In what ratio should a 30% solution be mixed with a 3% solution to

Question

In what ratio should a 30% solution be mixed with a 3% solution to achieve a 12% solution?

A. 1:3
B. 1:2
C. 2:3
D. 3:4
E. 4:5

Bunuel · Answer

In what ratio should a 30% solution be mixed with a 3% solution to achieve a 12% solution?

A. 1:3
B. 1:2
C. 2:3
D. 3:4
E. 4:5

Let  x  denote the volume of the 30%-solution and  y  the volume of the 3%-solution.
 
Using the mixture equation, we get:  \frac{0.3x + 0.03y}{x + y} = 0.12 , which simplifies to  30x + 3y = 12x + 12y . From this, we derive  18x = 9y , leading to the ratio  x:y = 1:2 .

Answer: B

MartyMurray · Answer

In what ratio should a 30% solution be mixed with a 3% solution to achieve a 12% solution?

We can answer this one quickly using alligation.

Difference between 3 and 30 is 27.

Distance from 3 to 12 is 9, which is 1/3 of 27.

So, the percentage of the final mixture, 12%, is 1/3 of the way from 3% to 30%.

Thus, 1/3 of the final mixture must be the 30% mixture.

2/3 is the 3% mixture.

So, the ratio of 30% to 3% is 1:2.

A. 1:3
B. 1:2
C. 2:3
D. 3:4
E. 4:5

Correct answer:  B

RonPurewal · Answer

Since you only find out the ratio—not the actual amounts of the two components—you can also pick a total amount for one of the two components, and then backsolve from the answer choices (which will give concrete amounts for everything, once you've picked that one value) to see which choice ends up producing the required 12% solution overall.

If we want to make up a total amount for the first solution, then ideally that amount should be a whole-number multiple of 1, 2, 3, and 4 (to make all the ratios work out to whole-number amounts), and also a multiple of 10 so that 30% of the total is another whole number.
So, let's pick 120 mL (could be ounces, or whatever other unit) of the 30% solution.  With that figure chosen, 30% of 120 = 36 mL of that solution consists of the active chemical.

Start with choice C:
If there are  x  mL of the 3% solution, then 2/3 = 120/ x , so that  x  = 180 mL.  So there are 180 mL of the 3% solution, of which (0.03)(180) = 5.4 mL is active ingredient.
In total, then, there are 120 + 180 = 300 mL of solution, containing 36 + 5.4 = 40.4 mL of active ingredient. 
We only  WANT  (0.12)(300) = 36 mL of active ingredient in this case, though.  So choice C gives us   too much   of the active ingredient—meaning there's proportionally too much of the 30% solution.
Eliminate C, and also eliminate D and E (in which the relative proportion/weight of the 30% solution is even greater than in choice C).

Now try choice B:
If there are  x  mL of the 3% solution, then 1/2 = 120/ x , so that  x  = 240 mL.  So there are 240 mL of the 3% solution, of which (0.03)(240) = 7.2 mL is active ingredient.
In total, then, there are 120 + 240 = 360 mL of solution, containing 36 + 7.2 = 43.2 mL of active ingredient.
43.2 is exactly 12% of 360, so B is the correct answer.

In what ratio should a 30% solution be mixed with a 3% solution to

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In what ratio should a 30% solution be mixed with a 3% solution to

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