A laboratory technician prepares a chemical mixture containing water, ethanol, and acid in… — GRE General Test

A laboratory technician prepares a chemical mixture containing water, ethanol, and acid in the volume ratio $5 : 3 : 2$ , respectively. After $12\text{ liters}$ of pure ethanol are added to the mixture, the ratio of the volume of water to the volume of ethanol becomes $1 : 1$ . What was the total volume, in liters, of the chemical mixture before the extra ethanol was added?

$60\text{ liters}$ Answer
B
$48\text{ liters}$
C
$72\text{ liters}$
D
$18\text{ liters}$
E
$30\text{ liters}$

Answer

60\text{ liters}

The initial ratio of water, ethanol, and acid is

5 : 3 : 2

, which means the original amounts can be expressed as

5x

3x

, and

2x

liters, respectively, giving a total initial volume of

10x

liters. Adding

12\text{ liters}

of ethanol increases the ethanol amount to

3x + 12

, while water remains

5x

. Since the new ratio of water to ethanol is

1 : 1

, we set

5x = 3x + 12

, which solves to

2x = 12

and

x = 6

. The original total volume is therefore

10(6) = 60\text{ liters}

Step-by-Step Solution

Define initial volumes using a common ratio multiplier

x

Water volume

= 5x

, Ethanol volume

= 3x

, Acid volume

= 2x

, and Total initial volume

= 5x + 3x + 2x = 10x

Ratios represent relative parts of a whole, so multiplying each term by

x

gives the actual quantities.

Express the new volumes after adding

12\text{ liters}

of pure ethanol

New Ethanol volume

= 3x + 12

, while Water volume remains

5x

Ethanol is increased by

12\text{ liters}

, whereas the amount of water remains unchanged.

Set up an equation using the new water-to-ethanol ratio of

1 : 1

5x = 3x + 12 \implies 2x = 12 \implies x = 6

A ratio of

1 : 1

means the volumes of water and ethanol are equal.

Calculate the original total volume of the mixture

Total initial volume

= 10x = 10(6) = 60\text{ liters}

Substituting

x = 6

back into the original total volume expression

10x

yields the required initial volume.

Key Concept

Multi-component ratio modification and proportional equivalence

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

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