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# A 100-litre mixture of milk and water contains 36 litres of

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

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19 Nov 2017, 21:40
2
2
alphonsa wrote:
A 100-litre mixture of milk and water contains 36 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 25%. What is the value of x?

A) 17.5 litres
B) 16.67 litres
C) 17.67 litres
D) 16.5 litres
E) 16 litres

Source: 4Gmat

Responding to a pm:

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

You are removing a part of the solution and adding water. When you add water, the amount of milk remains the same.

C1*V1 = C2*V2
This is repeated once more.

C2 = C1 * (V1/V2)^2

$$.25 = .36 * [\frac{(100 - x)}{100}]^2$$

$$\frac{(100 - x)}{100} = \frac{5}{6}$$

x = 100/6 = 16.67 litres
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Karishma
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Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

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20 Nov 2017, 16:18
VeritasPrepKarishma wrote:
alphonsa wrote:
A 100-litre mixture of milk and water contains 36 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 25%. What is the value of x?

A) 17.5 litres
B) 16.67 litres
C) 17.67 litres
D) 16.5 litres
E) 16 litres

Source: 4Gmat

Responding to a pm:

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

You are removing a part of the solution and adding water. When you add water, the amount of milk remains the same.

C1*V1 = C2*V2
This is repeated once more.

C2 = C1 * (V1/V2)^2

$$.25 = .36 * [\frac{(100 - x)}{100}]^2$$

$$\frac{(100 - x)}{100} = \frac{5}{6}$$

x = 100/6 = 16.67 litres

many many thanks to you, mam
Manager
Status: A very long wait.
Joined: 05 Jan 2015
Posts: 96
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Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

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08 Sep 2019, 06:43
alphonsa wrote:
:-D I just found a direct way of doing this.

For replacement problems

C(Final)/C(Initial) = $$(1-x/y)^n$$

Where C is the concentration
x is the amount replaced
y is the total amount
and
n is the number of replacement

Therefore for the given problem
(25/36) = $$(1- x/100 )^2$$

Take Square root on both sides
5/6 = (1- x/100)

x= 16.67 litres

As per question, only one replacement to be done.
But answer is based on 2 replacements. Correct me if i am wrong.
Re: A 100-litre mixture of milk and water contains 36 litres of   [#permalink] 08 Sep 2019, 06:43

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