Percentage problem

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Percentage problem

by seema19 » Sun Oct 02, 2011 10:47 am
The quantity of water (in ml) needed to reduce 9 ml shaving lotion containing 50% alcohol to a lotion containing 30% alcohol is:

a. 4
b. 5
c. 6
d. 7
e. 8

Answer : c

this is how i solved it, but it was wrong -
In 9 ml lotion, 4.5 ml - alcohol and 4.5 - water.
Let X be the amount to water added to bring down the alcohol level to 30%. Then,
[(X + 4.5)/ (9 + X) ] * 100 = 30
This way, i get a negative value for X. Where am i going wrong? Someone please help
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by GmatMathPro » Sun Oct 02, 2011 10:57 am
the numerator should just be 4.5, not 4.5+x. remember, the top is how much alcohol is in the solution. water is 0% alcohol, so adding water doesn't add any alcohol.
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by shankar.ashwin » Sun Oct 02, 2011 11:04 am
Ya it should be

4.5/(X+9) = 3/10

15 = X+9

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by factor26 » Sun Oct 02, 2011 1:02 pm
i think the best way to solve this question is to form a chart and document what information step by step.


The quantity of water (in ml) needed to reduce 9 ml shaving lotion containing 50% alcohol

this means the orig ratio of solution to water is 4.5 ; 4.5 or 1;1

from this we can make a chart ... and us the answer choices given to solve... see attached.
Attachments
solve.xlsx
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by narenkr » Sun Oct 02, 2011 6:57 pm
Probably, plugging in values in this problem saves time as well!!