Aptitude - Alligation or Mixture - Discussion

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.

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).

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).

At last, we have to find 8/5 litre is how many litres of 8 litres.
So it is 8/5 divide by 8 = 8/5 * 1/8.

Let's assume Syrup reduced by R.

Then the syrup available is 5/8 and reduced to 1/2.

So, 5/8x r = 1/2.
r = 4/5.

Syrup was reduced to 4/5, so the mixture was removed 1/5.

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.