[tex]\huge{\boxed {\tt{Solution : }}}[/tex]
[tex]\tt {We\: can\: write\: \dfrac{b}{10} = \dfrac{3}{5}\:as:}[/tex]
[tex]\longrightarrow \sf{b : 10 : :3 : 5}[/tex]
[tex]\tt{ \because {Product\:of \:extremes=Product\:of \:means}}[/tex]
[tex]\sf { : \implies{ b:10 : :3 :5 }} \\ \\ \sf { : \implies{b \times 5 = 10 \times 3 }} \\ \\ \sf { : \implies{5b = 30}} \\ \\ \sf { :\implies{b = \dfrac{30}{5}}} \\ \\ \sf { : \implies{\boxed{\tt{b = 6}}}}[/tex]
[tex]\bf{\therefore{The\: value\:b\:is\:6.}}[/tex]
[tex]\rule{307}{2}[/tex]
