The price

The price of the calculator gradually decreased. From 65 euros to 30 euros, then to 10 euros and finally to 4 euros. What percentage were the individual reductions? What percentage of the original price was reduced by a total of?

Correct answer:

p₁ =  53.8462 %
p₂ =  66.6667 %
p₃ =  60 %
p₄ =  93.8462 %

Step-by-step explanation:

$$\begin{gathered} c_1=65\text{ Eur } \\ {c}_2=30\text{ Eur } \\ {c}_3=10\text{ Eur } \\ {c}_4=4\text{ Eur } \\ {p}_1=100\cdot {\displaystyle \frac{c_1-c_2}{c_1}}=100\cdot {\displaystyle \frac{65-30}{65}}={\displaystyle \frac{700}{13}}\mathrm{\%}=53.8462\mathrm{\%} \end{gathered}$$

$p_2=100\cdot {\displaystyle \frac{c_2-c_3}{c_2}}=100\cdot {\displaystyle \frac{30-10}{30}}={\displaystyle \frac{200}{3}}\mathrm{\%}=66.6667\mathrm{\%}$

$p_3=100\cdot {\displaystyle \frac{c_3-c_4}{c_3}}=100\cdot {\displaystyle \frac{10-4}{10}}=60\mathrm{\%}$

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