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Ratio

by abhirup1711 » Tue Jul 02, 2013 9:48 pm
Bob just filled his car's gas tank with 20 gallons of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If his car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many gallons of ethanol must he add into the gas tank for his car to achieve optimum performance?
a) 9/10
b) 1
c) 10/9
d) 20/19
e) 2

May I ask the experts to please post a list of such questions. I need to practice more of these.
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by srcc25anu » Tue Jul 02, 2013 10:28 pm
By Allegation Method:
5% ------- 100%
-----10%-----
90:5 or 18:1

Since 18 is 20 gallons, how much is 1?
1 = 20/18 = 10/9 gallons
Ans C
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by luckypiscian » Wed Jul 03, 2013 2:43 am
let the amount of ethanol to be added be x

equate percentage of ethanol after addition
100 *(1 + x)/(20 + x) = 10
10(1 + x) = 20 + x
9x = 10
x = 10/9
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by GMATGuruNY » Wed Jul 03, 2013 3:44 am
abhirup1711 wrote:Bob just filled his car's gas tank with 20 gallons of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If his car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many gallons of ethanol must he add into the gas tank for his car to achieve optimum performance?
a) 9/10
b) 1
c) 10/9
d) 20/19
e) 2
Current amount of ethanol = .05(20) = 1 gallon.
We can plug in the answers, which represent the amount of ethanol that must be added to yield a 10% solution.

Answer choice C: 10/9 gallons
New ethanol = current ethanol + 10/9 = 1 + 10/9 = 19/9.
New total = current total + 10/9 = 20 + 10/9 = 190/9.
Result:
(new ethanol)/(new total) = (19/9) / (190/9) = 1/10 = 10%.
Success!

The correct answer is C.
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by Brent@GMATPrepNow » Sat Nov 16, 2019 9:18 am
abhirup1711 wrote:Bob just filled his car's gas tank with 20 gallons of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If his car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many gallons of ethanol must he add into the gas tank for his car to achieve optimum performance?
a) 9/10
b) 1
c) 10/9
d) 20/19
e) 2
Bob just filled his car's tank with 20 gallons of gasohol, a mixture containing of 5% ethanol and 95% gasoline.
5% of 20 gallons is 1 gallon.
So, PRESENTLY, there is 1 gallon of ethanol in the car's tank.


We want to add some PURE ethanol to the tank in order to get a 10% mixture of ethanol.
Let x = number of gallons of pure ethanol we ADD to the tank.

FACT #1: Once we add x more gallons of pure ethanol, the car's tank contains 1+x gallons of ethanol.

FACT #2: Once we add x gallons of ethanol, the car's tank contains a TOTAL of 20+x gallons of mixture.

We want the tank to have a 10% mixture of ethanol. In other words, we want the mixture in the tank to contain 1/10 ethanol.
So, we can write the equation: (1+x)/(20+x) = 1/10
Cross multiply to get: 10(1 + x) = 1(20 + x)
Expand: 10 + 10x = 20 + x
Rearrange: 9x = 10
Divide both sides by 9 to get: x = 10/9

Answer: C

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Brent
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