Mixtures: Milk and Water

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RadiumBall: Master | Next Rank: 500 Posts; Posts: 132; Joined: Thu Dec 02, 2010 2:49 am; Thanked: 5 times

Mixtures: Milk and Water

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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Source: Beat The GMAT — Problem Solving | Sun Mar 13, 2011 5:45 pm

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pm; Thanked: 127 times; Followed by:10 members

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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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

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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