Mixture and Alligation
What is Mixture and Alligation?
A substance made by mixing two or more other substances together.
Key formula / rule: Ratio of Quantities in Mixture
Key points
- Understand the concept of mixing quantities.
- Learn the method of alligation to find mixing ratios.
- Apply the concept to solve problems involving prices, quantities, and averages.
- Solve problems related to alcohol-water mixtures and profit/loss on mixtures.
Common exam trap
Confusing the ratio of quantities with the ratio of differences.
Definitions
- Term
Mixture
- Meaning
A substance made by mixing two or more other substances together.
- Term
Alligation
- Meaning
A method used to find the ratio in which two or more ingredients of different prices/qualities are to be mixed to produce a mixture of a desired price/quality.
- Term
Mean Value
- Meaning
The average value of the mixture, which lies between the values of the individual components.
Learning objectives
Understand the concept of mixing quantities.
Learn the method of alligation to find mixing ratios.
Apply the concept to solve problems involving prices, quantities, and averages.
Solve problems related to alcohol-water mixtures and profit/loss on mixtures.
Formulae
- Name
Ratio of Quantities in Mixture
- Note
Where V1 and V2 are the values (e.g., price, percentage) of the two components, and Vmean is the desired mean value of the mixture. Q1 and Q2 are the quantities of the components.
- Expression
Q1 / Q2 = (V2 - Vmean) / (Vmean - V1)
- Name
Mean Value of Mixture
- Note
This formula calculates the average value of the mixture based on the quantities and values of its components.
- Expression
Vmean = (Q1 * V1 + Q2 * V2) / (Q1 + Q2)
- Name
Profit/Loss on Mixture
- Note
When dealing with profit/loss, the 'value' used in alligation can be the Cost Price (CP) or Selling Price (SP), but consistency is key. Often, profit percentages are used directly as values.
- Expression
Profit % = (SP of Mixture - CP of Mixture) / CP of Mixture * 100
Prerequisites
Basic Arithmetic (Addition, Subtraction, Multiplication, Division)
Fractions and Percentages
Ratio and Proportion
Understanding of Averages
Common mistakes
Confusing the ratio of quantities with the ratio of differences.
Incorrectly calculating the mean price.
Applying the alligation rule when the quantities are not mixed but one is replaced by another.
Errors in basic arithmetic operations.
Keywords
Mixture
Alligation
Ratio
Average
Weighted Average
Mean Price
Components
Quantities
Practice preview
A mixture contains milk and water in the ratio 5:3. If the total volume of the mixture is 40 litres, what is the quantity of milk in the mixture?…
easy
A vessel contains 100 litres of milk. 10 litres of milk is taken out and replaced with water. This process is repeated one more time. What is the final quantity of milk in the vessel?…
medium
In what ratio must a grocer mix two varieties of pulses costing Rs. 15 per kg and Rs. 20 per kg respectively, so as to get a mixture worth Rs. 16.50 per kg?…
easy