Aptitude - Alligation or Mixture - Discussion

Consider: water is 30 lr and Syrup is 50 lr.

We have to take out 10lr syrup from 50lr. it is clearly 20%.

Note:
It means we are taking out 20 % (= 10 lr) syrup and 20 % (= 6lr) water.
Now we have 40-liter syrup and 24-liter of water remaining. Then we are adding 16-liter water.
Now we have 40-liter syrup and 40-liter water.

Hey, their is a simple way.
Using the left value rule
Left value= intial value * (1- fraction replaced)
We need to find fraction replaced,
Left v = 1/2.
Initial value = 5/8.

Therefore;
1/2 = 5/8 * (1-f).
4/5 = 1-f.
f = 1/5.

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

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.

@All.

The reason in the last step 8/5 is multiplied with 1/8 (or you could say 8/5 is divided by 8) is because we have found x in liters and the answer is required in parts. The 8 that we have used to divide in the last step is not the total 8 parts but it is the 8 liters we have assumed in the beginning of the answer.

Can anyone please explain how 8/5X1/8 come? Please explain.

@Kamakshi Puri.

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

NOTE: Liquid = Mixed substance (water,syrup)
Let the volume of the vessel = x liters.
Out of this x liters 3/8(x) is water & 5/8(x) is syrup.
Let y liters of liquid is taken out. So out of this y liters 3/8(y) is water and 5/8(y) is syrup.
The water in the remaining liquid is 3/8(x-y) .
The syrup in the remaining liquid is 5/8(x-y).
Now y liters of water is added to the remaining liquid so that the final liquid contains half water and half syrup.
=> 3/8(x-y)+y=5/8(x-y)
=>y=1/5(x)
or y = 1/5(x).
Answer: The amount of liquid drawn out = The amount of water added = 1/5 of x.

Answer: 1/5th of the vessel volume. Let's assume the capacity of vessel be (3+5=) 8 litres.

Now, the basic principle of all such questions is that when you remove any amount of the mixture, it removes both the liquids in the same ratio as the mixture itself. So, let's suppose we take x litresout of the vessel. This means 5x/8 amount of syrup and 3x/8 amount of water gets removed. which means the remaining mixture has (3-(3x/8)) litres of water & (5-(5x/8)) syrup. Now when we add x litres of water to this mixture, the amount of water and syrup becomes equal. Thus, (x+3-(3x/8)) = (5-(5x/8)) => x=1.6 ltrs.

Since we assumed that vessel is 8 ltrs. in volume=> 1.6/8 = 1/5th of the mixture in the vessel needs to be replaced with water. Hope it helps.

Well said @Surender.

Good explaintion I am not getting this but you solve very well & I get it now.