Aptitude - Alligation or Mixture - Discussion

Let 100 ltr mixture.

So, 5/8x 100 = 62.5 ltr syrup.
3/8x100 = 37.5 ltr water.

We need to remove syrup and add that much quantity of water so make it 1:1,
62.5- x/37.5+x = 1/1,
62.5- x = 37.5 +x.
2x = 25.
x = 12.5 (need to remove from syrup and this quantity into water),
12.5/62.5(syrup) = 1/5.

I didn't get this clearly. Please anyone help me.

Why multiply with 1/8? Please explain to me.

Let
The total mixture be 8 litres.
3 l is water and 5 l is syrup.

Now we need an equal quantity to be replaced as filled.
so let the quantity be x.
5-x/3+x = 1/1.
x=1.
Part that x forms the whole quantity
= 1/5.

@Kamakshi Puri.

The question is about not removing syrup but removing a mixture of the same quantity. So, the water should be added.

We need 2 parts of water to be added to make water and syrup equal.

5 parts of water = 5 parts of syrup.
Total = 10 parts.
No of items = 2 (Water, Syrup).
= 2/10.
= 1/5.

Let's say after removing some part of the mixture.

The ratio of the remaining mixture is the same i.e. 3:5 for water to syrup.
Now consider this mixture is 8L in total (3+5).
Now once we add 2L of water in the mixture the ratio becomes 5:5 which was desired.
5+5 =10.

So we can say that even in the original mixture the quantity was 10L as 2L was removed from that.
(2L mixture removed and 2L water added).
This satisfies the condition.
Now,
The question is how much of the mixture is to be removed and replaced.
2L/10L i.e.1/5.
1/5 will be the answer.

If we remove 1 amt of the mixture -> 5/8 amt of syrup is removed.
Let's say our ans is x -> remove x amt of mixture -> (5/8)x or syrup is removed.
for both water and syrup to be in the same amount, the syrup should be 4/8 that is 1/8 of the syrup should be removed from the mixture.
Therefore (5/8)x = 1/8 => x = 1/5 =>ANSWER.