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Bunuel
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
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Bunuel
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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Bunuel
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

Answer: B
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VeritasKarishma
Bunuel
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.

Answer (B)

Check this post: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/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

Answer (B).
Thanks in advance.
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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
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If 2x-3x = 1x

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

So, 1x= 10
Ans:B
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Given: 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.

Asked: What is the value of x?

60 litres mixture: -
Milk = 24 litres
Water = 36 litres

x litres sample: -
Milk = 2x/5 litres
Water = 3x/5 litres

60 litres mixture after replacement of sample with x litres milk: -
Milk = 24 - 2x/5 + x = 24 + 3x/5
Water = 36 - 3x/5
Since the container will have milk and water in equal proportions.
24 + 3x/5 = 36 - 3x/5
6x/5 = 12
x = 12*5/6 = 10 litres

IMO B
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Amount of milk in original mixture is 24L

Amount of water is 36L

If x quantity was removed, amount of milk left

24-0.4x

Amount of water left

36-0.6x

Now let m be amount of milk needed to have equal mixture therefore


24-0.4x + m = 36-0.6x

M= 36-0.6x-24+0.4x

= 12-0.2x

But m is x

So x = 12-0.2x

1.2x = 12
x = 10L.

Posted from my mobile device
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gracie
Bunuel
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


Can you please tell me why did you write +x in the equation?

Posted from my mobile device
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Zareensoobuh
gracie
Bunuel
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


Can you please tell me why did you write +x in the equation?

Posted from my mobile device

That solution equates the amount of milk after the replacement.

Initially, the milk in the mixture is 2/5 of the total amount. When x liters of the mixture are replaced, the milk proportion in the remaining 60 - x liters is still 2/5. Then, x liters of pure milk are added, making the milk quantity 2/5*(60 - x) + x liters.

The condition is that the milk should be half of the total solution, or 1/2*60 liters.

So, we set up the equation: 2/5*(60 - x) + x = 1/2*60. Solving this gives x = 10 liters.

Answer: B.

Hope this helps.
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