Aptitude - Alligation or Mixture - Discussion

Suppose 1 liter of whisky and x of it removed,
(1-x).

Now x part id added with 19 % of alcohol content and the total we know is 26%.
Hence 40 per cent of (1-x)summed with 19% of x gives 26 per cent.
40(1-x)/100+19x/100 = 26/100.
= > x = 2/3.

By using alligation method we can easily get the ratio in which they were mixed together.

So,
= (26-19) : (40-26),
= 7:14,
= 1:2.
So 1/3 of first and 2/3 of second are mixed to make the third mixture in which 26% alcohol is there;

Now the question is asking for the quantity which is removed or taken out from the first jar
If 1/3 of jar A is used to make a new mixture.
So, 2/3 of jar A is taken out or replaced.

Here, after solving we get 1:2.

If asked 1/3 will be original and 2/3 will be replaced.

@All.

Who is asking how did 2/3 come? Here is the explanation.

It is because the total we have now is 1+2 that is 3;. And 2 out of that is 2nd part hence 2/3 was replaced.

Here, 1:2 is not mixture ratio.it's ratio between 1st mixture quantity after removal and 2nd added mixture quantity.

Here a word used same amount of mixture "replaced".

Mixture amount ratio = 1:2 means total mixture amount =3 part.

Added mixture amount = 2/3. Which was replaced.

Consider 100L of Whiskey Mixture.
40L alcohol and 60L Water.

Let x be the amount of whiskey replaced in Litres. So 0.4x is the alcohol removed and 0.19x is the alcohol added. 26L is the new alcohol content.
We will do an alcohol balance.
40-0.4x+0.19x = 26 -----> x = 200/3.
x/100 = 2/3.

The replaced parts are 2.
And total parts are 3.
Then, the required answer is 2/3.

Its too simple,

According to allegation rule,

Chip/Deep = (Deep-Common)/(Common-Chip).

Chip/Deep = (0.40-0.26)/(0.26-0.19).

Chip/Deep = 0.14/0.07.

Chip/Deep = 2/1.

So, Chip (whisky with 19% alcohol) = 2/3rd of total final mixture.

Deep (whisky with 40% alcohol) = 1/3rd of total final mixture.

Now here is the logic. According to question, whisky containing 40% alcohol (deep) was replaced with whisky containing 19% alcohol (chip) to make this final mixture. So 2/3rd of whisky (40%) was replaced with 2/3rd of whisky (19%).

So answer = 2/3.

Container 1 has 40% alchol.

They mixed 19% of alcohol and they get 26% alcohol mix.

By using of allegation rule we are getting 1:2. This means we add 1 part from container 1 and remaining from container two. That 2 parts.

The total is 3 parts.

So, the Answer is 2/3.

What is wrong in this approach?

Let us assume that there is x L of whiskey and we are replacing y L of whiskey.

Therefore the quantity of alcohol is:

(40/100)x-(40/100)y+(19/100)y = (26/100)(x-y).