Aptitude - Alligation or Mixture - Discussion

X litres to start with so it contains in the below ratio of alcohol and water(assume).

40*x/100 - alcohol and 60*x/100 water,
Now, y litres of whisky to be taken away and added by 19% of y litres of whisky,

So we know when anything is taken away in the mixture, it takes out equal amounts out from the mixture.

hence since y litres is taken out it takes out alcohol in equal ratio i.e(40*y/100), we get the below equation for remaining alchol in the mixture.

(40*x/100 )- (40 *y/100),
Now they say 19% of y litres of alcohol is added so, equations become,
(40*x/100 )- (40 *y/100 ) + 19*y/100 = 26*x/100.

Solving we get 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.

1/3 is the wrong answer.

As per Prakash' method, 2/3* 100 is right but it is the amount of alcohol and 1-2/3=1/3 is the answer of whisky which has 19% alcohol. In a question, they told that whisky which has 40% alcohol replaced by whisky of 19 % alcohol so its prove that 1/3 is the answer of whisky which has 19% & 40% combined alcohol. But in a problem, they asked replaced whisky means whisky which has 40% alcohol. So please tell anyone in detail what is the answer still I am not getting the answer.

Let, the total original amount of whiskey = 10 ml, i.e. 4 ml alcohol and 6 ml non-alcohol.

Let x ml be the amount removed,
Total alcohol left = 4-0.4x.

New quantity of whiskey added = x ml out of which 0.19 is the alcohol.

Thus, the final quantity of alcohol,
= 4-0.4x+0.19x=4-0.21x.
ATQ, (4-0.21x)= 26% of 10 [Here, initially 10],
=> x = 20/3 ml.

As per the question, we need to find the x ml removed as a ratio of the initial volume,
= (20/3)/10 = 2/3 (Answer).

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.

Suppose the vessel initially contains 100 litres of liquid.
So, it contain 40 lit alchohal, 60 lit water.
Let x litres of this liquid be replaced .

Quantity of alchohal in new mixture =(40-40x/100+19x/100)
=40-21x/100
Now vessel contain 26% alcohol

So, 40-21x/100=26
x=2/3*100.

According to mixture allegation rule.. we have place the chaeper one on left side and the dearer one on right side... why here that rule is not followed

acoording to that 14:7 comes..so lastly 2:1 is the ratio and
and the first jar is compared s 2/3 parts (i.e)2:3 .. is this correct ?? plz answer this !!!

I think this is the easy method.

If the 40% will alcohol is a1 = 40% and another 19% is a2 = 19%.

And in the resultant is A = 26%.

Any solution Alligation is given as:

Average A = (n1a1*n2a2)/(n1+n2).

n1:n2 = (a1-A)/(A-a2).

n1:n2 = (40-26):(26-19) then the result is 14:7 that will give 2:1.

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.