Just like averages, ratios, and proportions, we can use the concept of weighted averages, which is nothing but the formula version of alligation, to solve many questions.
If $$x_1$$, $$x_2$$, $$x_3$$, $$...$$, $$x_n$$ are the percentage or fractional values of the concentrations of a solute in $$n$$ solutions, which are respectively mixed in the ratio $$y_1:y_2:y_3:...:y_n$$, we get the concentration of that solute in the resultant mixture as:
$$\frac{x_1y_1 + x_2y_2 + x_3y_3 + ... +x_ny_n}{y_1+y_2+y_3+...+y_n}$$
The result will be a percentage or fractional value of concentration of the solute, depending on what we start with.
Another way of approaching such questions with only 2 solutions can be the Alligation - Cross Method.
If 2 solutions having concentrations of a particular solute as X and Y in percentage or fractional form, and they are mixed to get a concentration of Z percentage or fraction, then the ratio in which they are mixed can be calculated as:
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The required ratio will be $$Z-Y\ :\ X-Z$$.
