A pharmacist has 80 milliliters of a topical liquid formulation that is 5\% active ingredi… — GMAT

A pharmacist has $80$ milliliters of a topical liquid formulation that is $5\%$ active ingredient by volume. How many milliliters of pure active ingredient must the pharmacist add to this formulation so that the resulting mixture is $24\%$ active ingredient by volume?

Answer: 20 mL

Answer

The pharmacist must add

20

milliliters of pure active ingredient.

Adding

20

mL of pure active ingredient increases the amount of solute from

4

mL to

24

mL and the total mixture volume from

80

mL to

100

mL, yielding a final concentration of

\frac{24}{100} = 24\%

Step-by-Step Solution

Determine initial amount of solute

Initial active ingredient volume =

80 \times 0.05 = 4

Before adding pure active ingredient, the solution contains

5\%

active ingredient of the total

80

mL volume.

Formulate algebraic expressions for total active ingredient and total volume

Total active ingredient =

4 + x

mL; Total mixture volume =

80 + x

Adding

x

mL of pure active ingredient increases both the solute volume and the total mixture volume by

x

Set up and solve the mixture concentration equation

\frac{4 + x}{80 + x} = \frac{6}{25} \implies 100 + 25x = 480 + 6x \implies 19x = 380 \implies x = 20

Setting the solute ratio equal to the target concentration of

24\%

yields a linear equation in

x

Key Concept

Mixture Concentration and Algebraic Dilution/Fortification

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