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

Question

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

gracie · Answer

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

OhsostudiousMJ · Answer

Hi Gracie,
Can you please elaborate the formulae and the approach that you've used here?

HAPPYatHARVARD · Answer

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.

ZoltanBP · Answer

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 .

ScottTargetTestPrep · Answer

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

KarishmaB · Answer

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

96Chris · Answer

My Solution:

Cf = Ci x (Vi/Vf) where Cf = Concentration final, Ci = Concentration initial, Vi = Volume initial, Vf = Volume final.

We know the final ratio is 2:3, so in 5 pieces there is 2 liters of milk and 3 liters of water, therefore Cf = 2/5 (40%)

Now let the Volume initial be 10 liters. We get:

2/5 = Ci * (8/10) \ (8/10 because we take 20 percent out, 20 percent taken out from 10 liters is 2, so we arrive at 8)

Ci = 20/40 -> 2/4 -> 1/2 -> 50%

so in in the initial Concentration there are 50% milk, so the ratio is 1:1.

Please kindly correct me if i am wrong anywhere here.

veejoy · Answer

Eyeballing answers, #2/#3/#4 unlikely on their face. Either calls for more milk, which isn't case or too much water. Leaves 1 and 5 as viable possibilities.

Assume 1:1 (choice 1). Say 10g solution

5m/5w. Take away 20%, which is 2g. Now it's 4m/4w. Add back 2g of water, now it's 4m/6w, or 2:3.

Therefore choice 1 (1:1) was original concentration.

Posted from my mobile device

Jaya6 · Answer

Hey, I am wondering about the fractions here. If you have considered 100 as initial volume then after removing 20% the resultant becomes 80ltr but you have taken 0.80. Also, the second time when 20% is added back you have considered 20ltr. I feel there no synchronization.

Jaya6 · Answer

can you explain where did the 50% of milk come from in the end?

96Chris · Answer

Our formular is the following:

Cf = Ci x (Vi/Vf) where Cf = Concentration final, Ci = Concentration initial, Vi = Volume initial, Vf = Volume final.

In order to find out the ratio of the milk in the initial solution, we need to rearrange the formula to:

Ci = Cf / (Vi/Vf)

We know the Cf is 2/5 (we know that because in the problem it is given the final ratio is 2:3, so in 5 liters, there are 2 liters of milk and 3 of water, hence we have 40% milk).

Now let's say our initial Volume was 10 liters. Then we arrive at the equation:

Ci = 2/5 / 8/10 
Ci = 20 / 40
Ci = 1/2 (---> 50%)

So now we know the concentration of milk was 50% in the initial solution.

Hope i could explain it clearly.

AnishTrivedi99 · Answer

Post addition of 20 L pure water, 100 L solution - ratio 2:3 (m:w)

we've 40 L Milk and 60 L Water

Before addition - 40L M and 40L W

Original ratio = 1:1 (because when if 20L was removed earlier, 10 parts water and 10 parts milk must have been removed as we've 40 L M and 40 L W)

Sorry if I'm not too clear

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

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