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

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Math Expert
Joined: 02 Sep 2009
Posts: 64999
A vessel is full of a mixture of milk and water, with 9% milk. Nine li  [#permalink]

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01 Jun 2020, 10:37
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Difficulty:

45% (medium)

Question Stats:

66% (02:13) correct 34% (02:44) wrong based on 61 sessions

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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 Nine litres are withdrawn and then replaced with pure water.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]

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01 Jun 2020, 10:48
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 Nine litres are withdrawn and then replaced with pure water.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

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Re: A vessel is full of a mixture of milk and water, with 9% milk. Nine li  [#permalink]

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01 Jun 2020, 11:12
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 Nine litres are withdrawn and then replaced with pure water.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9 liters is withdrawn so left with 9x/100- (9/100) * 9 which becomes equal to 6x/100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
Director
Joined: 25 Jul 2018
Posts: 731
A vessel is full of a mixture of milk and water, with 9% milk. Nine li  [#permalink]

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01 Jun 2020, 11:44
$$\frac{91}{100 }$$—the amount of water in 1 liter mixture.

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

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

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

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Re: A vessel is full of a mixture of milk and water, with 9% milk. Nine li  [#permalink]

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01 Jun 2020, 14:47
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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Re: A vessel is full of a mixture of milk and water, with 9% milk. Nine li  [#permalink]

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02 Jun 2020, 16:52
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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Re: A vessel is full of a mixture of milk and water, with 9% milk. Nine li  [#permalink]

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02 Jun 2020, 18:35
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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Joined: 22 Oct 2018
Posts: 47
Re: A vessel is full of a mixture of milk and water, with 9% milk. Nine li  [#permalink]

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06 Jun 2020, 15:29
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
Re: A vessel is full of a mixture of milk and water, with 9% milk. Nine li   [#permalink] 06 Jun 2020, 15:29