amberly wants to create a 40% saline solution combining solution A,

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