Practice With Solutions: Alligation Alternate For Multiple Components

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Alligation alternate is a useful method for solving problems involving the mixing of multiple components with different concentrations or qualities. It simplifies the process of finding the ratio in which components should be mixed to achieve a desired concentration or quality.

Understanding Alligation Alternate

The alligation alternate method is particularly handy when dealing with more than two components. It involves calculating the differences between each component’s value and the target value, then using these differences to determine the mixing ratios.

Step-by-Step Solution with Examples

Let’s consider an example to understand the process better.

Example 1: Mixing Solutions of Different Concentrations

Suppose you have three solutions with concentrations of 10%, 20%, and 30%. You want to prepare a mixture with a concentration of 25%. Find the ratios in which the solutions should be mixed.

  • Solution A: 10%
  • Solution B: 20%
  • Solution C: 30%

Step 1: Identify the target concentration, which is 25%. List the concentrations of the solutions.

Step 2: Calculate the differences between each solution’s concentration and the target:

  • Difference for 10%: |10 – 25| = 15
  • Difference for 20%: |20 – 25| = 5
  • Difference for 30%: |30 – 25| = 5

Step 3: Assign these differences to the opposite solutions:

  • 10% solution: 5 (from 20%) and 5 (from 30%)
  • 20% solution: 15 (from 10%)
  • 30% solution: 15 (from 10%)

Step 4: Find the ratio of the solutions based on these differences:

  • Ratio of 10% : 20% : 30% = 5 : 15 : 5

Simplify the ratio: 1 : 3 : 1. Therefore, the solutions should be mixed in the ratio 1:3:1 to obtain a 25% concentration.

Example 2: Multiple Components with Different Qualities

Imagine three types of metals with purity levels of 80%, 90%, and 95%. You want to create an alloy with 92% purity. Find the ratios in which these metals should be combined.

  • Metal A: 80%
  • Metal B: 90%
  • Metal C: 95%

Step 1: The target purity is 92%. Calculate the differences:

  • 80%: |80 – 92| = 12
  • 90%: |90 – 92| = 2
  • 95%: |95 – 92| = 3

Step 2: Assign differences to the other components:

  • 80%: 2 (from 90%) and 3 (from 95%)
  • 90%: 12 (from 80%)
  • 95%: 12 (from 80%)

Step 3: Determine the ratios:

  • 80% : 90% : 95% = 2 : 12 : 12

Simplify the ratio: 1 : 6 : 6. The metals should be combined in the ratio 1:6:6 to achieve 92% purity.

Tips for Using Alligation Alternate Effectively

Here are some useful tips:

  • Always identify the target value before starting.
  • Calculate differences carefully to avoid mistakes.
  • Simplify ratios to their lowest terms for clarity.
  • Use this method for multiple components to save time.

Practice regularly with different problems to become proficient in using the alligation alternate method for various applications.