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# When 10% of a solution of milk and water is removed and replaced with

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Senior Manager
Joined: 29 Nov 2018
Posts: 282
Concentration: Marketing, Strategy
When 10% of a solution of milk and water is removed and replaced with  [#permalink]

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20 Mar 2019, 11:13
10
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65% (hard)

Question Stats:

56% (02:13) correct 44% (02:44) wrong based on 93 sessions

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When 10% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 3 : 1. Find the ratio of milk and water before the water is added to the solution.

1. 2 : 1
2. 4 : 1
3. 5 : 1
4. 5 : 2
5. 4 : 3
Intern
Joined: 18 May 2017
Posts: 12
When 10% of a solution of milk and water is removed and replaced with  [#permalink]

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20 Mar 2019, 11:40
2
3
let, initially there was x unit milk and y unit water.
in the removed 10% mixture, milk is 0.1x unit and water is 0.1y unit. we also have to add equal amount of water, that is 0.1(x+y)
new milk amount= x-0.1x= 0.9x
new water amount= y-0.1y+ 0.1(x+y)= y+0.1x
as per the question, 0.9x/(y+0.1x) = 3/1
solution, x/y= 5/1
ans C
##### General Discussion
Intern
Joined: 10 Apr 2018
Posts: 2
Re: When 10% of a solution of milk and water is removed and replaced with  [#permalink]

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20 Mar 2019, 23:50
arimich wrote:
let, initially there was x unit milk and y unit water.
in the removed 10% mixture, milk is 0.1x unit and water is 0.1y unit. we also have to add equal amount of water, that is 0.1(x+y)
new milk amount= x-0.1x= 0.9x
new water amount= y-0.1y+ 0.1(x+y)=y+0.1x
as per the question, 0.9x/(y+0.1x) = 3/1
solution, x/y= 5/1
ans C

Intern
Joined: 18 May 2017
Posts: 12
Re: When 10% of a solution of milk and water is removed and replaced with  [#permalink]

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21 Mar 2019, 03:19
DakshaBafna wrote:
arimich wrote:
let, initially there was x unit milk and y unit water.
in the removed 10% mixture, milk is 0.1x unit and water is 0.1y unit. we also have to add equal amount of water, that is 0.1(x+y)
new milk amount= x-0.1x= 0.9x
new water amount= y-0.1y+ 0.1(x+y)=y+0.1x
as per the question, 0.9x/(y+0.1x) = 3/1
solution, x/y= 5/1
ans C

here, that '0.1x' is the amount not the material
solving the equation
0.9x= 3y +0.3x
=> 0.6x = 3y
=> x= 5y
=> x/y = 5/1
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Location: India
Concentration: Sustainability, Marketing
GPA: 4
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Re: When 10% of a solution of milk and water is removed and replaced with  [#permalink]

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21 Mar 2019, 09:47
1
cfc198 wrote:
When 10% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 3 : 1. Find the ratio of milk and water before the water is added to the solution.

1. 2 : 1
2. 4 : 1
3. 5 : 1
4. 5 : 2
5. 4 : 3

hello could you please advise on how to solve this question using weighted avg formula?
VP
Joined: 07 Dec 2014
Posts: 1218
Re: When 10% of a solution of milk and water is removed and replaced with  [#permalink]

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31 Mar 2019, 08:36
cfc198 wrote:
When 10% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 3 : 1. Find the ratio of milk and water before the water is added to the solution.

1. 2 : 1
2. 4 : 1
3. 5 : 1
4. 5 : 2
5. 4 : 3

let m=volume of milk before removal
w=volume of water before removal
.9m/[.9w+.1(m+w)]=3/1➡
.9m/(w+.1m)=3➡
.2m=w➡
m/w=1/.2=5:1 ratio
GMAT Club Legend
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Posts: 5428
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: When 10% of a solution of milk and water is removed and replaced with  [#permalink]

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31 Mar 2019, 10:24
gracie wrote:
cfc198 wrote:
When 10% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 3 : 1. Find the ratio of milk and water before the water is added to the solution.

1. 2 : 1
2. 4 : 1
3. 5 : 1
4. 5 : 2
5. 4 : 3

let m=volume of milk before removal
w=volume of water before removal
.9m/[.9w+.1(m+w)]=3/1➡
.9m/(w+.1m)=3➡
.2m=w➡
m/w=1/.2=5:1 ratio

gracie
hi could you please share the formula or logic behind use of the formula... i want to understand how did you deduce this formula...
Intern
Joined: 03 Mar 2019
Posts: 27
GMAT 1: 640 Q45 V32
When 10% of a solution of milk and water is removed and replaced with  [#permalink]

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15 May 2019, 13:33
1
Archit3110 wrote:
cfc198 wrote:
When 10% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 3 : 1. Find the ratio of milk and water before the water is added to the solution.

1. 2 : 1
2. 4 : 1
3. 5 : 1
4. 5 : 2
5. 4 : 3

hello could you please advise on how to solve this question using weighted avg formula?

Hi, I can solve this question based on VeristasKarishma's weighted average formula.
C2=C1*(V1/V2)
in which C1 is the original ratio of the milk and total amount
C2 is the later ratio which is 3/4
V1/V2=9/10 (because we take out 10% of the mixture)
=> 3/4=C1*9/10 => C1=5/6 => the original ratio of the milk and total 5:6 => the original ratio of the milk and water is 5:1

U can see the explanation behind this formula here: https://www.veritasprep.com/blog/2012/0 ... -mixtures/
Intern
Joined: 04 Feb 2018
Posts: 44
Re: When 10% of a solution of milk and water is removed and replaced with  [#permalink]

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27 Oct 2019, 04:06
Cfinal = Cinitial x (v2/V1)^n
where cfinal = final concentrtaion
Cinitial = initial concentration
v2 = final volume
V1= initial volume
Assume an initial volume of 10liters
The replacement of 10 percent implies that the final volume is 9
The final ratio of 3:1 implies that the final concentration is 75%
Therefore 0.75=C1(9/10)
75=90c1
c1=75/90= 5/6
Therefore initial ratio = 5:1
Manager
Joined: 09 Nov 2015
Posts: 153
Re: When 10% of a solution of milk and water is removed and replaced with  [#permalink]

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21 Nov 2019, 23:43
Let's assume the total quantity of the solution is 40 ml (which,by the way, remains unchanged since the qty that is removed is replaced by water) and the initial qty of milk in the solution is 'x' ml. The quantity of milk in the final solution is thus 30 ml (since Milk:Water=3:1) and the quantity of solution replaced with water is 4 ml.
The remaining qty of milk after removal of 4 ml of solution = x - (x/40)*4 = 9x/10 = 30....> x=100/3
Thus, qty of water in the initial solution was 40 - 100/3 = 20/3
The ratio of Milk:Water in the initial solution was (100/3):(20/3) or 5:1. ANS: C
Re: When 10% of a solution of milk and water is removed and replaced with   [#permalink] 21 Nov 2019, 23:43
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