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Math Expert V
Joined: 02 Sep 2009
Posts: 58434
A sample of x litres from a container having a 60 litre mixture of mil  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 63% (02:42) correct 37% (02:36) wrong based on 137 sessions

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A sample of x litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x?

A. 6 litres

B. 10 litres

C. 15 litres

D. 20 litres

E. 30 litres

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Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India
A sample of x litres from a container having a 60 litre mixture of mil  [#permalink]

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Bunuel wrote:
A sample of x litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x?

A. 6 litres

B. 10 litres

C. 15 litres

D. 20 litres

E. 30 litres

Conc of milk in mixture (C1) = 2/5
Conc of milk in pure milk (C2) = 1
Conc of milk in new mix (Cavg) = 1/2

w1/w2 = (1 - 1/2) / (1/2 - 2/5) = (1/2) / (1/10) = 5/1

So original mixture was 5 parts and pure milk was 1 part to get equal proportions of milk and water. Total 6 parts is actually 60 litres which means the 5 parts are 50 litres and 1 part is 10 litres.
Hence 10 litres of original mix was replaced with pure milk.

Check this post: https://www.veritasprep.com/blog/2012/0 ... -mixtures/
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Re: A sample of x litres from a container having a 60 litre mixture of mil  [#permalink]

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Bunuel wrote:
A sample of x litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x?

A. 6 litres

B. 10 litres

C. 15 litres

D. 20 litres

E. 30 litres

use weighted avg formula
w1/w2 = ( a2-aavg)/ ( aavg-a1)
here a2= 1
aavg= 1/2
and a1= 2/5

w1/w2= ( 1-1/2) / ( 1/2-2/5)
w1/w2 = 5/1
total 60 liters
5/6 * 60 = 50 ltrs w1 and w2 = 10 liters
so x= 10
IMO B
Math Expert V
Joined: 02 Aug 2009
Posts: 7988
Re: A sample of x litres from a container having a 60 litre mixture of mil  [#permalink]

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1
Bunuel wrote:
A sample of x litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x?

A. 6 litres

B. 10 litres

C. 15 litres

D. 20 litres

E. 30 litres

A great weighted average method above by VeritasKarishma..
But let me give you another method..
M:W=2:3 means M = $$\frac{2}{5}$$ and W=$$\frac{3}{5}$$
Total 60 liters means M = $$\frac{2}{5}*60=24$$ and W=$$\frac{3}{5}*60=36$$
To be equal both should be 30 each, so a decrease of 6 liters of water from initial 36 liters...

Now if reduction of 1 liter would mean reduction of $$\frac{3}{5}$$ of water, reduction of x liter would mean $$\frac{3}{5}*x$$, but this should be equal to 6..
thus $$\frac{3}{5}*x=6.....x=\frac{5}{3}*6=10$$

B
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Re: A sample of x litres from a container having a 60 litre mixture of mil  [#permalink]

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Bunuel wrote:
A sample of x litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x?

A. 6 litres

B. 10 litres

C. 15 litres

D. 20 litres

E. 30 litres

2/5*(60-x)+x=1/2*60
x=10 litres
B
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Re: A sample of x litres from a container having a 60 litre mixture of mil  [#permalink]

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Bunuel wrote:
A sample of x litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x?

A. 6 litres

B. 10 litres

C. 15 litres

D. 20 litres

E. 30 litres

Since milk and water is in a ratio of 2 to 3, we can create the following equation:

2n + 3n = 60

5n = 60

n = 12

So originally, the container has 24 litres of milk and 36 liters of water. We are told that x liters of the mixture are removed. Note that these x liters that are removed will consist of 3x/5 liters of water and 2x/5 liters of milk. . The x liters of liquid that were removed are replaced by x liters of pure milk. Therefore, we can create the equation:

(24 - 2x/5 + x)/(36 - 3x/5) = 1

24 + 3x/5 = 36 - 3x/5

120 + 3x = 180 - 3x

6x = 60

x = 10

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A sample of x litres from a container having a 60 litre mixture of mil  [#permalink]

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Bunuel wrote:
A sample of x litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x?

A. 6 litres

B. 10 litres

C. 15 litres

D. 20 litres

E. 30 litres

Conc of milk in mixture (C1) = 2/5
Conc of milk in pure milk (C2) = 1
Conc of milk in new mix (Cavg) = 1/2

w1/w2 = (1 - 1/2) / (1/2 - 2/5) = (1/2) / (1/10) = 5/1

So original mixture was 5 parts and pure milk was 1 part to get equal proportions of milk and water. Total 6 parts is actually 60 litres which means the 5 parts are 50 litres and 1 part is 10 litres.
Hence 10 litres of original mix was replaced with pure milk.

Check this post: https://www.veritasprep.com/blog/2012/0 ... -mixtures/

Hi Karishma,
Could you verify the following:
Given that water stays the same and pure milk is added, then…
Cf water =Ci water (Vi solution/Vf solution)
50% = 60% (60-x/60-x+x)
5/6=(60-x/60)
x=60-50=10

Intern  B
Joined: 28 Apr 2016
Posts: 16
Re: A sample of x litres from a container having a 60 litre mixture of mil  [#permalink]

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1
Quantity of milk in original = 24L
Quantity of milk in final =30L
Quantity of milk removed = 2x/5 L
Quantity of milk added = x L
Therefore, 24-2x/5 +x = 30
x=10
Intern  B
Joined: 27 Aug 2019
Posts: 5
A sample of x litres from a container having a 60 litre mixture of mil  [#permalink]

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If 2x-3x = 1x

2/5= 24
3/5= 36
Now, 36-24 = 10

So, 1x= 10
Ans:B A sample of x litres from a container having a 60 litre mixture of mil   [#permalink] 14 Oct 2019, 10:20
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