Container X initially contains 30 liters of a solution that is 20\% acid by volume. Contai… — GMAT

Container X initially contains $30$ liters of a solution that is $20\%$ acid by volume. Container Y contains $V$ liters of a solution that is $50\%$ acid by volume. If $10$ liters of pure water are added to Container X and the entire contents of Container X are then mixed with Container Y, the resulting mixture is $30\%$ acid by volume. What is the value of $V$ , in liters?

A
$12$
B
$15$
C
$20$
$30$ Answer
E
$40$

Answer

30

liters

The option stating

30

liters is correct because Container X initially contains

6

liters of acid (

0.20 \times 30

). After adding

10

liters of water, Container X holds

40

liters of solution with

6

liters of acid. Container Y contributes

0.50V

liters of acid out of

V

liters. Equating the total acid ratio to

30\%

yields

(6 + 0.50V) / (40 + V) = 0.30

, which solves cleanly to

V = 30

Step-by-Step Solution

Calculate the volume of pure acid initially present in Container X.

\text{Acid in X} = 20\% \text{ of } 30 = 0.20 \times 30 = 6 \text{ liters}

Determining the absolute amount of solute is required to set up the mixture equation.

Determine the new total volume of Container X after adding pure water.

\text{New Volume of X} = 30 + 10 = 40 \text{ liters}

. The acid amount remains

6

liters.

Adding pure water increases the solution's total volume while leaving the acid quantity unchanged.

Express the amount of acid in Container Y in terms of

V

\text{Acid in Y} = 50\% \text{ of } V = 0.50V \text{ liters}

Container Y contains a

50\%

concentration of acid across

V

liters.

Formulate and solve the concentration equation for the final combined mixture.

\frac{6 + 0.50V}{40 + V} = 0.30 \implies 6 + 0.50V = 0.30(40 + V) \implies 6 + 0.50V = 12 + 0.30V \implies 0.20V = 6 \implies V = 30

Setting total combined acid over total combined volume equal to the final concentration of

30\%

gives the unknown volume

V

Key Concept

Two-stage dilution and mixture concentration using weighted average equations

Estimated Time:2m 0s

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