# Difficult Alligations or Mixtures Solved QuestionAptitude Discussion

 Q. A sample of $x$ litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of $x$?
 ✖ A. 6 litres ✔ B. 10 litres ✖ C. 30 litres ✖ D. None of these

Solution:
Option(B) is correct

The best way to solve this problem is to go from the answer choices.

The mixture of 60 litres has in it 24 litres of milk and 36 litres of water. (2 : 3 :: milk : water)
When you remove $x$ litres from it, you will remove $0.4 x$ litres of milk and $0.6 x$ litres of water from it.

Take choice (2). According to this choice, $x = 10$.

So, when one removes, 10 litres of the mixture, one is removing 4 litres of milk and 6 litres of water.

Therefore, there will be 20 litres of milk and 30 litres of water in the container.

Now, when you add 10 litres of milk, you will have 30 litres of milk and 30 litres of water - i.e. milk and water are in equal proportion.

Edit: For an alternative method, check comment from David.

## (9) Comment(s)

Abhishek Patil
()

Understanding that quantity of water will remain constant after x lits are removed implies,

$(60-x)*(3/5)=(1/2)*(60)$

gives, $x=10$

Chakarya
()

Where did they mentioned the quantity of water will remain constant?

It is said that they make equal proportion and since milk is getting added, water remains constant. So 60% of water gets converted to 50% when milk is added. 36/.6 = 72 litres, which is 12 litres extra. So the answer can be 12 right?

Balvinder
()

m = 24 l

water= 36 lit

so using replacement and removal method. let x litre of quantity has been removed from mixture

n in resultant mix mlik 30 lit and water 30 lit

so left quant of water=initial qty of water(total qty - removed qty)/total qty

30=36(60-x)/60

x=10 litre

Manjeet Singh
()

60 liters in 2:3 means 24 milk and 36 water

[{24-(2/5)x + x}/60] = 1/2

x=10 liter

Rishikesh Agrawani
()

The 3rd line from last is incorrect,this is because of my mistake...

It will be (0.6-0.4+1)x = 36-24

Rishikesh Agrawani
()

Sorry

The 3rd line from last is incorrect,this is because of my mistake...

It will be (0.6-0.4+1)x = 36-24

David
()

The original mixture has to contain 24 liters milk and 36 liters water.

Now we are doing a replacement, so the final volume is still 60. It should end up as 30 of milk and 30 of water.

Since we won't be adding any water, we need to take out 6 liters of water, which means 10 liters of the mixture i.e 4 ltr. milk and 6 ltr water.So $x=10$

Prasanna Jd
()

Good logic, thank you :)

Rishikesh Agrawani
()

The ratio of milk an water in the mixture of 60 liters is 2:3

Therefore,

The amount of milk = 60(2/5) = 24 liters

and amount of water = 60(3/5) = 36 liters

Now x liters removed means

2x/5 = 0.4x liters of water and 3x/5 = 0.6x liters removed

& x liters of milk is added.

Now the quantity of milk remained in container = 24-0.4x+x

quantity of milk remained in container = 36-0.6x

According to the question,

(24-0.4x+x)/(36-0.6x) = 30/30

(0.6-0.4+1)x = 36-12

1.2x = 12

x = 10

It means the 10 liters of sample is replaced with pure milk.