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How many liters of pure alcohol must be added to a 100-liter [#permalink]

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31 Mar 2011, 10:25

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How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol?

How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol?

(A) 7/2 (B) 5 (C) 20/3 (D) 8 (E) 39/4

Hi guys just a bit lost in this question...would appreciate if someone could help me out

20% Alcohol solution means; in the 100 liter solution, 20 liters of solution is alcohol and 80 liters other solvents.

If we add "x" liters of alcohol to the solution, the solution becomes "100+x" liters and alcohol, which was 20 liters, becomes 20+x liters.

According to the statement; 20+x = 25% of (100+x) OR 20+x=(100+x)/4 80+4x=100+x 3x=20 x=20/3

How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol?

(A) 7/2 (B) 5 (C) 20/3 (D) 8 (E) 39/4

Hi guys just a bit lost in this question...would appreciate if someone could help me out

Here is my crack at it:

Given:

20% of solution is alcohol

80% of solution is other

Total volume = 100 liters

Derived:

20% * 100 liters = 20 liters

Now, if we add additional alcohol to the solution, we are altering the volume, so it's no longer going to be just 100 liters, it's going to be 100 plus some arbitrary amount. This gives us 100 + x liters of solution after adding more alcohol. In addition, when we added more alcohol, there is not just 20 liters of alcohol anymore (we just added some more), there is going to be 20 + x liters of alcohol.

What we're wanting to figure out is: how much alcohol must be added to result in there being 25% alcohol.

As mentioned before, we started out with:

20% * 100 = 20 liters

But, now we have:

25% * (100 + x) = (20 + x)

Now, let's just solve for x:

Convert the percentage and multiply: \({ \frac{25}{100} * (100 + x) = (20 + x) }\)

\({ \frac{(2500 + 25x)}{100} = (20 + x) }\)

Simply the left side: \({ \frac{25(100 + x)}{100} = (20 + x) }\)

We have 20% alcohol and 80% water. As per the question in the final mixture alcohol should be 25% and water should be 75%. Hence we can say that 80% water will be mixed with 0% water to yield a solution that will contain 75% water. So using alligations:

80%---------0%

75

75-----------5 75:5 = 15:1

Say we added x units of alcohol to the original mixture. These x units will have 0% water. And from above we see 80% water solution is mixed with 0% water solution in 15:1.

How many liters of pure alcohol must be added to a 100-liter sol [#permalink]

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03 Jun 2015, 03:05

We can solve such weighted average problem by understanding the underlying concept. You need to look at the difference between the alcohol level of the 20% solution and the pure alcohol. _ The 20% solution has a alcohol level that is 5% lower than the level of alcohol of the final mixture, let's say -5 differential. _ The pure (100%) alcohol has a alcohol level that is 75% higher than the level of alcohol of the final mixture, let's say +75 differential. You need to make these differentials cancel out, so just multiply both differentials by respective volumes so that the positive will cancel out with the negative: 75x - 5.100 = 0 -> x = 500/75 = 20/3

Since this question is built around the concept of a "weighted average", there are several different ways that you can go about solving it. Since the question asks how much alcohol must be added, and the answer choices are NUMBERS, we can TEST THE ANSWERS and do some basic arithmetic to get to the solution.

We're told that a 100-liter solution is 20% alcohol. This means that 20 liters are alcohol and 80 liters are not alcohol. We're asked how many liters must be added to this 100-liter solution to get a solution that is 25% alcohol.

Let's start with ANSWER B: 5 liters IF....we add 5 liters of alcohol to this existing mixture.... Total alcohol = 20+5 = 25 liters Total liquid = 100+5 = 105 liters 25/105 is LESS than 25% alcohol (since 25/100 = 25%, 25/105 is LESS than 25%), thus Answer B CANNOT be the answer. We need MORE alcohol to raise the percentage. Eliminate Answers A and B.

Next, let's TEST ANSWER D: 8 liters IF....we add 8 liters of alcohol to this existing mixture.... Total alcohol = 20+8 = 28 liters Total liquid = 100+8 = 108 liters 28/108 is MORE than 25% alcohol (since 28/112 = 25%, 28/108 is MORE than 25%), thus Answer D CANNOT be the answer. We need LESS alcohol to raise the percentage. Eliminate Answers D and E.

Re: How many liters of pure alcohol must be added to a 100-liter [#permalink]

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01 Aug 2015, 03:49

yenh wrote:

We can solve such weighted average problem by understanding the underlying concept. You need to look at the difference between the alcohol level of the 20% solution and the pure alcohol. _ The 20% solution has a alcohol level that is 5% lower than the level of alcohol of the final mixture, let's say -5 differential. _ The pure (100%) alcohol has a alcohol level that is 75% higher than the level of alcohol of the final mixture, let's say +75 differential. You need to make these differentials cancel out, so just multiply both differentials by respective volumes so that the positive will cancel out with the negative:75x - 5.100 = 0 -> x = 500/75 = 20/3

Hope it's clear.

Hi, could you please explain this concept in a simple form? or in graphical form? and Why the positive will cancel out with the negative?

Re: How many liters of pure alcohol must be added to a 100-liter [#permalink]

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17 Mar 2016, 05:15

How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol?

(A) 7/2 (B) 5 (C) 20/3 (D) 8 (E) 39/4

Alcohol-------------------- Total solution--------------% of alcohol 20 -------------------------100 --------------------------20% 20+x-----------------------100+x ----------------------25% (20+x)/(100+x) =25/100 x=20/3

Re: How many liters of pure alcohol must be added to a 100-liter [#permalink]

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Re: How many liters of pure alcohol must be added to a 100-liter [#permalink]

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01 Apr 2017, 20:23

Acer86 wrote:

How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol?

(A) 7/2 (B) 5 (C) 20/3 (D) 8 (E) 39/4

let x=liters of alcohol to be added .2*100+x=.25(100+x) x=20/3 C

Re: How many liters of pure alcohol must be added to a 100-liter [#permalink]

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01 Apr 2017, 23:35

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Acer86 wrote:

How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol?