It is given that
a, \[12,16\] and b are in continued proportion
\[a/12\text{ }=\text{ }12/16\text{ }=\text{ }16/b\]
We know that
\[a/12\text{ }=\text{ }12/16\]
By cross multiplication
\[a/12\text{ }=\text{ }12/16\]
Similarly
\[12/16\text{ }=\text{ }16/b\]
By cross multiplication
\[\begin{array}{*{35}{l}}
12b\text{ }=\text{ }16\text{ }\times \text{ }16\text{ }=\text{ }256 \\
b\text{ }=\text{ }256/12\text{ }=\text{ }64/3\text{ }=\text{ }21\text{ }1/3 \\
\end{array}\]
Therefore, \[a\text{ }=\text{ }9\text{ }and\text{ }b\text{ }=\text{ }64/3\text{ }or\text{ }21\text{ }1/3\]