The expenses

The expenses on rice, fish and oil of a family are in the ratio 12:17:3.The prices of these articles are increased by 20%, 30% and 50% respectively. Find the total increased percent.

Correct answer:

p =  28.125 %

Step-by-step explanation:

$$\begin{gathered} 12:17:3 \\ {r}_1=\frac{12}{12+17+3}=\frac{3}{8}=0.375 \\ {r}_2=\frac{17}{12+17+3}=\frac{17}{32}\doteq 0.5313 \\ {r}_3=\frac{3}{12+17+3}=\frac{3}{32}\doteq 0.0938 \\ {p}_1=100\%+20\%=1+\frac{20}{100}=1.2 \\ {p}_2=100\%+30\%=1+\frac{30}{100}=1.3 \\ {p}_3=100\%+50\%=1+\frac{50}{100}=1.5 \\ r=p_1\cdot r_1+p_2\cdot r_2+p_3\cdot r_3=1.2\cdot 0.375+1.3\cdot 0.5313+1.5\cdot 0.0938=\frac{41}{32}\doteq 1.2813 \\ p=100\cdot (r-1)=100\cdot (1.2813-1)=28.125\% \end{gathered}$$

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