Aptitude - Alligation or Mixture - Discussion

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.

@Kiran.

Nice explanation.

Well said, Thank you so much @Ameer.

Well said @Surender.

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

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.

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.

It is not Volume of vessel.

It's a Volume of mixture at initial.

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

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

= 2/10.
= 1/5.

Anyone, Please explain in the simplest way to understand.

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.