Mixture and Alligation

Mixture and Alligation are important concepts in quantitative aptitude used to determine the ratio and cost of sale for a mixture made up of two or more materials. In competitive exams, mixture and alligation questions are commonly asked to test a candidate’s ability to calculate the mean value of a mixture with different ratios and amounts of ingredients, as well as to find the proportions of elements being mixed.

Mixture and Alligation: Concept and Formulas

• A mixture is a combination of two or more elements to form a third element. The questions from the mixture are usually based on Ratio and Proportion and do not require any special formula.

• The Alligation is a rule that enables us to quickly calculate the price of a mixture, given that it is a mix of two elements having different prices.
  • Alligation Rule :
• Here, the mean price is the price of 1 unit of the mixture. Please note that in the above formula, everything has to be calculated by considering one unit only. Another point to be noted is that the mean price would always be between a cheaper price and a dearer price.

• In questions of replacement where we initially have some quantity of pure element (like petrol), and we keep on replacing a fixed portion of this pure liquid every time with some other element (like water) thus making it a mixture, we apply the following formula for finding the quantity of pure element after ‘n’ replacements : P x [1 – (R / P)]n, where P is the initial quantity of pure element R is the quantity replaced every time n is the number of replacement

Tips and Tricks to Solve Mixture and Alligation Questions

• The alligation rule is a mixture problem-solving technique that can be used to calculate the rate at which an article can be sold. 
• By using this technique, one can figure out the ratio between two different ingredients in a given mixture. 
• Questions from topics such as partnerships, time and work, and wages can also be solved easily with this concept. 
• It may seem complicated at first but once you get familiar with the formulas involved, it becomes much simpler.

Mixture and Alligation - Examples

Example 1:

Problem Statement: A 30-liter vessel contains pure juice. If 2 liters are taken out and replaced with water, keeping the volume constant at 30 liters, and this process is repeated 4 times, what percentage of pure juice remains in the vessel after 4 replacements?

Solution:

Here, we apply the formula (1−R/P)ⁿ

Let
P = Initial quantity of pure element = 30 liters
R = Quantity replaced each time = 2 liters
n = Number of replacements = 4

So, the quantity of pure juice after 4 replacements is:

(1 − 2/30)⁴ = (0.9333)⁴ ≈ 0.7536

Therefore, the percentage of pure juice left after 4 replacements is:

0.7536 × 100 = 75.36%

Example 2:

Problem Statement: A 60 kg alloy mixed with 90 kg of another alloy. If the first alloy contains zinc and aluminum in the ratio 4: 1, and the second alloy has aluminum and magnesium in the ratio 2:5, what is the amount of aluminum in the new alloy?

Solution:

Alloy A: 60 kg contains zinc and aluminum in the ratio 4 : 1.
So, 4 + 1 = 5
5 units → 60 kg
1 unit → 12 kg
Amount of aluminum in alloy A is 1 × 12 = 12 kg.

Alloy B: 90 kg contains aluminum and magnesium in the ratio 2 : 5.
So, 2 + 5 = 7
7 units → 90 kg
1 unit → 12.857 kg
Amount of aluminum in alloy B is 2 × 12.857 ≈ 25.714 kg.

Hence, the total amount of aluminum in the new alloy is 12 + 25.714 ≈ 37.7141 kg.

Related Articles:

• Practice Aliigation and Mixture Aptitude Quizzes.
• Problems on Mixture and Alligation | Set 2.