Understanding how to calculate mixture ratios is essential in many fields such as chemistry, pharmacy, and food industry. The alligation medial method provides a straightforward way to determine the ratio of components in a mixture. This article presents practice problems to help students master this technique.

What Is Alligation Medial?

Alligation medial is a method used to find the ratio in which two or more ingredients are mixed to obtain a mixture of a desired concentration. It involves comparing the individual concentrations of the ingredients with the concentration of the final mixture.

Basic Steps in Alligation Medial

  • Identify the concentrations of the two ingredients and the desired mixture.
  • Calculate the difference between each ingredient's concentration and the desired concentration.
  • Use these differences to determine the ratio of the ingredients.
  • Simplify the ratio if necessary.

Practice Problems

Problem 1

Two solutions, one of 40% concentration and another of 20%, are mixed to obtain 30% solution. Find the ratio in which the solutions are mixed.

Problem 2

A pharmacist has a 60% alcohol solution and a 20% alcohol solution. They want to prepare 50% alcohol solution. What is the ratio of the two solutions needed?

Problem 3

In a mixture of two dyes, one of 80% strength and another of 50% strength, the final mixture has a strength of 65%. Find the ratio of the dyes used.

Solutions to Practice Problems

Solution to Problem 1

Concentrations: 40%, 20%, desired 30%

Differences: |40 - 30| = 10, |20 - 30| = 10

Ratio of solutions: 20% : 40% = 10 : 10 = 1:1

Solution to Problem 2

Concentrations: 60%, 20%, desired 50%

Differences: |60 - 50| = 10, |20 - 50| = 30

Ratio of solutions: 20% : 60% = 10 : 30 = 1:3

Solution to Problem 3

Concentrations: 80%, 50%, desired 65%

Differences: |80 - 65| = 15, |50 - 65| = 15

Ratio of dyes: 50% : 80% = 15 : 15 = 1:1

Summary

Alligation medial is a simple and effective method for calculating mixture ratios. Practice solving various problems to strengthen your understanding and improve accuracy in real-world applications.