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Mixtures: Milk and Water

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by RadiumBall » Sun Mar 13, 2011 5:45 pm
In 60 litres of a milk solution the concentration of water is 20%. When some quantity of pure milk is added to this, the concentration of milk changes to 90%. What is the total quantity of milk solution formed?
A) 96 litres
B) 120 litres
C) 114 litres
D) 108 litres
E) 54 litres
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by Night reader » Sun Mar 13, 2011 6:05 pm
the answer to this problem is 120 litres choice B

By using alligation method, we take pure milk's concentration of the second solution %%(100-90)=10 and assign this rate to 80% concentration of milk. We do the same with the 80% concentrated solution and assign %%(90-80)=10 to pure milk. Next we take the ratio of the final quantity received after mixing of two solutions, name this as X and divide it by %%(10+10) numbers Only. Here (X/20)*10=60 OR X=120 liters

for more explanation about alligation method please see this post https://www.beatthegmat.com/those-of-you ... 71770.html
RadiumBall wrote:In 60 litres of a milk solution the concentration of water is 20%. When some quantity of pure milk is added to this, the concentration of milk changes to 90%. What is the total quantity of milk solution formed?
A) 96 litres
B) 120 litres
C) 114 litres
D) 108 litres
E) 54 litres
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by Anurag@Gurome » Sun Mar 13, 2011 6:41 pm
RadiumBall wrote:In 60 litres of a milk solution the concentration of water is 20%. When some quantity of pure milk is added to this, the concentration of milk changes to 90%. What is the total quantity of milk solution formed?
A) 96 litres
B) 120 litres
C) 114 litres
D) 108 litres
E) 54 litres

Solution:
Let the quantity of pure milk added be 'x'.
Now, initially, the quantity of pure milk in 60 liters of milk solution was (80/100) * 60 = 48 liters.
After adding x liters, new quantity of pure milk is 48+x liters.
Also, new quantity of milk with water is 60+x liters.
So, (48+x)/(60+x) = 90/100 = 9/10.
Or, 480+10x = 540+9x.
Or x = 60 liters.
Hence, total quantity of milk solution formed is 60+60 = 120 liters.
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by GMATGuruNY » Sun Mar 13, 2011 7:16 pm
RadiumBall wrote:In 60 litres of a milk solution the concentration of water is 20%. When some quantity of pure milk is added to this, the concentration of milk changes to 90%. What is the total quantity of milk solution formed?
A) 96 litres
B) 120 litres
C) 114 litres
D) 108 litres
E) 54 litres
Almost no math is needed here.

The original solution is 20% water.
The added milk is 0% water.
Since the percentage of water in the final solution -- 10% -- is halfway between 20% and 0%, the final solution must contain equal amounts of the original solution and the added milk.

Thus, added milk = 60 liters, and the total volume = 60+60 = 120 liters.

The correct answer is B.
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by RadiumBall » Sun Mar 13, 2011 8:39 pm
Wow perfect OA: B
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