Question

Are the following in proportion?

$9boys:12boys=8girls:6girls$

Answer 1

Given

$9boys:12boys=8girls:6girls$

It is written as $9:12::8\hspace{0.17em}:6$

First and last term is called extreme terms, that is $9$ and $6$ and $8$ and $12$ is called middle terms.

product of extreme terms = product of middle terms

$$\begin{gathered} 9\times 6=8\times 12 \\ 54\ne 96 \end{gathered}$$

Hence $9boys:12boys=8girls:6girls$ are not in proportion.