Discussion
The price of an article is increased by 30% and then decreased by 30%. What is the resultant price of the article?
Answer: B
The price decreases by 9%.
An increase of 30% followed by a decrease of 30% gives a net factor of 1.3 × 0.7.
\[ 1.3\times0.7=0.91 \]
The final price is 91% of the original, a fall of 9%. 'No change' wrongly assumes that the two percentages cancel because they are applied to different amounts.
The percentages are applied to different bases, since the 30% decrease is taken on the increased price and not on the original. For a price of 100 the price goes to 130 and then falls by 39 to 91. This gives the net fall of 9%, a result that is true for any equal rise and fall of p%, which is p squared over 100 percent.
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