Discussion
If the price of an article is decreased by 25%, and then the new price is increased by 45%, what is the net change (in %) in the price?
Answer: C
The net change is 8.75%, an increase.
Successive percentage changes multiply, they do not add.
\[ \begin{aligned} 0.75 \times 1.45 &= 1.0875 \\ \text{change} &= +8.75\% \end{aligned} \]
The shortcut formula for changes x and y is \(x + y + xy/100 = -25 + 45 - 11.25 = 8.75\). −11.25 is only the cross term, 20 is the simple sum \(-25 + 45\), and −1.25 is a sign slip.
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