Aptitude - Alligation or Mixture - Discussion

First extract & refill. 36l milk, 4l water.

Milk in solution = 9/10; water = 1/10.

2nd extract: 4l taken out.

Milk = 9/10*4 = 3.6 water taken out = 0.4.

Milk remaining = 32.4, water remaining = 7.6.

Milk in solution = 32.4/40; water in solution = 7.6/40.

3rd extract: Milk extracted = 4*81/100.

Milk left will be 32.4-3.24 = 29.16.

It's just taking 10% away each time.

I don't understand why milk is getting reduced 10% each time while every time ratio of milk and water is getting changed.

Milk, water.

40, 0.

36, 4 10% of 40 is 4.

32.4, 7.6 10% of 36 is 3.6.

19.16 10% of 32.4 is 3.24.

Somebody please explain why percentage is constant?

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.

@Munna: Here the key is every time we are removing same 4 L from the 40 L of mixture which constitutes to 10% of entire solution.

Hence the percentage remains constant.

Please explain with simple steps!

@Shobana.

Step1: 40-(10% of 40) = 36.
Step2: 36-(10% of 36) = 32.4.
Step3: 32.4-(10% of 32.4) = 29.16.

This is the simplest method. But if you want to understand the method clearly, go through my first comment.

Must follow this to all this type of questions.

4 lit drawn then ratio: 4/40 => 1/10.
Rest liquid: 9/10.

Total : Rest
(10) power 3 : 9 power is 3

Ratio becomes 1000 : 729.

Now according to question 1000 : 40,
then,
1 : 0.04

Rest liquid 729=> 729 * 0.04=> 29.16.

You are right @Manoj.

Given 40L milk.

Step1: 4L milk is replaced & 4L water is added, i.e. it now contains 40L mix of 36L M & 4L W in d ratio 9:1,

So even if you take 1L of the mix it will contain (9parts M & 1 part W) & this is repeated 2mor times.

So to calculate the amount of milk present :

1st time: 40 * 9/ (9 + 1 =10).

2nd time: 40 * (9/10) * (9/10), 3rd time: 40 * (9/10) * (9/10) * (9/10) = 29.16.