Mixtures Question: Remove & Replace

This aptitude practice question is a mixtures and alligation question. Concept tested: Remove a part of a mixture and replace with equal quantities of one of the two components in the mixture to arrive at a different ratio.

Question

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?

1. 6 litres
2. 10 litres
3. 30 litres
4. None of these

  Correct Answer      Choice (2). 10 litres

Explanatory Answer

Let us solve this question by back substituting answer choices.
The rigorous method of solving is outlined in the previous question on removing and replacing mixtures.
The mixture of 60 litres has milk and water in the ratio 2 : 3
i.e., 24 litres of milk and 36 litres of water.
When x litres of the mixture is removed, 0.4 x litres of milk and 0.6 x litres of water are removed from it.

Take choice (2). According to this choice, x = 10.
So, 10 litres of the mixture is removed.
4 litres of milk and 6 litres of water are removed.
Therefore, there will be 20 litres of milk and 30 litres of water in the container.
Subsequently, when 10 litres of milk is added, the mixture will contain 30 litres of milk and 30 litres of water - i.e. milk and water are in equal proportion.

  The correct answer is Choice (2).