Discussion
A number is increased by 10% and then decrease by 10%. Find the net decrease percent.
Answer: B
The net decrease is 1%.
Take the number as 100. After a 10% increase it becomes 110; a 10% decrease of 110 removes 11, leaving 99. The net change is 100 to 99, a decrease of 1%.
\[ \begin{aligned} &\left(1 + \frac{10}{100}\right)\left(1 - \frac{10}{100}\right) \\ &= 1.1 \times 0.9 = 0.99 \end{aligned} \]
The shortcut for an equal rise and fall of \(x\)% is a net fall of \(\frac{x^{2}}{100}\)%. 0% is the trap of assuming the two changes cancel; they do not, because the decrease is taken on a larger base.
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