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

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

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New post 19 Nov 2017, 21:40
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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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Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

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New post 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
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Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

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New post 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 :-D



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

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