The ratio of milk to water in a 100 litres mixture is 2 : 3. 10 litres of this mixture is withdrawn and replaced with milk. This process is repeated 2 more times. What is the percentage of milk in final mixture?

\[\begin{array}{*{20}{c}} {{\text{Milk}}}&{}&{{\text{Water}}}&{} \\ \begin{gathered} 2 \hfill \\ \downarrow \hfill \\ \end{gathered} &\begin{gathered} : \hfill \\ \hfill \\ \end{gathered} &\begin{gathered} 3 \hfill \\ \downarrow \hfill \\ \end{gathered} &\begin{gathered} = 5 \to 100 \hfill \\ \,\,\,1 \to 20 \hfill \\ \end{gathered} \\ {40}&{}&{60}&{} \end{array}\]
$$\eqalign{ & = 60{\left( {1 - \frac{{10}}{{100}}} \right)^3}\% \cr & = 60{\left( {\frac{9}{{10}}} \right)^3}\% \cr & = 60 \times \frac{{729}}{{1000}}\% \cr & = 43.74\% \cr & \therefore {\text{Final milk }}\% = \left( {100 - 43.74} \right)\% \cr & = 56.26\% \cr} $$