Mixtures Alligation Practice Question

This aptitude practice question is a mixtures and alligation question. Concept tested: Ratio of mixture changes after adding more milk. A word problem in mixtures and alligation

Question

A 20 litres mixture of milk and water comprising 60% pure milk is mixed with "x" litres of pure milk. The new mixture comprises 80% milk. What is the value of "x"?

1. 40 litres
2. 20 litres
3. 8 litres
4. 16 litres

  Correct Answer      Choice (2). 20 litres

Explanatory Answer

The quantity of the initial mixture of milk and water is 20 litres.
Out of the 20 litres, 60% is pure milk. i.e., 12 litres is milk and the remaining 8 litres is water.
When "x" litres of pure milk is added, we will have (12 + x) litres of milk in the new mixture.
And there will be 20 + x litres of the new mixture.

The question states that (12 + x) litres of milk accounts for 80% of (20 + x) litres of the mixture.
Therefore, 12 + x = \\frac{80}{100}) * (20 + x)
12 + x = \\frac{4}{5}) * (20 + x)
5(12 + x) = 4(20 +x)
60 + 5x = 80 + 4x
x = 20 litres

  The correct answer is Choice (2).