Aptitude - Alligation or Mixture - Discussion

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.

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.

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.

@Kamakshi Puri.

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

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.

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

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

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.

The above solution states that we first assume the quantity to be 5+3=8 for easier understanding.
And since the question directly states we need to first remove some amount from the mixture and then add the same amount. for ex : from 8 litres remove 2 , 8 - 2 and then add 2 litres of water 6 + 2 =8.

So clearly, the quantity remains the same.

Now while removing we need to keep in mind that we are removing an amount from the mixture and not individually from water and juice (because that would be insane) as it's a mixture.

Hence, if we remove the same amount we add the same amount.

The mixture has water and syrup in a ratio, and the mixture consists of 3/8 part of water (3 litres) and 5/8 (5 litres) part of syrup. If we remove x litres from the whole mixture, the part of juice and water removed will be calculated in this manner :

new Water = 3 - (3x/8).
new Syrup = 5 - (5x/8).

Now since the same x amount of water must be added to keep the mixture in the same volume,
new Water = 3 - (3x/8) + x.

The whole point of this transaction according to the question is that both quantities take up the same ratio or are equally present in the mixture,

New Water amount = New Syrup amount.

Anyone, Please explain in the simplest way to understand.