smc

We have $$10\cdot {\left(\frac{1}{2}+\frac{1}{5}+\frac{1}{10}\right)}^{-1}$$ Making the denominators equal gives $$⟹10\cdot {\left(\frac{5}{10}+\frac{2}{10}+\frac{1}{10}\right)}^{-1}$$ $$⟹10\cdot {\left(\frac{5+2+1}{10}\right)}^{-1}$$ $$⟹10\cdot {\left(\frac{8}{10}\right)}^{-1}$$ $$⟹10\cdot {\left(\frac{4}{5}\right)}^{-1}$$ $$⟹10\cdot \frac{5}{4}$$ $$⟹\frac{50}{4}$$ Finally, simplifying gives $$⟹\boxed{\frac{25}{2}}$$