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Mixtures

by shankar.ashwin » Mon Sep 19, 2011 10:17 am
The concentration of alcohol in two wine tanks is 20% and 40% respectively and the rest is grape juice. If a wine glass is filled to its half by both tank 1 and 2 in the ratio 2:3 and the rest is filled again by pure alcohol, then what is the ratio of the grape juice to alcohol in the wine glass?

A) 17:16
B) 16:33
C) 17:50
D) 17:33
E) 17:34
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by cans » Mon Sep 19, 2011 10:38 am
A: 20% alcohol and 80% juice
B: 40% alcohol and 60% juice.
1/2 -> pure alcohol
(2/5)(1/2)*80% juice = 4/25
+ (3/5)(1/2)*60% juice = 9/50
Thus juice = 8/50 + 9/50 = 17/50.
alcohol = 1 - 17/50 = 33/50
ratio: 17:33
IMO D
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by gmatclubmember » Mon Sep 19, 2011 10:40 am
The first solution is 20:80 and second one is 40:60.
When you take the solution in the ration of 2:3 then in half glass of wine you get the alcohol and grape in the ratio of 16:34.
When you fill up the glass you are adding 50 units of alcohol which means in the new solution the ration will be 66:34 = 33:17.

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by knight247 » Mon Sep 19, 2011 10:49 am
The answer is D

Wine A contains 1/5 alcohol and 4/5 grape juice
Wine B contains 2/5 alcohol and 3/5 grape juice

(I've skipped the conversion of percents into fractions...If you need me to elaborate on those steps then plz lemme know)

Wine A:Wine B is 2:3
Let x be the common factor. So the actual quantity of A is 2x and that of B is 3x

A=2x can be broken up into 2x(1/5)=2x/5 alcohol and 8x/5 grape juice
B=3x can be broken up into 3x(2/5)=6x/5 alcohol and 3x(3/5)=9x/5 grape juice

Total alcohol content in the new mixture is (2x/5)+(6x/5)=8x/5
Total grape juice content in the new mixture is (8x/5)+(9x/5)=17x/5

The ratio of grape juice to alcohol is 17x/5:8x/5=17:8

The proportion of grape juice is 17/25
The proportion of alcohol is 8/25

If the glass is 200 litres then only half i.e. 100 litres will be filled with the above mixture
17(100)/25=68 Litres will be grape juice and 8(100)/25=32 Litres will be alcohol.

But this is only half the glass. The remaining 100 litres will be completely filled only with alcohol. So the total grape content remains 68 Litres but the quantity of alcohol will be 132 Litres

Ratio of Grape Juice : Alcohol = 68/132 = 17/33 Hence D
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by mehrasa » Mon Sep 19, 2011 12:07 pm
cans wrote:A: 20% alcohol and 80% juice
B: 40% alcohol and 60% juice.
1/2 -> pure alcohol
(2/5)(1/2)*80% juice = 4/25
+ (3/5)(1/2)*60% juice = 9/50 why here you choose to multiply the percentage of juice but if we multiply the percentage of alcohol, all the numbers will change
thus juice = 8/50 + 9/50 = 17/50.
alcohol = 1 - 17/50 = 33/50
ratio: 17:33
IMO D
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by GMATGuruNY » Mon Sep 19, 2011 1:23 pm
shankar.ashwin wrote:The concentration of alcohol in two wine tanks is 20% and 40% respectively and the rest is grape juice. If a wine glass is filled to its half by both tank 1 and 2 in the ratio 2:3 and the rest is filled again by pure alcohol, then what is the ratio of the grape juice to alcohol in the wine glass?

A) 17:16
B) 16:33
C) 17:50
D) 17:33
E) 17:34
Composition in the wine glass:
Let the amount from tank 1 = 20 units and the amount from tank 2 = 30 units.
Alcohol from tank 1 = .2(20) = 4 units.
Alcohol from tank 2 = .4(30) = 12 units.
Since 20+30 = 50 units, and this amount represents 1/2 the wine glass, the whole wine glass = 100 units.
Alcohol in the rest of the glass = 50 units.
Total alcohol = 4+12+50 = 66.
Thus, total grape juice = 100-66 = 34.
Grape juice:alcohol = 34:66 = 17:33.

The correct answer is D.
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