Aptitude - Alligation or Mixture - Discussion

3Lwater + 5L syrup = 8L mix.
Now 1 unit of mix will also have 3 parts water and 5 parts syrup,
Let 1 unit be 800 ml for easy calculation.
And in 800ml we have 300ml water + 500ml syrup
Now, remove 1 unit from the total, you will have a mix of 7.2L.
removed 1unit = 800ml in 7.2L × 5/8 = 4.5 L syrup left.
And add 800ml of water in its place.
New ratio of mix 4.5l syrup: 2.7 old +0.8 newly added
4.5:3.5 we need 4:4 for both equal
Remove 1 more unit from the mix.
7.2 - 0.8 = 6.4L.
Syrup left 6.4L × 5/8 = 4.0L
Add water in place of 800ml
Now you have 4L syrup: 4L water.

Replacement of syrup with water = 800ml × 2 = 1.6L.

Now, how much replacement from the original 8L in ratio?
So, 1.6/8 total replacement reduces to 1/5(ans).

So we practically need to turn a 3:5 ratio into a 1:1 ratio.
3+5 = 8.
8÷2 = 4.
The required ratio is 4:4 to get an equal ratio of liquids.

That means we have to:
3+1 = 4.
5- 1 = 4.
That means we are taking 1 part of 5 and adding it.

it to 3 to get 4:4, which then converts to our required 1:1 ratio.

So, the final answer is 1/5(1 part of 5 is taken out)

Another example: let's say the ratio is 7:11 instead of 3:5.
7+11 =18
18÷2 = 9.

Then the 9:9 ratio is what keeps the mixture 1:1 (half water and half syrup)
To get that, we do :
7 + 2 = 9.
11 - 2 = 9.
That means we take 2 parts of 11 out and add it to 7 parts.
So the answer becomes 2/11 (2 parts of 11 liquid are taken out).

In the question, they state that the water and the syrup should be in equal quantities. They have already given three parts of water and five parts of syrup. The total is 8 parts.

So, to make them equal, I have to replace one part of syrup with water so that both are balanced. So, out of the given five parts, we have to replace only one part; therefore, the answer is 1/5.