$\frac{2}{3a}=\frac{5}{6b}=\frac{3}{4c}=k$ olsun
$a=\frac{2}{3k} \\ b=\frac{5}{6k} \\ c=\frac{3}{4k} $
$a:b:c:=\frac{2}{3}:\frac{5}{6}:\frac{3}{4}=8:10:9$