Mixture and Alligation is an important concept in arithmetic used to find the ratio in which two items of different values must be mixed to achieve a required average or mean value. This topic appears frequently in competitive exams and is also applied in real-life cases such as mixing commodities, preparing alloys, blending ingredients, and comparing costs. The formula is simple but powerful because it instantly gives the mixing ratio without long calculations.
Mixture and Alligation Formula Overview
| Formula | Variables | When It Is Used |
|---|---|---|
| (C Quantity) : (D Quantity) = (D – M) : (M – C) | C = cheaper price | To mix cheaper and dearer items |
| D = dearer price | Compare with mixture average | |
| M = mean price | Used to find mixture cost/average |
What is Mixture and Alligation in Maths?
A mixture is a combination of two or more ingredients, such as milk and water, rice of different qualities, or metals forming an alloy.
Alligation is the rule that helps determine the exact ratio in which two items of different prices or values must be mixed to achieve a desired average price.
The alligation method uses the differences between the mean price and the individual prices to find the mixing ratio.
Steps involved include:
- Identify the cheaper price (C), dearer price (D), and mean price (M).
- Apply the formula: (C Quantity) : (D Quantity) = (D – M) : (M – C).
- Simplify the values to get the final mixing ratio.
This method is widely used in SSC, Banking, CUET, Railways, CAT, and also in everyday blending activities like mixing grains, fuels, liquids, medicines, and alloys.
Examples to Calculate Mixture and Alligation
Example 1: Mixing Rice at Rs. 20/kg and Rs. 30/kg to Get Rs. 25/kg
Step 1: C = 20, D = 30, M = 25
Step 2: Apply formula: (D – M) : (M – C)
= (30 – 25) : (25 – 20)
= 5 : 5
Step 3: Ratio = 1 : 1
So, the two types of rice should be mixed in an equal ratio.
Example 2: Milk at Rs. 40/litre and Rs. 60/litre to Get Rs. 50/litre
Step 1: C = 40, D = 60, M = 50
Step 2: (D – M) : (M – C)
= (60 – 50) : (50 – 40)
= 10 : 10
Step 3: Ratio = 1 : 1
So, the milk types should be mixed in an equal ratio.
FAQs about Mixture and Alligation Formula
Q1. What is the main formula of alligation?
The formula is: (C Quantity) : (D Quantity) = (D – M) : (M – C).
Q2. Where is alligation used in exams?
It appears in SSC, Banking, CUET, CAT, and Railways arithmetic and aptitude sections.
Q3. Can alligation be applied to more than two items?
Yes, but the method is used stepwise, pairing two items at a time.
Q4. What is the difference between mixture and alligation?
Mixture is the actual combination, while alligation is the rule that determines the mixing ratio.
Q5. Is alligation used in real life?
Yes, it is used in shops, business, medicines, alloys, and daily cost comparison.
Q6. How is the mean price calculated?
It is the average cost of the mixture, often given or found using weighted averages.