Two solutions of 90% and 97% purity are mixed resulting in 21 litres

Question

Two solutions of 90% and 97% purity are mixed resulting in 21 litres of mixture of 94% purity. How much is the quantity of the first solution in the resulting mixture?

(A) 15 litres 
(B) 12 litres
(C) 9 litres 
(D) 6 litres
(E) 4 litres

ganand · Answer

Hi,

Please refer attached diagram.

Mixture 1: Mixture 2 = 3:4 => 3k+4k = 21 => k =3 liters.

Quantity of the first solution = 3k = 3*3 = 9 liters.

Definitely, not a 700 level question.

Thanks.

GMATinsight · Answer

Where allegation method as mentioned below looks like Awesome and Impressive method, in complete agreement with it I prefer to teach students to learn to make the equation which is strongest way to solve such question of any difficulty.

Let, 90% solution has quantity A
Let, 97% solution has quantity B
So total Solution will be A+B = 21 (Given)

The equation is formed as mentioned here
Concentrate of A + Concentrate of B = Concentrate of (A+B)

i.e. (90/100)*A + (97/100)*B = (94/100)*(A+B)

i.e. 4A = 3B
Also, A+B = 21
i.e. A+(4A/3) = 21
i.e. A=9

Answer: Option C

KarishmaB · Answer

Use weighted average:

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (97 - 94)/(94 - 90) = 3/4

So the ratio of solution1:solution2 = 3:4 which is a total of 7 on ratio scale. The multiplier is 3.
So solution1 is 9 litres and solution2 is 12 litres.

Answer (C)

JeffTargetTestPrep · Answer

We can let x = the number of liters of the 90% purity solution and y = the number of liters of the 97% purity solution. We need to determine the value of x.

Since there are 21 liters of the solution:

x + y = 21

y = 21 - x

Since after mixing the two solutions the new mixture has 97% purity:

0.9x + 0.97y = 0.94(x + y)

90x + 97y = 94x + 94y

3y = 4x

Since y = 21 - x, we can substitute 21 - x for y in the equation 3y = 4x:

3(21 - x) = 4x

63 - 3x = 4x

63 = 7x

x = 9

Answer: C

IdiomSavant · Answer

No math for this one.

94% is closer to 97% but barely meaning the mixtures will not be equal parts but will be slightly more of the higher purity. Quickly eliminate A and B. Out of the others 9 is the easy choice. If the other choices were closer to half this wouldn't work.

generis · Answer

Weighted average, one variable, slightly different formula.
The two solutions have the  same  pure ingredient (e.g. alcohol)

Let A = the 90% pure solution
Let B = the 97% pure solution
Total resultant  volume  = (A+B) = 21
If A + B = 21, then
B = (21 - A)
A + B,  purity  /concentration, given: 91%

Let x = the quantity (volume) of A
Multiply decimal purities by 100 = integers
Weighted average is not affected.

(% A)(Vol A) + (% B)(Vol B) = (% A+B)(Vol A + B)

90(x) + 97(21 - x) = 94(21) 
 90x + 2036 - 97x = 1974 
 63 = 7x 
 x = \frac{63}{7} = 9

Answer C

seed · Answer

(A) 15 litres 
(B) 12 litres
(C) 9 litres 
(D) 6 litres
(E) 4 litres

Scale Method:

(Sol 1) 90%------4-------------94%-----3----97% (Sol 2)

\frac{Sol1}{Sol2} = \frac{3}{4}

How much is the quantity of the first solution in the resulting mixture?

\frac{Sol1}{ -> Total}  =  \frac{3}{(3+4)}  =  \frac{3}{7}

Hence, the Sol1 is  \frac{3}{7}*21 = 9  litres.

Answer: (C).

akadiyan · Answer

Known Data
Solution 1 purity = 90%
Solution 2 purity = 97%

Mixed solution 3 = 94%

Critical information:
If you see the mixed solution , its 94% pure and 94% is slightly higher than the average 93.5%

Solution 3 is higher than average means ,solution 2 might be on a higher side than solution 1.

Solution:
Step 1: The resulting solution is 21 liters. Half of which is 10.5 liters. Based on the information above , solution 1 would be lesser than 50% i.e solution is < 10.5 liters and solution 2 is > 1.5 liters. Based on this info we can eliminate A,D and E. We are left with B and C.

Step 2:
We know that solution 2 is higher than 50%, so this means we can eliminate option B.

Option C - 9 liters is the answer

Ans:   C

vaibhav1221 · Answer

A simpler method without doing any calculation.

90-91-92-93- 94 -95-96-97

94 is closer to 97 than it is to 90. This means that a greater amount of the 97% purity solution was mixed in the 21 litres (more than half). So, option A and B are out.
It could've been 6 or 4 litres had the resulting solution been more close to 97. Right now it is somewhere in the middle. Option C seems to be the most appropriate one.

The more the difference between the purity of the two solutions, the harder it is to estimate your answer like in the above method.
For example, had the two solutions had the following purity levels, it would've been difficult to estimate like shown above.

33% & 89% purity solutions are mixed to form a 57% purity solution of 21 litres.

It becomes difficult to estimate. So, this method is feasible only if the two purity levels of the initial solution are closer to each other.

Hope this helps.

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Two solutions of 90% and 97% purity are mixed resulting in 21 litres

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