Price reduction

The product is sold for 360 CZK, and the sales profit is 30%. If I reduce the product's price by 10%, what percentage will the sales profit be reduced?

Final Answer:

p =  43.3 %

Step-by-step explanation:

$$\begin{gathered} 360=x\cdot 1.30 \\ 1.3x=360 \\ x=\frac{360}{1.3}=276.92307692 \\ x=\frac{3600}{13}\doteq 276.923077 \\ {z}_1=360-x=360-276.9231=\frac{1080}{13}\doteq 83.0769 \\ {c}_2=360\cdot (1-10/100)=324\text{kc} \\ {z}_2=c_2-x=324-276.9231=\frac{612}{13}\doteq 47.0769\text{Kc} \\ p=100\cdot \frac{z_1-z_2}{z_1}=100\cdot \frac{\frac{1080}{13}-\frac{612}{13}}{\frac{1080}{13}}=\frac{130}{3}\%=43.3\% \end{gathered}$$

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