01 Key Concepts
Total Value Method
Total value of mixture = sum of (quantity x property) of each part.
Alligation Rule
A shortcut to find the ratio in which two ingredients must be mixed to get a desired average, based on how far each ingredient's value is from the mean.
Concentration Problems
When mixing solutions of different concentrations, track the total amount of the 'pure' substance separately from the total volume.
Replacement Problems
When part of a mixture is removed and replaced with another substance, track what fraction of the original substance remains after each replacement.
03 Key Formulas
- Alligation: Ratio of quantities = (d2 - Mean) : (Mean - d1), where d1 and d2 are the two given values
04 Solved Examples
Example 1 In what ratio should tea worth $40/kg be mixed with tea worth $60/kg to get a mixture worth $50/kg?
- Using alligation: difference of $60 from mean $50 = 10.
- Difference of $40 from mean $50 = 10.
- Ratio = 10:10 = 1:1.
Answer: 1:1
Example 2 How many liters of a 20% acid solution must be mixed with a 50% acid solution to make 30 liters of a 30% solution?
- Using alligation: distance of 50% from 30% = 20. Distance of 20% from 30% = 10.
- Ratio of 20% solution to 50% solution = 20:10 = 2:1.
- Total parts = 3, so 20% solution = (2/3)x30 = 20 L, 50% solution = (1/3)x30 = 10 L.
Answer: 20 L of 20% solution and 10 L of 50% solution
Example 3 A shopkeeper mixes 20 kg of rice at $30/kg with 10 kg of rice at $45/kg. Find the price per kg of the mixture.
- Total value = (20x30) + (10x45) = 600 + 450 = 1050.
- Total quantity = 20 + 10 = 30 kg.
- Price per kg = 1050 / 30.
Answer: $35/kg
05 Practice Questions
1Mix rice at $20/kg and $30/kg to get a mixture at $25/kg. Find the ratio.
1:1
2Find the average price mixing 5 kg at $10/kg with 5 kg at $20/kg.
$15/kg
3Mix nuts at $5/kg and $8/kg to get a mixture at $6/kg. Find the ratio.
2:1
4Mix 10 kg at $40/kg with 20 kg at $55/kg. Find the average price.
$50/kg
5Find the ratio to mix 10% and 40% acid to get 20% acid.
2:1
📄 Mixture Problems — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.