Aptitude - Alligation or Mixture - Discussion

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

If mixture has two types of liquids say A and B. If you remove x% of the entire mixture it is obvious that same x% is removed from both the types of liquids from their respective quantities.

In the above example whenever we remove 4 lit of solution out of 40 lit. We are removing 10% of entire solution which means we are removing 10% of milk and also 10% of water.

After Step 1: We have 36 lit of milk and 4 lit of water.

Step 2: Here we are removing 4 lit of entire solution, which means we are removing (10% of 36 = 3.6 L of milk) and (10% of 4 = 0.4 of water). So now we are left with (36 - 3.6 = 32.4L of milk) and (4 - 0.4 = 3.6 L of water). But again the mixture is added with 4 lit of water which makes (32.4L of milk + 7.6L of water) = 40 L of solution.

Step 3: Here we are again removing 4 lit of entire solution, which means we are removing (10% of 32.4 = 3.24L of milk) and (10% of 7.6 = 0.76 of water). So now we are left with (32.4 - 3.24 = 29.16L of milk) and (7.6 - 0.76 = 6.84L of water)

But again the mixture is added with 4 lit of water which makes (29.16L of milk + 10.84L of water) = 40 L of solution.

And this process goes on. Here using Percentage method is more effective rather going with ratios.

There are 40 litres of milk in the container.
Now, 4 litres of milk is taken out and replaced by water.
So milk left in the mixture is 40-4=36 litres in the container.

Now this process is repeated twice:

Means again 4 litres of mixture (Milk + Water) is taken out from the container and replaced by water.
=> In the container, the mixture is in the ratio 36:4.

So, 4 litres of mixture that is to be replaced contains 4*(36/40) = 3.6 litres (parts of milk).
Now Total milk taken out after this process = 4+3.6 = 7.6 litres.
=> Now the mixture left in the container is 36-3.6 (parts of milk) : 8 (parts of water).
= 32.4 : 8.

Now again this process is repeated for the last time.
So 4 litres of mixture is taken out, this 4 litres contains => 4*32.4/40 = 3.24 (parts of milk).
Total milk parts taken out in the whole process = 7.6+3.24 = 10.84.
Now total milk left in the mixture (container) = 40-10.84 = 29.16.

Here's the ratio of Milk to water at different stages:

Stage 1: 40:0

Stage 2: 36:4 or 9:1

At Stage 3: 4 litres of this mixture was taken out and replaced with water.

In 4 liters of mixture, there are 9 parts milk and 1 part water. So it means that 3.6 litres of milk was removed and 0.4 litres of water was removed.

When we add 4 litres of water, that leaves us with 36 - 3.6 = 32.4 litres of milk and 7.6 litres of water. The ratio of milk to water now is 32.4 : 7.6.

At Stage 4: 4 litres of this mixture was taken out and replaced with 4 litres of water.

4 litres of this mixture will have 0.76 litres of water and 3.24 litres of milk.

So that leaves us with 29.16 litres of milk.

Dont mind this is too long but i have a procedure to explain

Consider 3 times added water as 3 cases

case 1:after removal of milk and addition of water
water,milk are 4,36 lit ratio is 1:9

case2:when 4 lit are removed in that mix water,milk are (1/10)*4,(9/10)*4 of that mix
so presently water=4-2/5=18/5,milk=36-18/5=162/5
after addition of water,milk is same quantity but water=(18/5)+4
=38/4

case3:now ratio of water,milk=38:162=19:81
after removal of water,water,milk are (19/100)*4,(81/100)*4
so 19/25, 81/25
now milk=(162/5)-(81/25)=729/25=29.16 lit
antha length vodu anna dilogue gurthostundi kada so its simple to remember formula its better if we have only 1 or 2 cases

Initial Status 1 => Milk = 40 {Volume = 40}.

Water = 0.

Iteration 1 => Milk = 40-4 = 36 {Volume = 40}.

Water = 4.

Fraction of water = 4/40 = 1/10.

Fraction of milk = 36/40 = 9/10.

Iteration 2 => Milk = 36-(9/10) 4 = 324/10 {Volume = 40}.

[Since 4 litres mixture has been removed].

Water = 4+(4-(1/10)4) = 76/10.

[Since 4 litres water has been added].

Fraction of water = (76/10)/40 = 76/400.

Fraction of milk = (324/10)/40 = 324/400.

Iteration 3 => Milk = 324/10-(324/400)4 = 729/25 = 29.16 {Vol = 40}.

[Since 4 litres mixture has been removed].

Water = 4+(76/10-(76/400) 4) = 271/25 = 10.84.

[Since 4 llitres water has been added].

Can it it solved by x and why quantity? like:

Currently, we have 36(M), 4(W). Now 4 litres is taken out.

So let milk remains: 36-x.

Water 4-(4-x).

Now add 4 litres water: so, milk = 36-x, water = [4-(4-x)]+4.

Again 4 litres taken out. Now suppose in that 4 lit why lit was milk. So milk remains: (36-x) -y and water = [[4-(4-x)]+4]-(4-y).

Now 4 lit water mixed so, milk = 36-x-y.

Water = [[4-(4-x)]+4]-(4-y)+4.

= [[4-4+x]+4]-4+y+4.

= [x+4+y].

But where is the problem in this approach? I just want to know that.

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.

If the same amount of milk is drawn the formula is applicable but when different amounts of milk is drawn in different cases what have to do I have a problem here please solve this and explain.

There was 40 litres of pure milk in a vessel 16 litres of pure milk was taken out and replaced with equal amount of water again 10 litres of mixture was taken out and replaced with equal amount of water, what is the amount of water in the vessel now? (in litres).

Case 1: total milk = 40lits.
Case 2 : 4lits are replaced by water = 40 - 4 = 36lits of Milk.
So the total = 36lits of milk + 4lits of water.

Two times repeat again.
Case 3 : 36lits of milk-4lits of milk +4lits of water=32lits of milk +8lits of water =total 40lits of milk and water.

36lits of milk - 4lits of milk + 4lits of water = 28lits of milk - 4lits of milk +1 2lits of water
So total 28lits of milk and 12lits of water.