Aptitude - Alligation or Mixture - Discussion

A venal contains a mixture of milk and water. Milk being 49% of the solution. Two times the mixture is taken out and replaced by water. Now the mixture contains only 9%of milk. How many litres of mixture is taken out?

Find the solution of the problem.

Best Answer @Manoj Kumar.

Simple: in question given he replace milk with water three times. Once he replaces then further repeat process two times.

40 litre milk ----> 4 litre milk removed (4 is 10% of 40) = 36 litre left.

Now again 4 litre milk removed (again 10% removed) from 36 litre mean 3.6 litre removed = 32.4 litre left.

Now again 4 litre removed = mean 10% of 32.4 is 3.24 so 3.24 litre remove and you left with 29.16 litre!

Your logic is good Now, I can understand the solution. Thanks @Krishna.

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.

It compare with the basic formula, to calculate the amount in case of Simple interest but here rate is negative.

It is more or less analogous to that.

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.

Thanks @Bhargava reddy.

Thanks for the given explanation.

Thanks for explaining the answer.