A liquid chemical solution is composed of Chemical A, Chemical B, and Water in the volume … — GRE General Test

A liquid chemical solution is composed of Chemical A, Chemical B, and Water in the volume ratio $2 : 3 : 5$ , respectively. If $40\text{ liters}$ of Chemical A and $20\text{ liters}$ of Water are added to the mixture, the ratio of Chemical A to Water becomes $1 : 2$ . What was the total volume, in liters, of the original solution?

A
$120$
B
$200$
C
$300$
D
$420$
$600$ Answer

Answer

600\text{ liters}

Let the original volumes of Chemical A, Chemical B, and Water be

2x

3x

, and

5x

liters, respectively. The total volume of the original solution is

2x + 3x + 5x = 10x

liters. After adding

40\text{ liters}

of Chemical A and

20\text{ liters}

of Water, the ratio of Chemical A to Water is given as

1 : 2

. Setting up the proportion

\frac{2x + 40}{5x + 20} = \frac{1}{2}

and cross-multiplying yields

2(2x + 40) = 5x + 20

, which simplifies to

4x + 80 = 5x + 20

. Solving for

x

gives

x = 60

. Substituting

x = 60

into the total volume formula gives

10(60) = 600\text{ liters}

. Thus,

600

is the correct answer.

Step-by-Step Solution

Represent the initial volumes of each component in terms of a common multiplier

x

Chemical A

= 2x

, Chemical B

= 3x

, Water

= 5x

. Total volume

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

Ratios

2 : 3 : 5

mean the actual quantities are proportional to these ratio parts.

Set up an equation based on the new volumes of Chemical A and Water.

\frac{2x + 40}{5x + 20} = \frac{1}{2}

Adding

40\text{ L}

of Chemical A and

20\text{ L}

of Water changes their ratio to

1 : 2

Cross-multiply and solve for

x

2(2x + 40) = 1(5x + 20) \implies 4x + 80 = 5x + 20 \implies x = 60.

Solving the linear equation yields the common ratio unit value.

Calculate the total original volume using

x = 60

\text{Total Volume} = 10x = 10(60) = 600\text{ liters}.

The total solution consists of

10

parts in total.

Key Concept

Three-part ratio algebra and proportion adjustments

Estimated Time:1m 30s

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