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A vessel is full of a mixture of milk and water, with 9% milk. Nine li

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Bunuel
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A vessel is full of a mixture of milk and water, with 9% milk. Nine li [#permalink] New post  01 Jun 2020, 11:37
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A vessel is full of a mixture of milk and water, with 9% milk. Nine litres are withdrawn and then replaced with pure water. If the milk is now 6%, how much does the vessel hold?

(A) 18 litres
(B) 27 litres
(C) 36 litres
(D) 40 litres
(E) 47 litres
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A vessel is full of a mixture of milk and water, with 9% milk. Nine li [#permalink] New post  01 Jun 2020, 11:48
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Bunuel wrote:
A vessel is full of a mixture of milk and water, with 9% milk. Nine litres are withdrawn and then replaced with pure water. If the milk is now 6%, how much does the vessel hold?

(A) 18 litres
(B) 27 litres
(C) 36 litres
(D) 40 litres
(E) 47 litres


Let, initial quantity of mixture = x liters
Initial quantity of milk in mixture = (9/100)*x liters

Milk in 9 litres of mixture = (9/100)*9

9 litre mixture gets replaced by pure water i.e. the net quantity of milk reduced in mixture = (9/100)*9 liters

i.e. Milk now = (9/100)*x - (9/100)*9 = (9/100)*(x-9) = (6/100)*x (Given)

i.e. 9x - 81 = 6x
i.e. 3x = 81
i.e. x = 27 liters

Answer: Option B
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Re: A vessel is full of a mixture of milk and water, with 9% milk. Nine li [#permalink] New post  01 Jun 2020, 12:12
Bunuel wrote:
A vessel is full of a mixture of milk and water, with 9% milk. Nine litres are withdrawn and then replaced with pure water. If the milk is now 6%, how much does the vessel hold?

(A) 18 litres
(B) 27 litres
(C) 36 litres
(D) 40 litres
(E) 47 litres


let total qty be x liters
so milk 9x/100
9 liters is withdrawn so left with 9x/100- (9/100) * 9 which becomes equal to 6x/100
we have
9/100 * ( x-9) = 6x/100
3x-27 = 2x
x= 27 litres
OPTION B
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A vessel is full of a mixture of milk and water, with 9% milk. Nine li [#permalink] New post  01 Jun 2020, 12:44
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\(\frac{91}{100 }\)—the amount of water in 1 liter mixture.

—>\(( \frac{91}{100})x —(\frac{91}{100})*9 + 9 = (\frac{94}{100})x \)

\(\frac{( 94 —91)}{100} x = \frac{(100 —91)}{100}*9\)

\((\frac{3}{100})x = \frac{81}{100} \)
—> \(x = 27\)

Answer (B)

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Re: A vessel is full of a mixture of milk and water, with 9% milk. Nine li [#permalink] New post  01 Jun 2020, 15:47
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Bunuel wrote:
A vessel is full of a mixture of milk and water, with 9% milk. Nine litres are withdrawn and then replaced with pure water. If the milk is now 6%, how much does the vessel hold?

(A) 18 litres
(B) 27 litres
(C) 36 litres
(D) 40 litres
(E) 47 litres



--------------------------Milk--------------------------Water-----------------------------Total
Before -------------- 0.09 T (Lit)--------------------0.91T------------------------------T Lit

After----------------0.09T-9*0.09 (Lit)-------------0.91T+9---------------------------T


So 0.09T-9*0.09 = 0.06 T => T = 9* 3 = 27 Lit .
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gracie
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Re: A vessel is full of a mixture of milk and water, with 9% milk. Nine li [#permalink] New post  02 Jun 2020, 17:52
A vessel is full of a mixture of milk and water, with 9% milk. Nine litres are withdrawn and then replaced with pure water. If the milk is now 6%, how much does the vessel hold?

(A) 18 litres
(B) 27 litres
(C) 36 litres
(D) 40 litres
(E) 47 litres

let c=vessel capacity
focus on water:
.91c-(9)(.91)+9(1)=.94c→
.03c=.81
c=27 litres
B
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satya2029
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Re: A vessel is full of a mixture of milk and water, with 9% milk. Nine li [#permalink] New post  02 Jun 2020, 19:35
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Bunuel wrote:
A vessel is full of a mixture of milk and water, with 9% milk. Nine litres are withdrawn and then replaced with pure water. If the milk is now 6%, how much does the vessel hold?

(A) 18 litres
(B) 27 litres
(C) 36 litres
(D) 40 litres
(E) 47 litres


0.09*(V-9)=.0.06(V)
V=27
B:)
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Re: A vessel is full of a mixture of milk and water, with 9% milk. Nine li [#permalink] New post  06 Jun 2020, 16:29
Bunuel wrote:
A vessel is full of a mixture of milk and water, with 9% milk. Nine litres are withdrawn and then replaced with pure water. If the milk is now 6%, how much does the vessel hold?

(A) 18 litres
(B) 27 litres
(C) 36 litres
(D) 40 litres
(E) 47 litres



Can this question be solved using teetor totter method ? Could someone please post the answer for that ?

Instead of using milk as a quantity, I used water instead and found that the ratio of water in the (100% solution (pure water)) to the ratio of water in the (91% solution (mixture)) is 1/2 --> 1 part / 2 parts

I am probably doing this all wrong. Need help :(
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Re: A vessel is full of a mixture of milk and water, with 9% milk. Nine li [#permalink] New post  29 Apr 2021, 21:39
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If one thinks about it logically, removing 9 liters of solution removed 1/3 of the milk. Removing 27 liters would remove all of the milk and all the water. The container must then hold 27 liters.
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adityasuresh
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Re: A vessel is full of a mixture of milk and water, with 9% milk. Nine li [#permalink] New post  14 Oct 2022, 23:07
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A vessel is full of a mixture of milk and water, with 9% milk. Nine litres are withdrawn and then replaced with pure water. If the milk is now 6%, how much does the vessel hold?

(A) 18 litres
(B) 27 litres
(C) 36 litres
(D) 40 litres
(E) 47 litres

Replacement formula : From the pov of the element in the mixture whose concentration is being reduced
Concenentration of final = Concentration of initial *\( Volume of initial/Volume of final\)
6 = 9 *\( V - 9/V\)
6 = 9V -\(81/V\)
V =27
\(B\)
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donu
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Re: A vessel is full of a mixture of milk and water, with 9% milk. Nine li [#permalink] New post  10 Dec 2023, 19:26
Can we clarify the question to say "how much milk" does the vessel hold. Because it's confusing. Thought it was the total vessel. Thanks.
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Re: A vessel is full of a mixture of milk and water, with 9% milk. Nine li [#permalink]
10 Dec 2023, 19:26
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