\[\boxed{\mathbf{689\ (689)}\mathbf{.}\mathbf{\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[10\ :\frac{1}{6} = 10 \cdot 6 = 60\]
\[a\ :2 = 60 \Longrightarrow a = 60 \cdot 2 = 120\]
\[b\ :\frac{3}{4} = 60 \Longrightarrow b = 60 \cdot \frac{3}{4} =\]
\[= \frac{60 \cdot 3}{4} = 45\]
\[Ответ:\ \ a = 120;\ \ b = 45.\]