1951 AHSME Problems/Problem 8

Problem

The price of an article is cut $10 \%.$ To restore it to its former value, the new price must be increased by:

$\textbf{(A) \ } 10 \% \qquad\textbf{(B) \ } 9 \% \qquad \textbf{(C) \ } 11\frac{1}{9} \% \qquad\textbf{(D) \ } 11 \% \qquad\textbf{(E) \ } \text{none of these answers}$

Solution

Without loss of generality, let the price of the article be 100. Thus, the new price is $.9\cdot  100= 90$. Then, to restore it to the original price, we solve $90x=100$. We find $x=1\dfrac{1}{9}$, thus, the percent increase is $1\dfrac{1}{9}-1=\dfrac{1}{9}=\boxed{\textbf{(C) \ } 11\frac{1}{9}\%}$.

See Also

1951 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
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