A mixture of 125 gallons of wine and water contains 20% water .How much water must be added to the mixture in order to increase the percentage of water to 25% of the new mixture.
a 10 gals
b 8.5 gals
c 8 gals
d 6.66 gals
e 8.33 gals
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mixture problem
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vkb001
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Two ways to solve this:
Method 1:
125 gallons of solution has 25 gallons of water (20%). Let's add x gallons of water to the solution to bump the concentration to 25%.
So, the new concentration is: (25 + x)/(125+x) = 25/100. Solve for x. x = 25/3 or 8.33 gallons.
Method 2:
You are adding solution which is 100% concentrated water (pure water, of course). Resulting solution is 25%. If you are adding x gallons of 100% concentrated water,
(125*20 + x*100)/(125+x) = 25
=> 125*20 + x*100 = 125*25 + x*25
=> 75*x = 125*5
=> x = 25/3 or 8.33 gallons
Method 1:
125 gallons of solution has 25 gallons of water (20%). Let's add x gallons of water to the solution to bump the concentration to 25%.
So, the new concentration is: (25 + x)/(125+x) = 25/100. Solve for x. x = 25/3 or 8.33 gallons.
Method 2:
You are adding solution which is 100% concentrated water (pure water, of course). Resulting solution is 25%. If you are adding x gallons of 100% concentrated water,
(125*20 + x*100)/(125+x) = 25
=> 125*20 + x*100 = 125*25 + x*25
=> 75*x = 125*5
=> x = 25/3 or 8.33 gallons
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GMATGuruNY
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Wine = .8*125 = 100 gallons.ankurmit wrote:A mixture of 125 gallons of wine and water contains 20% water .How much water must be added to the mixture in order to increase the percentage of water to 25% of the new mixture.
a 10 gals
b 8.5 gals
c 8 gals
d 6.66 gals
e 8.33 gals
The amount of wine is not changing and must be 75% of the new mixture:
100 = .75x
x = 100/.75 = 133.33 gallons.
Since the volume of the new mixture is 133.33 gallons, the amount of water that must be added = 133.33-125 = 8.33 gallons.
The correct answer is E.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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ankurmit
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Thanks dear..i was looking out this method only.vkb001 wrote:
Method 2:
You are adding solution which is 100% concentrated water (pure water, of course). Resulting solution is 25%. If you are adding x gallons of 100% concentrated water,
(125*20 + x*100)/(125+x) = 25
=> 125*20 + x*100 = 125*25 + x*25
=> 75*x = 125*5
=> x = 25/3 or 8.33 gallons
Thank you Mitch
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Ankur mittal
Ankur mittal
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venmic
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Mitch great understandng of the underlying concept
Thanks
Thanks
GMATGuruNY wrote:Wine = .8*125 = 100 gallons.ankurmit wrote:A mixture of 125 gallons of wine and water contains 20% water .How much water must be added to the mixture in order to increase the percentage of water to 25% of the new mixture.
a 10 gals
b 8.5 gals
c 8 gals
d 6.66 gals
e 8.33 gals
The amount of wine is not changing and must be 75% of the new mixture:
100 = .75x
x = 100/.75 = 133.33 gallons.
Since the volume of the new mixture is 133.33 gallons, the amount of water that must be added = 133.33-125 = 8.33 gallons.
The correct answer is E.
