# Price reduction

The product is sold for 360 CZK and the sales profit is 30%. By what percentage the sales profit will be reduced if I reduce the price of the product by 10%?

Result

p =  43.3 %

#### Solution:

$\ \\ 360=x \cdot \ 1.30 \ \\ \ \\ 1.3x=360 \ \\ \ \\ x=\dfrac{ 3600 }{ 13 } \doteq 276.923077 \ \\ c_{2}=360 \cdot \ (1-10/100)=324 \ \text{kc} \ \\ \ \\ z_{1}=0.30 \cdot \ x=0.30 \cdot \ 276.9231 \doteq \dfrac{ 1080 }{ 13 } \doteq 83.0769 \ \text{Kc} \ \\ z_{2}=c_{2}-x=324-276.9231 \doteq \dfrac{ 612 }{ 13 } \doteq 47.0769 \ \text{Kc} \ \\ \ \\ p=100 \cdot \ \dfrac{ z_{1}-z_{2} }{ z_{1} }=100 \cdot \ \dfrac{ 83.0769-47.0769 }{ 83.0769 } \doteq \dfrac{ 130 }{ 3 } \doteq 43.3333 \doteq 43.3 \%$

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