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When 20% of a solution of milk and water is removed and replaced with

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When 20% of a solution of milk and water is removed and replaced with  [#permalink]

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New post 14 Apr 2019, 10:33
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When 20% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 2 : 3. Find the ratio of milk and water in the original solution.

(1) 1 : 1
(2) 1 : 2
(3) 2 : 1
(4) 1 : 3
(5) 3 : 2
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When 20% of a solution of milk and water is removed and replaced with  [#permalink]

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New post 14 Apr 2019, 18:25
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cfc198 wrote:
When 20% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 2 : 3. Find the ratio of milk and water in the original solution.

(1) 1 : 1
(2) 1 : 2
(3) 2 : 1
(4) 1 : 3
(5) 3 : 2


let m=volume of milk in original solution
w=volume of water in original solution
.8m/[.8w+.2(m+w)]=2/3→
.8m/(w+.2m)=2/3→
m=w
m:w=1:1
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Re: When 20% of a solution of milk and water is removed and replaced with  [#permalink]

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New post 16 Apr 2019, 11:57
gracie wrote:
cfc198 wrote:
When 20% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 2 : 3. Find the ratio of milk and water in the original solution.

(1) 1 : 1
(2) 1 : 2
(3) 2 : 1
(4) 1 : 3
(5) 3 : 2


let m=volume of milk in original solution
w=volume of water in original solution
.8m/[.8w+.2(m+w)]=2/3→
.8m/(w+.2m)=2/3→
m=w
m:w=1:1


Hi Gracie,
Can you please elaborate the formulae and the approach that you've used here?
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Re: When 20% of a solution of milk and water is removed and replaced with  [#permalink]

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New post 17 Apr 2019, 18:59
Total volume =100.
Milk Volume=X.
Water Volume=100-X.
After taking out 20% of volume out.
Milk volume= 0.8X
Water Volume =0.8(100-X)
When 20 l water is added to it
Total volume of water will be 0.8(100-X)+20
Hence ratio of milk to water will be
0.8x : 0.8(100-x)+20 =2:3
solving x=50
hence initial solution will have 1:1 ratio.
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Re: When 20% of a solution of milk and water is removed and replaced with  [#permalink]

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New post 18 Apr 2019, 02:51
cfc198 wrote:
When 20% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 2 : 3. Find the ratio of milk and water in the original solution.

(1) 1 : 1
(2) 1 : 2
(3) 2 : 1
(4) 1 : 3
(5) 3 : 2


This is a global ratio problem, which we can solve by using the weighted arithmetic average formula.

First, focus on the ratio of the volume of milk to the total volume, \(M:Total\).

Let \(x\) be the partial ratio for the original solution in the above context. The partial ratio for the water added is obviously 0.

The weights used in the formula will be the volumes of the remaining original solution and the water added, respectively. In this case, we don't know the weights in natural units, but fortunately only the relative size of the weights matter in weighted averages. If 20% of the original solution is replaced with water, then 80% of the new solution will be from the original one.

\(\frac{80x+20\cdot 0}{100}=\frac{2}{2+3}\)

\(\frac{4}{5}x=\frac{2}{5}\)

\(x=\frac{1}{2} \implies M:Total=1:2 \implies M:W:Total=1:1:2\)

Answer: A

If you would like to see more solutions using the concept of global and partial ratios/averages, then download my book below and search for the keyword partial.
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Re: When 20% of a solution of milk and water is removed and replaced with  [#permalink]

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New post 18 Apr 2019, 19:10
cfc198 wrote:
When 20% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 2 : 3. Find the ratio of milk and water in the original solution.

(1) 1 : 1
(2) 1 : 2
(3) 2 : 1
(4) 1 : 3
(5) 3 : 2


Let m = the amount of milk originally in the solution and w = the amount of water originally in the solution, we can create the equation:

(m - 0.2m)/(m + w) = 2/5

0.8m/(m + w) = 2/5

4m = 2m + 2w

2m = 2w

m/w = 2/2 = 1/1

Answer: 1
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Re: When 20% of a solution of milk and water is removed and replaced with  [#permalink]

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New post 18 Apr 2019, 20:14
cfc198 wrote:
When 20% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 2 : 3. Find the ratio of milk and water in the original solution.

(1) 1 : 1
(2) 1 : 2
(3) 2 : 1
(4) 1 : 3
(5) 3 : 2


Using our weighted average formula:

Say concentration of milk in the original solution = C1
Concentration of milk in water = 0
Concentration of milk in the final solution = 2/5
Since 20% of the solution is removed and replaced, the new solution has 80% original solution and 20% water.

4/1 = (0 - 2/5) / (2/5 - C1)

4*(2/5 - C1) = - 2/5

C1 = 1/2

Hence, milk:water = 1:1
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Re: When 20% of a solution of milk and water is removed and replaced with   [#permalink] 18 Apr 2019, 20:14
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