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Math Expert V
Joined: 02 Sep 2009
Posts: 58396
In a certain solution, the ratio of water to alcohol is 3:1. If water  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 62% (01:27) correct 38% (01:21) wrong based on 49 sessions

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In a certain solution, the ratio of water to alcohol is 3:1. If water and alcohol combined make up half of the volume of the solution, what percentage of the solution is water?

A 12.5%
B 25%
C 37.5%
D 50%
E 75%

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Location: India
Concentration: Sustainability, Marketing
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Re: In a certain solution, the ratio of water to alcohol is 3:1. If water  [#permalink]

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Bunuel wrote:
In a certain solution, the ratio of water to alcohol is 3:1. If water and alcohol combined make up half of the volume of the solution, what percentage of the solution is water?

A 12.5%
B 25%
C 37.5%
D 50%
E 75%

water : alcohol ; 3:1

let total vol ; 100
half ; 50
3*50 / 4 = 37.5%
IMO C
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3565
Re: In a certain solution, the ratio of water to alcohol is 3:1. If water  [#permalink]

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Bunuel wrote:
In a certain solution, the ratio of water to alcohol is 3:1. If water and alcohol combined make up half of the volume of the solution, what percentage of the solution is water?

A 12.5%
B 25%
C 37.5%
D 50%
E 75%

Use totals of ratio parts. We need nothing else.

We have two "halves" of a solution. One half contains only water and alcohol.
The other half contains some liquid other than water and alcohol (mercury or oil, e.g.)

• The water-and-alcohol portion: from its ratio parts, derive total parts of that portion

W : A : TOTAL parts
$$3 : 1 : 4$$
Total parts = $$(3 + 1) = 4$$

(Water is 3 of 4 parts. Alcohol is 1 of 4 parts. The concentration here does not matter.
We need total volume, total parts, of the whole amount of the solution.
We use the water/alcohol ratio to calculate what amount "half" of the solution equals.)

• The entire solution contains how many parts?

The 4 parts of water-and-alcohol make up only half of all the liquid in the solution

If 4 parts =$$\frac{1}{2}$$ of total parts in the solution, then
8 parts = total number of parts in the solution

The number of parts of water does not change.

• Water is what percentage of the solution [the solution made up of 8 parts]?

Water = 3 parts of 8 parts

Percentage: $$\frac{Part}{Whole}* 100$$

$$\frac{3}{8} = .375 * 100 = 37.5$$

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Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver Re: In a certain solution, the ratio of water to alcohol is 3:1. If water   [#permalink] 22 Jan 2019, 15:41
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