Jack bought a batch of goods that he hoped to earn a $$50\textbackslash\%$$ profit after selling them. On the first day, he sold $$60\textbackslash\%$$ of his goods at a profit of $$50\textbackslash\%$$. On the second day, he sold all remaining goods for a discount. If the total profit is $$76\textbackslash\%$$ of the planned profit, what was the discount rate? 
Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Complex Money Word Problems
Let the cost for the batch of goods be $$m$$ dollars.  Jack finally earned: $$m\times 50\textbackslash\%\times 92\textbackslash\%=0.38m$$.  On the first day he earned: $$m\times 60\textbackslash\%\times 50\textbackslash\%=0.30m$$.  Profit for the second day: $$0.38m-0.30m=0.08m$$.  Profit rate for the second day: $$\frac{0.08m}{\left( m-0.6m \right)}=20\textbackslash\%$$.  Percentage discount: $$1-\frac{\left( 1+20\textbackslash\% \right)}{\left( 1+50\textbackslash\% \right)}=20\textbackslash\%$$. 