There are x liters of a solution that is 15 percent salt by volume, an

Question

There are x liters of a solution that is 15 percent salt by volume, and there are y liters of a solution that is 30 percent salt by volume. if the two solutions are combined to form x + y liters of a solution that is 20 percent salt by volume, then x/y =

(A) 1/3
(B) 1/2
(C) 2/3
(D) 2
(E) 3

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Official Answer

D

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ShivamDho · Accepted Answer

The volume of salt in the first solution (15% salt) is 0.15x

The volume of salt in the second solution (30% salt) is 0.30y

The total volume of the combined solution is x+y.

We can set up an equation

.15x + .30y = .20(x+y) 
.15x + .30y = .20x + .20y
.10y = .05x
x/y = 2

Bunuel · Answer

Could you please post a screenshot of the question from the source? Thank you!

SatvikVedala · Answer

0.15x + 0.3y = 0.2(x+y)
0.1y = 0.05x
x/y = 2/1

cjcalero24 · Answer

https://gmatclub.com/forum/download/file.php?id=83088 GMAT-Club-Forum-q8fqugzz.png

Bunuel · Answer

Thank you very much!

GMAT-Club-Forum-6gny7ka0.png

GMATinsight · Answer

You can use two methods here 1) Allegation method (weighted average) 2) Forming an equation P.S. Success of student in solving such questions is much higher with traditional method of forming an equation instead while shorter and impressive method remains to be weighted average method My Suggestion: Keep priority straight and follow traditional method first and keep allegation method secondary till you gain enough confidence to solve questions using that method. Salt = (15/100)*x +(30/100)*y = (20/100)*(x+y) Solving this we get, 5x = 10 y i.e. x:y = 1:2 Answer: Option B GMAT-Club-Forum-enjtce9x.png

MartyMurray · Answer

There are x liters of a solution that is 15 percent salt by volume, and there are y liters of a solution that is 30 percent salt by volume. if the two solutions are combined to form x + y liters of a solution that is 20 percent salt by volume, then x/y =

(A) 1/3
(B) 1/2
(C) 2/3
(D) 2
(E) 3

Show Spoiler

A quick way to answer this question is to use alligation, sometimes called the teeter totter method.

To use this method, we consider the position of 20 percent between the percentages of salt in each solution.

15 ---- 20 --------- 30

We see that 20 is closer to 15 than 30. So, before doing any math, we can intuitively tell that there must be more of the 15 percent solution than of the 30 percent solution in the final mixture.

Now, to determine the exact ratio, we consider the following: the distance between 15 and 30 is 15, and the position of 20 is 2/3 of the way from 30 to 15 and 1/3 of the way from 15 to 30.

So, for the new solution to be 20 percent salt by volume, the mixture must be 2/3 15 percent solution and 1/3 30 percent solution.

Thus, the ratio of x to y is (2/3)/(1/3) = 2.

(A) 1/3
(B) 1/2
(C) 2/3
(D) 2
(E) 3

Correct answer:  D

vinayaks01 · Answer

The Answer to this Question is D

Let's solve Assuming a whole 1 as 100 percent we get 15% as 0.15 of l. As per the question 0.15x similarly for the other solution 0.30y. So 0.15x + 0.30y /x+y = 0.20. Therefore 0.15x + 0.30y = 0.20( x+y). Moving on you get 0.15x + 0.30y = 0.20x + 0.20y. Further by moving x and y to other sides u get 0.05x = 0.10y therefore X/y = 2/1

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There are x liters of a solution that is 15 percent salt by volume, an

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