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How many liters of pure alcohol must be added to a 90-liter solution

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How many liters of pure alcohol must be added to a 90-liter solution  [#permalink]

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New post 30 Jun 2017, 02:34
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A
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Question Stats:

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How many liters of pure alcohol must be added to a 90-liter solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol?

(A) 4.5
(B) 5.0
(C) 5.5
(D) 6.0
(E) 6.5

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Re: How many liters of pure alcohol must be added to a 90-liter solution  [#permalink]

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New post 30 Jun 2017, 03:10
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We are given 90 liters of 20% alcohol,
for 18 liters of alcohol, we will have 72 liters of water.

If we want the solution to become 25% alcohol and add pure alcohol,
let the liters of pure alcohol to be added be x

\(\frac{18+x}{72} = \frac{1}{3}\)
54 + 3x = 72
3x = 18
Solution of pure alcohol to be added(x) = 6(Option D)
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Re: How many liters of pure alcohol must be added to a 90-liter solution  [#permalink]

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New post 30 Jun 2017, 05:33
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The amount of alcohol in the 90% solution is 90*\(\frac{1}{5}\)=18 litres

We need to add some solution of pure alcohol to make the total alcohol 25% of the solution

We can use answer choices as it is easier
From D, if we add 6 litres alcohol to the solution, total alcohol will become 18+6=24 litres

Alcohol percent = \(\frac{24}{(90+6)}\) = \(\frac{24}{96}\) = \(\frac{1}{4}\) = 25%

This fits the question, so D is the answer.
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How many liters of pure alcohol must be added to a 90-liter solution  [#permalink]

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New post 30 Jun 2017, 05:38
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Bunuel wrote:
How many liters of pure alcohol must be added to a 90-liter solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol?

(A) 4.5
(B) 5.0
(C) 5.5
(D) 6.0
(E) 6.5

Let x = amount of alcohol to be added

(.20)90 + (1)x = .25 (90 + x)**

18 + x = 22.5 + .25x

.75x = 4.5

x = 6

Answer
**
The method:

90 liter solution is A

Amount of alcohol to be added is B

A + B = total volume of resultant solution

Concentration of pure alcohol is 100%, in decimal form = 1

(Concen. of A)(Vol of A) + (Concen of B)(Vol of B) = (Desired concentration of resultant solution)(Vol of resultant solution)
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Re: How many liters of pure alcohol must be added to a 90-liter solution  [#permalink]

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New post 04 Jul 2017, 06:48
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Bunuel wrote:
How many liters of pure alcohol must be added to a 90-liter solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol?

(A) 4.5
(B) 5.0
(C) 5.5
(D) 6.0
(E) 6.5


Our given solution has 90 x 0.2 = 18 liters of alcohol. We can let x = the number of liters of pure alcohol added and create the following equation:

1/4 = (18 + x)/(90 + x)

90 + x = 4(18 + x)

90 + x = 72 + 4x

18 = 3x

6 = x

Answer: D
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Re: How many liters of pure alcohol must be added to a 90-liter solution  [#permalink]

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New post 10 Jul 2017, 15:37
Alcohol solution= 20% pure alcohol=100%

Required Alcohol%age= 25%

Therefore, alcohol solution must be=75% & pure alcohol must be= 5%
Which in ration is 15:1

We need the mixture in 15:1 form which contains 15 part of the alcohol solution and 1 part of pure alcohol. Since we are asked how many litres of pure alcohol needs to be added.

If 15 parts of alcohol solution is 90 litres, 1 part must be be 90/15 = 6

Answer: D

I'm not good at explanations.
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Re: How many liters of pure alcohol must be added to a 90-liter solution  [#permalink]

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