$$T\arg et\ question=>What\ is\ the\ retail\ price\ of\ the\ machine?$$
$$Wholesales\ price=\$90$$
$$Let\ retail\ price\ =\ x$$
$$Retailer\ sold\ the\ machine\ after\ a\ discount\ of\ 10\%$$
$$=>\ 10\%\ of\ x\ =\ \frac{10}{100}\cdot x\ =\ 0.1x$$
$$New\ retail\ price\ =\ x\ -\ 0.1x\ =\ 0.9x$$
$$New\ retail\ price\ =\ 20\%\ profit\ on\ wholesale\ price$$
$$20\%\ profit\ on\ wholesale\ price\ =\left(20\%\ of\ $90\right)\ +90$$
$$=\left(\frac{20}{100}\cdot90\right)+90$$
$$=18+90=108$$
$$\frac{0.9x}{0.9}=\frac{108}{0.9}$$
$$x=120$$


$$Answer\ =\ C$$