It is currently 17 Oct 2017, 19:20

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A 20 litre mixture of milk and water contains milk and water

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 29 Jan 2005
Posts: 5207

Kudos [?]: 434 [4], given: 0

A 20 litre mixture of milk and water contains milk and water [#permalink]

### Show Tags

29 Oct 2005, 10:32
4
KUDOS
22
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:35) correct 21% (01:57) wrong based on 514 sessions

### HideShow timer Statistics

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. 11: 2
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Jun 2012, 01:39, edited 1 time in total.
Edited the question and added the OA

Kudos [?]: 434 [4], given: 0

VP
Joined: 30 Sep 2004
Posts: 1480

Kudos [?]: 411 [0], given: 0

Location: Germany

### Show Tags

29 Oct 2005, 10:48
x/8=(1-10/20)^2 => x=amount of water left after 2 removements. its 9:1...
_________________

If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

Kudos [?]: 411 [0], given: 0

Manager
Joined: 01 Aug 2005
Posts: 68

Kudos [?]: 19 [8], given: 0

### Show Tags

29 Oct 2005, 10:51
8
KUDOS
5
This post was
BOOKMARKED
2) 9 : 1

From the beginning;
Initially milk to water is 12l : 8l
remove half 6 - 4
add 10l milk 16 - 4
remove half 8 - 2
add 10l milk 18 - 2
18:2 = 9:1

Kudos [?]: 19 [8], given: 0

Manager
Joined: 01 Aug 2005
Posts: 68

Kudos [?]: 19 [0], given: 0

### Show Tags

29 Oct 2005, 10:52
Chris I dont really understand your reasoning, care to explain a bit where the numbers come from. Thanks.

Kudos [?]: 19 [0], given: 0

VP
Joined: 30 Sep 2004
Posts: 1480

Kudos [?]: 411 [0], given: 0

Location: Germany

### Show Tags

29 Oct 2005, 11:27
1
This post was
BOOKMARKED
xennie wrote:
Chris I dont really understand your reasoning, care to explain a bit where the numbers come from. Thanks.

usually i use this formula for these kind of questions...
amount of x after removal/total amount of x=(1-(amount of y that is replaced)/total volume)^number of replacements...not the best but the fastest way unless its trickier...
_________________

If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

Kudos [?]: 411 [0], given: 0

Manager
Joined: 01 Aug 2005
Posts: 68

Kudos [?]: 19 [0], given: 0

### Show Tags

29 Oct 2005, 11:31
Where did you get it from? Might be useful to memorize a few of those formulas for the actual exam.

Kudos [?]: 19 [0], given: 0

Intern
Joined: 26 Apr 2012
Posts: 5

Kudos [?]: 2 [2], given: 0

Re: A 20 litre mixture of milk and water contains milk and water [#permalink]

### Show Tags

26 Apr 2012, 03:41
2
KUDOS
he 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,{W_r}/{W_o}= (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, {W_r}/{W_o} =(1/2)^2  =1/4
Therefore, "W_r ={W_o}/4= 8/4 = 2 litres

Hope it helps

Kudos [?]: 2 [2], given: 0

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7670

Kudos [?]: 17338 [8], given: 232

Location: Pune, India
Re: A 20 litre mixture of milk and water contains milk and water [#permalink]

### Show Tags

26 Apr 2012, 06:29
8
KUDOS
Expert's post
6
This post was
BOOKMARKED
GMATT73 wrote:
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?

(1) 17 : 3
(2) 9 : 1
(3) 3 : 17
(4) 5 : 3
(5) 11: 2

Use this:

New Concentration of Water = Old concentration of Water * (V1/V2)^n

New Concentration of Water = 2/5 * (1/2)^2 = 1/10

Ratio of milk:water = 9:1

Complete explanation of this formula and method is given here: http://www.veritasprep.com/blog/2012/01 ... -mixtures/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17338 [8], given: 232

Manager
Joined: 28 Jul 2011
Posts: 234

Kudos [?]: 160 [2], given: 16

Re: A 20 litre mixture of milk and water contains milk and water [#permalink]

### Show Tags

31 May 2012, 20:23
2
KUDOS
1
This post was
BOOKMARKED
I just learned the new method to solve this problem as discussed by Karishma from veritas link, Trying to solve this question using that method

For future reference

total solution : 20 liters
milk : water 3:2

milk = 12 liters
water = 8 liters

Amount = Concentratio * volumn
therefore concentration of water in the solution is

8 = Cw * 20
Cw = 2/5

Step 1: 10 liters from 20 liters solution is removed - in the leftover solution the concentration of water remains the same. i.e. 2/5. Intial volume of solution was 20, new volumn is 10 (after 10 liter is removed)

Step 2: 10 liters of pure milk is added to the solution, therefore new solution is again 20 liters

Initial COncentration (Ci) * Initial Volumn (Vi) = Final Contentration (Cf) * final Volumn (Vf)
(2/5) * 10 = Cf * 20
Cf = 2/5 (1/2) (the amount of water will remain the same when as initial in (10 liter solution) but concentration of water will changes when milk is added to intial 10 liter water)

Step 3 now again from the Step 2 solution we remove 10 liter solution and added 10 liter pure milk

cf = (2/5) (1/2) (1/2)
cf = 1/10 (this is a new concentration of Water in the solution)

there fore concentration of milk is 9/10

therefore ratio of milk : water is 9:1

Kudos [?]: 160 [2], given: 16

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16760

Kudos [?]: 273 [0], given: 0

Re: A 20 litre mixture of milk and water contains milk and water [#permalink]

### Show Tags

30 Sep 2013, 14:43
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Manager
Joined: 23 May 2013
Posts: 122

Kudos [?]: 67 [0], given: 110

### Show Tags

19 Oct 2013, 19:54
christoph wrote:
xennie wrote:
Where did you get it from? Might be useful to memorize a few of those formulas for the actual exam.

here are some useful formulas...

The attachment is written with invisible ink
i cant see anything..pls can you upload it again thanks
_________________

“Confidence comes not from always being right but from not fearing to be wrong.”

Kudos [?]: 67 [0], given: 110

Math Expert
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128619 [0], given: 12180

### Show Tags

20 Oct 2013, 03:56
ankur1901 wrote:
christoph wrote:
xennie wrote:
Where did you get it from? Might be useful to memorize a few of those formulas for the actual exam.

here are some useful formulas...

The attachment is written with invisible ink
i cant see anything..pls can you upload it again thanks

This attachment is lost.
_________________

Kudos [?]: 128619 [0], given: 12180

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16760

Kudos [?]: 273 [0], given: 0

Re: A 20 litre mixture of milk and water contains milk and water [#permalink]

### Show Tags

15 Dec 2014, 05:33
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16760

Kudos [?]: 273 [0], given: 0

Re: A 20 litre mixture of milk and water contains milk and water [#permalink]

### Show Tags

19 Dec 2015, 06:22
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16760

Kudos [?]: 273 [0], given: 0

Re: A 20 litre mixture of milk and water contains milk and water [#permalink]

### Show Tags

03 Mar 2017, 16:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Re: A 20 litre mixture of milk and water contains milk and water   [#permalink] 03 Mar 2017, 16:13
Display posts from previous: Sort by