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# How many ounces of water must be added to 10 ounces of 3 % alcohol

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How many ounces of water must be added to 10 ounces of 3 % alcohol  [#permalink]

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01 Oct 2018, 03:48
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79% (01:10) correct 21% (01:14) wrong based on 34 sessions

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How many ounces of water must be added to 10 ounces of 3 % alcohol and water solution to reduce the solution to 1 % alcohol.
A)5
B)10
C)15
D)20
E)30

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Re: How many ounces of water must be added to 10 ounces of 3 % alcohol  [#permalink]

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01 Oct 2018, 04:03
1
Abhi077 wrote:
How many ounces of water must be added to 10 ounces of 3 % alcohol and water solution to reduce the solution to 1 % alcohol.
A)5
B)10
C)15
D)20
E)30

Alchohol Quantity = (3/100)*10 = 0.3 Ounce

Now, After adding water the same alcohol quantity should represent 1% of the total new quantity

i.e. $$0.3 = (1/100)*(10+x)$$ . where $$x$$ is the quantity of water added

i.e. $$10+x = 30$$

i.e. $$x = 20$$

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Re: How many ounces of water must be added to 10 ounces of 3 % alcohol  [#permalink]

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01 Oct 2018, 04:15
Let x be the no. of ounces of water to be added.
We know that 10 ounces of solution has 3% alcohol. That is 10*(3/100) = 0.3 ounces. So, 10 ounces of solution consists of 0.3 ounces of alcohol and 9.7 ounces of water.
Now, with the above information, since there is no addition of alcohol , the amount of alcohol in the resultant solution after addition of water will be the same 0.3 ounces. But, the percentage will change to 1%.
So, 0.3 = (10+x)(1/100)
Implies, 0.3 = 1/10 +x/100
0.3 = (10+x)/100
30 = 10 + x
x = 20.
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Re: How many ounces of water must be added to 10 ounces of 3 % alcohol  [#permalink]

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03 Oct 2018, 10:52
Top Contributor
Abhi077 wrote:
How many ounces of water must be added to 10 ounces of 3 % alcohol and water solution to reduce the solution to 1 % alcohol.
A)5
B)10
C)15
D)20
E)30

The original solution contains 10 ounces
3% of that is alcohol
3% of 10 = 0.3
So, the original solution contains 0.3 ounces of alcohol

Let x = the amount of water (in ounces) that must be added
So, the volume of the RESULTING solution = 10 + x ounces

IMPORTANT: Since we're adding water only, the volume of alcohol does not change.
In other words, there are 0.3 ounces of alcohol in the RESULTING solution

We want the RESULTING solution to be 1% alcohol
In other words: (volume of alcohol in solution)/(total volume of solution) = 1/100
Rewrite as: 0.3 /(10 + x) = 1/100
Multiply both sides by (10 + x) to get: 0.3 = (10 + x)/100
Multiply both sides by 100 to get: 30 = 10 + x
Solve: x = 20

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Re: How many ounces of water must be added to 10 ounces of 3 % alcohol  [#permalink]

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03 Oct 2018, 11:17
Abhi077 wrote:
How many ounces of water must be added to 10 ounces of 3 % alcohol and water solution to reduce the solution to 1 % alcohol.
A)5
B)10
C)15
D)20
E)30

Let´s do it with another technique: alligation!

$$? = x$$

$${{10} \over {10 + x}} = {{1 - 0} \over {3 - 0}}\,\,\left( { = {{10} \over {30}}} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 20$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: How many ounces of water must be added to 10 ounces of 3 % alcohol &nbs [#permalink] 03 Oct 2018, 11:17
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