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Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9772
Location: Pune, India
A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

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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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Senior Manager  G
Status: love the club...
Joined: 24 Mar 2015
Posts: 267
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

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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  G
Status: So far only Dreams i have!!
Joined: 05 Jan 2015
Posts: 134
WE: Consulting (Consulting)
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

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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.
Intern  B
Joined: 10 Aug 2019
Posts: 18
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

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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 This is coming out to be 82.33 what am i doing wrong?
Intern  B
Joined: 26 Aug 2017
Posts: 44
Location: Singapore
Concentration: Strategy, General Management
Schools: HBS '21
WE: Management Consulting (Consulting)
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

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Hey guys

Another way to look at this question is to simply see that it is akin to having an interest-rate problem:
- deposited \$X in a bank that pays negative interest, with a rate of X per year
- deposited the money in the bank for 2 years straight, any negative interest incurred in the first year is paid off with the amount you had in the bank account initially.
- Y amount of money is now left after 2 years (or periods)
36 * (1-X/100)^2 = 25, X=16.67%
Manager  S
Joined: 10 Dec 2017
Posts: 127
Location: India
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

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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

100 litres of mixture contains 36 litres of milk and 64 litres of water.
if X litres of mixture is removed and then replaced with an equal amount of water then quantity of milk in the mixture
(36-36/100*X)
36(1-X/100)
This process is repeated once
then quantity of milk is 36(1-X/100)^2
As the mixture is 100 litres, 25% of the mixture is final quantity of milk
so {36(1-X/100)}^2=25
X=16.666=16.67
B:)
Intern  B
Joined: 14 Sep 2019
Posts: 13
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

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gayam wrote:
gayam wrote:
For 100 lts of mixture, we have 36 lts of milk.(36%)
after removing some amount of mixture and adding the same quantity of water the milk content is 25lts.(25%)

Difference in milk = 9lts

100 lts of mixture has 36 lts of milk, so how much mixture will have 9lts of milk
100 - 36
? - 9

=>(9*100)/36 = 25

So 25 lts of mixture is replaced by 25lts of water.

Per my understanding there is something missing in the question???

OK, Thanks mate. I get it now.
I think the question would be more clear if it problem states "the process is repeated once again".
ACTUALLY THAT WOULD BE GRAMATICALLY AND GMAT-ICALLY WRONG, REPEAT MEANS AGAIN. SO REPEATING AGAIN IS REDUNDANT! HOPE THIS HELPS. Re: A 100-litre mixture of milk and water contains 36 litres of   [#permalink] 02 Nov 2019, 00:48

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