Alligation Calculator

Formula

The formula to calculate the Alligation is:

\[ C1 \times V1 + C2 \times V2 = C \times V \]

Where:

\(C1\) is the concentration of the first solution (%)
\(V1\) is the volume of the first solution (mL)
\(C2\) is the concentration of the second solution (%)
\(V2\) is the volume of the second solution (mL)
\(C\) is the concentration of the resulting mixture (%)
\(V\) is the volume of the resulting mixture (mL)

What is Alligation?

Alligation is a mathematical method used to solve problems related to mixtures and their ingredients. It is a rule that allows one to find the ratio in which two or more ingredients at given prices must be mixed to produce a mixture of a desired price. The method involves the use of a simple diagram known as an alligation chart, where the prices of the cheaper and dearer ingredients are written in the left and right columns, respectively, and the mean price in the middle column. The differences between the mean price and the prices of the ingredients are then calculated and written in the opposite columns. These differences represent the required ratio of the ingredients. Alligation is commonly used in pharmacy to calculate the amount of different substances required to make a particular medicine.

Example Calculation

Let's assume the following values:

Concentration of the first solution (C1) = 20%
Volume of the first solution (V1) = 100 mL
Concentration of the second solution (C2) = 40%
Volume of the second solution (V2) = 150 mL

Using the formula:

\[ C1 \times V1 + C2 \times V2 = C \times V \]

\[ 20 \times 100 + 40 \times 150 = C \times (100 + 150) \]

\[ 2000 + 6000 = C \times 250 \]

\[ 8000 = C \times 250 \]

\[ C = \frac{8000}{250} = 32 \% \]

The resulting concentration (C) is 32%.