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Percentage algebra

Source: AHSME 1986 problem 20

October 1, 2011
AMC

Problem Statement

Suppose xx and yy are inversely proportional and positive. If xx increases by p%p\%, then yy decreases by
<spanclass=′latex−bold′>(A)</span> p%<spanclass=′latex−bold′>(B)</span> p1+p%<spanclass=′latex−bold′>(C)</span> 100p%<spanclass=′latex−bold′>(D)</span> p100+p%<spanclass=′latex−bold′>(E)</span> 100p100+p% <span class='latex-bold'>(A)</span>\ p\%\qquad<span class='latex-bold'>(B)</span>\ \frac{p}{1+p}\%\qquad<span class='latex-bold'>(C)</span>\ \frac{100}{p}\%\qquad<span class='latex-bold'>(D)</span>\ \frac{p}{100+p}\%\qquad<span class='latex-bold'>(E)</span>\ \frac{100p}{100+p}\%
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