milk & water mixture

[gmatfordays]

A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture?

(A) 17 : 3
(B) 9 : 1
(C) 3 : 17
(D) 5 : 3
(E) 12 : 7

[Prepgmat]

[quote]Originally posted by gmatfordays

A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture?

(A) 17 : 3
(B) 9 : 1
(C) 3 : 17
(D) 5 : 3
(E) 12 : 7

Solution:
20 liter mixture with milk and water in the ratio of 3:2
Milk = 3/5(20) = 12L
Water = 2/5(20) = 8L
Remove 10L of Mixture so Milk = 1/2(12L) = 6L, Water = 1/2(8L) = 4L
Add 10L of milk, Milk = 16L & Water = 4L
Repeating the procedure Milk = 8L & Water = 2L.
Add 10L of milk, Milk = 18L & Water = 2L.
Therefore the ratio of Milk and Water = 18:2 = 9:1
The answer is B.[font=Andale Mono][/font=Andale Mono]

[pk]

i think the answer is 9:1. As it goes like this initial mixture of 20 lit is represented as 12:8. After first removal it becomes 6:4. After replacing it with 10lit of milk it becomes 16:4. Again after removal it becomes 8:2 redoing addition it becomes 18:2 which is 9:1

[dig12us]

You can solve this with traditional method which does not take more than 2 minutes.

Is there any other method to solve these type of problems

[GmatJunky]

see attachment

[goforisb]

How did u get 8-4-4 = 2 water from 20 ?

[manish8109]

Amount of water originally present=2/5 * 20 =8

Water left/water present = ( 1- 10/20)^2

=> water left/8 = 1/2^2
=> water left/8 =1/4
=> water left=2

Amount of milk=20-2=18
ratio of milk 7 water= 18/2=9:1 (ANS)

[jjaacc]

Agree with B. Traditional way is the easiest...

[Shirru]

The 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture.

Step 1. When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water.

Step 2. When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step.

Therefore, the ratio of milk and water is 18 : 2 or 9 : 1.

Shortcut.
We are essentially replacing water in the mixture with pure milk.

Let W_O be the amount of water in the mixture originally = 8 litres.
Let W_R be the amount of water in the mixture after the replacements have taken place.

Then, $Wr/Wo= (1-R/M)^n$, where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated.

Hence, $Wr/Wo =(1/2)^2 =1/4$
Therefore, $W_R =Wo/4=8/4 = 2 litres$
Hence the mixture will have 18 litres of milk and 2 litres of water.

I found this son on Alligation or Mixture | Aptitude Question and Answers | Interview Questions with Answers, you may check more questions there.
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