(i) Consider x as the mean proportion of 5 and 80
\[5:\text{ }x\text{ }::\text{ }x:\text{ }80\]
It can be written as
\[\begin{array}{*{35}{l}}
{{x}^{2}}~=\text{ }5\text{ }\times \text{ }80\text{ }=\text{ }400 \\
x\text{ }=\text{ }\surd 400\text{ }=\text{ }20 \\
\end{array}\]
Therefore, mean proportion of \[5\text{ }and\text{ }80\text{ }is\text{ }20\]
(ii) Consider x as the mean proportion of \[1/12\text{ }and\text{ }1/75\]
\[1/12:\text{ }x\text{ }::\text{ }x:\text{ }1/75\]
It can be written as
\[\begin{array}{*{35}{l}}
{{x}^{2}}~=\text{ }1/12\text{ }\times \text{ }1/75\text{ }=\text{ }1/900 \\
x\text{ }=\text{ }\surd 1/900\text{ }=\text{ }1/30 \\
\end{array}\]
Therefore, mean proportion of \[1/12\text{ }and\text{ }1/75\text{ }is\text{ }1/30\]