Practice Problems: Alligation Alternate For Different Concentration Scenarios

Alligation alternate is a useful method for solving problems involving the mixing of solutions with different concentrations. It helps find the ratio in which solutions should be mixed to achieve a desired concentration. This method is especially handy in chemistry and pharmacy but is also applicable in various other fields.

Understanding Alligation Alternate

Alligation alternate involves arranging the given concentrations and calculating the differences to determine the mixing ratio. The key idea is to find the proportion of solutions needed to obtain the target concentration efficiently.

Basic Steps in Alligation Alternate

Identify the concentrations of the available solutions.
Determine the desired concentration.
Arrange the concentrations in a line, with the lower and higher concentrations on either side.
Calculate the differences between each known concentration and the target concentration.
Use these differences to find the ratio of the solutions to be mixed.

Example Problem 1

Suppose you have two solutions: one with 30% concentration and another with 50% concentration. You want to prepare a solution with 40% concentration. Find the ratio in which these solutions should be mixed using alligation alternate.

Solution:

Lower solution concentration: 30%
Higher solution concentration: 50%
Desired concentration: 40%

Calculate the differences:

Difference between 50% and 40%: 10
Difference between 40% and 30%: 10

The ratio of solutions to be mixed is 10:10, which simplifies to 1:1. Therefore, equal parts of 30% and 50% solutions are needed.

Example Problem 2

You have solutions with concentrations of 20%, 40%, and 60%. You want to prepare 50% solution. Using alligation alternate, determine the ratios for mixing.

Solution:

Known solutions: 20%, 40%, 60%
Target concentration: 50%

First, consider the two closest concentrations: 40% and 60%.

Calculate differences:

Difference between 60% and 50%: 10
Difference between 50% and 40%: 10

Ratio of 40% to 60% solutions: 10:10, which simplifies to 1:1.

To include the 20% solution, note that it is farther from 50%. The difference between 50% and 20% is 30. Since 20% is less than 50%, it will be mixed with the solution at 40%.

Differences:

Between 40% and 20%: 20
Between 50% and 20%: 30

Thus, the ratio of 20% solution to the 40% solution is 30:20, which simplifies to 3:2. Combining this with the previous ratio, you can mix solutions in the ratio 3:2 (20% and 40%) and 1:1 (40% and 60%) to achieve the 50% concentration.