Traffic accidents

Of the total number of traffic accidents, 80% occur in the village and 20% outside the village. If the number of traffic accidents in the village were reduced by 40%, by what percentage would the total number of traffic accidents decrease?

Correct answer:

p =  32 %

Step-by-step explanation:

$$\begin{gathered} r_1=80\%=\frac{80}{100}=\frac{4}{5}=0.8 \\ {r}_2=20\%=\frac{20}{100}=\frac{1}{5}=0.2 \\ {r}_3=100\%-40\%=1-\frac{40}{100}=0.6 \\ {n}_2=r_3\cdot r_1\cdot n+r_2\cdot n \\ p=100\cdot \frac{n-n_2}{n} \\ p=100\cdot \frac{n-(r_3\cdot r_1\cdot n+r_2\cdot n)}{n} \\ p=100\cdot \frac{1-r_3\cdot r_1-r_2}{1}=100\cdot \frac{1-0.6\cdot 0.8-0.2}{1}=32\% \end{gathered}$$

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