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Math Expert V
Joined: 02 Sep 2009
Posts: 58327
8 liters of solution is removed from 20% milk solution and 8 liters of  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 73% (02:19) correct 27% (02:39) wrong based on 89 sessions

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8 liters of solution is removed from 20% milk solution and 8 liters of water is added to the solution. The resulting solution has 16% milk in it. What was the initial quantity of the 20% milk solution?

A. 38 liters
B. 40 liters
C. 42 liters
D. 44 liters
E. 45 liters

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Manager  S
Joined: 03 Mar 2017
Posts: 119
Location: India
GMAT 1: 650 Q45 V34 Re: 8 liters of solution is removed from 20% milk solution and 8 liters of  [#permalink]

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2
8 litres of mixture taken out also had 20% milk => milk taken out was 8 x 0.2=1.6 litres

milk/total mixture =0.2=> milk=0.2 total qty

as the total qty remains the same, substitute the above eq as shown below

=>(milk-1.6)/total qty=0.16
=>0.2 total qty - 0.16 total qty= 1.6
=>total qty= 1.6/0.04=40
IMO option B
Director  G
Joined: 22 Nov 2018
Posts: 557
Location: India
GMAT 1: 640 Q45 V35 GMAT 2: 660 Q48 V33 8 liters of solution is removed from 20% milk solution and 8 liters of  [#permalink]

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Bunuel wrote:
8 liters of solution is removed from 20% milk solution and 8 liters of water is added to the solution. The resulting solution has 16% milk in it. What was the initial quantity of the 20% milk solution?

A. 38 liters
B. 40 liters
C. 42 liters
D. 44 liters
E. 45 liters

Milk/total solution = 20% initially then 16%;
M=0.2T

16%=[M-(8*20%)]T;
16%=(0.2T-1.6)/T
0.04T=1.6; T=40 IMO B
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VP  P
Joined: 07 Dec 2014
Posts: 1222
Re: 8 liters of solution is removed from 20% milk solution and 8 liters of  [#permalink]

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Bunuel wrote:
8 liters of solution is removed from 20% milk solution and 8 liters of water is added to the solution. The resulting solution has 16% milk in it. What was the initial quantity of the 20% milk solution?

A. 38 liters
B. 40 liters
C. 42 liters
D. 44 liters
E. 45 liters

let x=initial quantity of 20% milk solution
.8x-8(.8)+8=.84x→
x=40 liters
B
GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 4996
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: 8 liters of solution is removed from 20% milk solution and 8 liters of  [#permalink]

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Bunuel wrote:
8 liters of solution is removed from 20% milk solution and 8 liters of water is added to the solution. The resulting solution has 16% milk in it. What was the initial quantity of the 20% milk solution?

A. 38 liters
B. 40 liters
C. 42 liters
D. 44 liters
E. 45 liters

total qty of milk ; .2*8 ; 16
milk /total = 20%
milk-1.6/total = 16%
milk = .2*total
.2*total-1.6/total = .16
solve for total = 40
IMO B
Manager  G
Joined: 08 Apr 2019
Posts: 148
Location: India
GPA: 4
Re: 8 liters of solution is removed from 20% milk solution and 8 liters of  [#permalink]

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4
Bunuel wrote:
8 liters of solution is removed from 20% milk solution and 8 liters of water is added to the solution. The resulting solution has 16% milk in it. What was the initial quantity of the 20% milk solution?

A. 38 liters
B. 40 liters
C. 42 liters
D. 44 liters
E. 45 liters

Let the initial quantity of the 20% milk solution be X, of which 0.2X would be milk and the remaining (0.8X) be water

Now since 8 litres of this solution is removed and is dilated by adding 8 litres of water, amount of milk reduced would be = 20% of 8 litres, i.e. 1.6 litres

The remaining portion of milk in the solution = 0.2X - 1.6 litres

Now, it is given that the concentration of the resulting solution (or to simply put, % of milk in the resulting solution) = 16%

We can write this as (0.2X - 1.6)/X *100 = 16, solving which we get 4X = 160, or X = 40 (D)

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Target Test Prep Representative D
Status: Founder & CEO
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Joined: 14 Oct 2015
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Re: 8 liters of solution is removed from 20% milk solution and 8 liters of  [#permalink]

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1
Bunuel wrote:
8 liters of solution is removed from 20% milk solution and 8 liters of water is added to the solution. The resulting solution has 16% milk in it. What was the initial quantity of the 20% milk solution?

A. 38 liters
B. 40 liters
C. 42 liters
D. 44 liters
E. 45 liters

When 8 liters of the solution is removed, the 8 liters consists of 0.2 x 8 = 1.6 L of milk, and 6.4 L or water. If we let s = the initial amount, in liters, of the solution, so originally there are 0.2s liters of milk and we can create the equation:

(0.2s - 1.6 + 0)/(s - 8 + 8) = 16/100

(0.2s - 1.6)/s = 4/25

25(0.2s - 1.6) = 4s

5s - 40 = 4s

s = 40

Alternate Solution:

We start with x liters of 20% milk. We remove 8 liters of this solution, so we are removing 8 liters of 20% milk. Then we add back 8 liters of water (which is 0% milk), and the result is x liters of 16% milk. We can summarize this in an equation as:

x(0.20) - 8(0.20) + 8(0) = x(0.16)

0.20x - 1.6 + 0 = 0.16x

0.04x = 1.6

4x = 160

x = 40

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Intern  B
Joined: 10 Oct 2017
Posts: 23
GMAT 1: 610 Q41 V35 Re: 8 liters of solution is removed from 20% milk solution and 8 liters of  [#permalink]

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2
Bunuel wrote:
8 liters of solution is removed from 20% milk solution and 8 liters of water is added to the solution. The resulting solution has 16% milk in it. What was the initial quantity of the 20% milk solution?

A. 38 liters
B. 40 liters
C. 42 liters
D. 44 liters
E. 45 liters

we can do witha allegations:

we see we have 80%water solution, 8 litre is removed and is replayed by 100% water solution to make a 84% water solution.
so

80 100
84
16:4
=4:1
So, 1/5 of the total solution was repplaced with 8 litres.
so, total solution is 40
Intern  B
Joined: 26 May 2019
Posts: 7
Re: 8 liters of solution is removed from 20% milk solution and 8 liters of  [#permalink]

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can we do it this way?

20/100 * x = 8 ltrs.
upon solving, we get x = 40 ltrs. ?

(percentage method?) Re: 8 liters of solution is removed from 20% milk solution and 8 liters of   [#permalink] 11 Jul 2019, 02:59
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