Aptitude - Alligation or Mixture - Discussion

Thank you @Manoj.

I get the solution with the help of given explanation, Thanks.

Very well explained @Akshay Aswati.

The logic here is whenever something is taken out,
As Now, the basic principle is that;

When you remove any amount of the mixture, it removes both the liquids in the same ratio as the mixture itself.

Hence for the second time and third time we are using 4/40*4 for milk and 36/40 *4 water
and 32.4 /40 *4 for milk (29.16) and 8/40 *4 for water.

@Parvy Govil.

Very well explained. Thanks.

Given amount of milk = 40 lit.

Amount of milk taken out = 4 lit.

Remaining milk = 36 lit.

Given it is replaced with water and process repeated for twice.

Let us consider it is not replaced with water and process repeated for twice.

Then amount of milk = 36-4-4 = 28 lit.

Now logic:.

Now let us consider it is replaced with water and process repeated for twice.

Because of mixing water and taking 4 lit out from mixture, the amount of milk should be grater than 28 lit.

Only option (d) is greater than 28 lit.

Thanks dilip I understood the solution very well.

Suppose a container contains x of liquid from which y units are taken out and replaced by water.
After n operations, the quantity of pure liquid = x 1 - y n units.

@ Krishna.

Your logic is correct but if its options are changed logically then your logic gets fail.

Please give a more suitable and simple explanation.

M.V. Krisna gave an excellent logic.

The total quantity of milk is 40.

Case:1. 4 lit pure milk is taken out and 4 lit water is added.
Now we have a mixture of milk and water that contains
36 lit milk and 4 lit water.(milk:water=36:4=9:1 means
In 10 lit mixture there is 9 lit milk and 1 lit water)

Case:2. 4 lit mixture taken out (i.e. 36 lit mixture remains).

Our 40(or 10) lit mixture contains 4(or 1) lit water
and 36(or 9) lit milk.

so 4 lit mixture which is taken out, contains
4*4/40=0.40 lit water and
4*36/40=3.6 lit milk.

(i.e., 4 - 4*9/10 = 4 - 3.6 = 0.4 lit water and
4 - 4*1/10 = 3.6 lit milk taken out.)
so, remained 36 lit contains 36 - 3.6 = 32.40 lit milk
and 4 - 0.4 = 3.6 lit water.

Now 4 lit water is added.
so, water in 40 lit mixture after addition is
3.6 + 4 = 7.6 lit.

At the end of second case we get
milk : water = 32.40 : 7.60 = 8.10 : 1.90

Case:3. 4 lit mixture taken out (i.e. 36 lit mixture remained).

Our 40 lit mixture contains 7.60 lit water and 32.40
lit milk.
so 4 lit mixture contains 4*7.60/40=0.76 lit water and
4*32.40/40=3.240 lit milk.

(i.e., 4 - 4*8.1/10 = 4 - 3.24 = 0.76 lit water and
4 - 4*1.9/10 = 3.24 lit milk taken out.)
so, remained 36 lit mixture contains
32.40 - 3.24 = 29.16 lit milk and 7.60 - 0.76 = 6.84
lit water.


Now 4 lit water is added.
so, water in 40 lit mixture after addition is
6.84 + 4 = 10.84 lit.

At the end of third case we get
milk : water = 29.16 : 10.84