Aptitude - Alligation or Mixture - Discussion

Let us say that the quantity in the vessel is 8x units. It has 3x water and 5x syrup.
Now, let's say we withdraw 8y units of the mixture are replace them with water. When we take out 8y units of the mixture, we are actually taking out 3y water and 5y syrup. We are adding pure water back into the vessel.

New quantity of syrup = 5x - 5y.
New quantity of water = 3x - 3y + 8y = 3x + 5y.
They are equal to each other.
=> 5x - 5y = 3x + 5y.
=> 2x = 10y,
=> y/x = 2/10 = 1/5,
=> 8y/8x = 1/5k.

So, 1/5th of the mixture should be taken out and replaced with water.

The ratio of syrup and water is 3:5 after replacing it will half-half(equal) -> 1:1
Because we are adding only water so the ratio of syrup will be same then ratio 1:1 become
5:5 means 2 ratio water is adding, total ratio is 5 + 5=10.
So 2/10=1/5

According to me, the solution is;

Water : syrup
30. :50

Total =80 then if x ltr mixture we tack out then the remaining ratio will be 1:1 .So
Take option 1/4 then try 1/4of 80 =20, or we can say 20/80*100= 25% of every (water and syrup).

But here we get vale in fraction, 25%of 30 = 7.5 ., 25%of 50= 12.5,
so this value.
30 - 7.5 =. 22.5
50 - 12.5 = 37.5 + 20 = 57.5.

This value not in ratio 1:1.

So, here ve take vale 1/5 or we can say 20 %of every part. 30*1/5=6
50 * 1/5 = 10.
Thus.
50 - 10 = 40.
30 + 10 = 40 this is in Ratio 1:1.

To make the given 3:5 equal we can take out 1 from 5 and add to 3(4:4). Since 1 is taken out from syrup so, the answer will be 1/5.

3 : 5 is given.
1:1 we need,
3 : 5
1*5 : 1* 5
Difference 3 to 5 = 2
Total now 5+ 5
Then 2/ 10 ans is 1/5.

Simply;

(3/8) - (3x/8) + x = (4/8);
This will give x = 1/5.

Can anyone tell me, how to find a total mixture here?

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

Final(syrup)=initial(syrup)*(1-(qt_replaced/total_mix).
X is a mixture replaced with water.
p is the total quantity of mixture.

4/8=5/8(1-x/p).

We need to find x/p which is 1/5 i.e answer.

The ratio of water/syrup is 3:5.
So, 3/8-3x/8+x = 5/8-5x/8
Solving X, we get 1/5.