Aptitude - Alligation or Mixture - Discussion

To solve the problem, we need to determine how much milk to mix from each of the two containers such that the final mixture is 12 liters with a water-to-milk ratio of 3:5.

Step 1: Understanding the Containers

1. Container 1:
- Contains 25% water and 75% milk.
- For every 1 litre, there are 0.25 litres of water and 0.75 litres of milk.

2. Container 2:
- Contains 50% water and 50% milk.
- For every 1 litre, there are 0.5 litres of water and 0.5 litres of milk.

Step 2: Setting Up the Equations
Let:
x = liters of milk from Container 1
y = liters of milk from Container 2

We want the total volume of the mixture to be 12 liters: x + y = 12

Next, we need to find the amount of water and milk in the final mixture. The desired ratio of water to milk is 3:5, which means:
Total parts = 3 + 5 = 8 parts
Water = (3/8)*12 = 4.5 liters
Milk = (5/8)*12 = 7.5 liters

Step 3: Calculating Water and Milk from Each Container

1. Water from Container 1 = 0.25x
2. Water from Container 2 = 0.5y
3. Total Water: 0.25x + 0.5y = 4.5
4. Milk from Container 1 = 0.75x
5. Milk from Container 2 = 0.5y
6. Total Milk: 0.75x + 0.5y = 7.5

Step 4: Solving the Equations

Now we have the following system of equations:
1. x + y = 12 -->(1)
2. 0.25x + 0.5y = 4.5 --> (2)
3. 0.75x + 0.5y = 7.5 -->(3)

We can solve equations (1) and (2) first.

From equation (1): y = 12 - x.

Substituting y in equation (2):

0.25x + 0.5(12 - x) = 4.5,
0.25x + 6 - 0.5x = 4.5,
-0.25x + 6 = 4.5,
-0.25x = 4.5 - 6,
-0.25x = -1.5.
x = 6.

Now substituting x = 6 back into equation (1):

6 + y = 12.
y = 12 - 6 = 6.

Step 5: Conclusion:

The milk vendor should mix 6 litres from Container 1 and 6 litres from Container 2 to obtain 12 litres of milk with a water-to-milk ratio of 3:5.

So the final answer is:
- From Container 1 ->6 liters.
- From Container 2 -> 6 liters.

Assume, can 1 and can 2 have the same volume.

Now can 1 have a water & milk ratio= 1 : 4.
Can2 have a water & milk ratio = 1 : 1.

And New mix is 12L then the water-milk ratio=3 : 5

Now put all the Options in Trial and error:
You will see option C is 5,7

By validating option C;
(5x1/5 + 7X1/2) Water/ (5x4/5+7x1/2)milk.
= 9/15.
= 3:5.

So, Option C would be the right answer.

Let x and (12-x) litres of milk be mixed from the first and second container respectively.

Amount of milk in x litres of the first container = .75x.
Amount of water in x litres of the first container = .25x.
Amount of milk in (12-x) litres of the second container = .5(12-x)
Amount of water in (12-x) litres of the second container = .5(12-x)
Ratio of water to milk = [.25x + .5(12-x)] : [.75x + .5(12-x)] = 3 : 5.
⇒(.25x+6−.5x)/(.75x+6−.5x)=3/5
⇒(6−.25x)/(.25x+6)=3/5
⇒30−1.25x=.75x+18
⇒2x=12
⇒x=6.
Since x = 6, 12-x = 12-6 = 6.
Hence 6 and 6 litres of milk should be mixed from the first and second containers respectively.

@Hardik.

Thanks for explaining the answer.

=>(dearer_mixture - mean) / (mean - cheaper_mixture),
=>(75%-(5/8)) / ((5/8) - 50%),
=>(6-5)/(5-4) = 1/1 or 1:1,
from milk ratio of (1/2) = 1/2 * 12 = 6litres.

Yes, right @Muslih.

Water by mixing 2 solutions:

1/3 * X + 1/1 * (12-X) = 3/5 * 12,
X = 7.2 L,
12-X = 4.8 L, so D is the right option.

Calculating the milk proportion.

=>(dearer_mixture - mean) / (mean - cheaper_mixture),
=>(75%-(5/8)) / ((5/8) - 50%),
=>(6-5)/(5-4) = 1/1 or 1:1,
from milk ratio of (1/2) = 1/2 * 12 = 6litres.

How it comes 3/4 in that? Please explain me.

I can't understand please explain in simplest way.

Ans :
For Each liter of the mixture in A we can see 0.25l of Water and 0.75l of Milk.
For Each liter of the mixture in B There will be 0.5l of Water and 0.5l of Milk.


Let x liter of mixture taken from A and y liter of mixture taken from B.
WKT the final ratio should be 3:5 and We need to find how much liters should be taken from both A and B.
Water/Milk = 0.25x + 0.75y/0.75x + 0.5y =3/5,
===>after simplification x = y ..take equal amount of liters in A and B that makes 12l.