Question

# A number is increased by $20%$ and the increased number is decreased by $20%$. Find the increase or decrease percent.

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Solution

## Let $x$ be the number.Increase in the number $=20%ofx$ $=\frac{20}{100}×x$ $=\frac{1}{5}×x=\frac{x}{5}$Increased number$=x+\frac{x}{5}$ $=\frac{5x+x}{5}=\frac{6x}{5}$The resulting number decreased by $20%$Decrease in the number $=20%of\frac{6x}{5}$ $=\frac{1}{5}×\frac{6x}{5}=\frac{6x}{25}$New number $=\frac{6x}{5}-\frac{6x}{25}$ $=\frac{30x-6x}{25}$ $=\frac{24x}{25}$The net decrease $=x-\frac{24x}{25}$ $=\frac{25x-24x}{25}=\frac{x}{25}$Net % decrease $=\frac{\frac{x}{25}}{x}×100$ $=\frac{x}{25}×\frac{1}{x}×100=4%$Hence, the net percent decrease $=4%$.

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