Original price: $$60\div \left( 1-20\textbackslash\% \right)=75$$.  Discount for Ana: $$\left( 75-67.5 \right)\div 75=10\textbackslash\%$$. 
Rina bought a handbag for＄$$60$$ at a discount of $$20\textbackslash\%$$. Ana paid＄$$67.5$$ for the same handbag. What was the discount rate given to Ana? 
Options:
1: $$10\textbackslash\%$$ 
2: $$12\textbackslash\%$$ 
3: $$15\textbackslash\%$$ 
4: $$18\textbackslash\%$$ 