Aptitude - Alligation or Mixture - Discussion

The initial ratio of water to milk in can 1 is 1:3.
Initial ratio of water to milk in can 2 is 1:1.
If we add both then we get the ratio of water to milk 2:4.
It is said that this ratio becomes 3:5.
So from 2:4, it becomes 3:5.

As we can see there is an equal amount of change 3-2 = 1 and 5-4 = 1.
Therefore the quantity also should be in the ratio of 1:1.
Hence the answer is 6:6.

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.

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.

=>(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.

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.

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.

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.

You can solve the math in this way as well,

In can1 there is 25% (1/4) water and 75% (3/4) milk.
Again, in can2 there is 50% (1/2) water and 50% (1/2) milk.
So, total volume of water = 1/4+1/2 = 3/4.

Total volume of milk = 3/4+1/2 = 5/4.

Now, as per the question, the ratio of water and milk must be 3x and 5x.

So, we can write, 3/4:5/4 = 3x:5x.
Or, 3/4* 5x = 5/4 * 3x.
Or, 15x/4 = 15x/4.

That's to say the volume of water and milk must be the same. Hence the answer will be 6 liters.

If 1 litre is drawn from the 1st container, we get 0. 25L water and 0. 75L milk and if 1 litre is drawn from the 2nd container, we get 0.5L water and 0.5L milk.

By combining 1L from each of the two containers, we get 0. 75L water and 1.25L milk. In which water to milk is in the ratio of 3:5.

Thus we need 2+2+2+2+2+2 to get 12L in total and 6L from each of the containers.