A number is increased by $40 %$ and then decreased by $40 %$ . Find the net increase or decrease percent.

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Solution

Let $x$ be the number.
Increase in the number $= 40 % o f x$
$= \frac{40}{100} \times x$
$= \frac{2}{5} \times x = \frac{2 x}{5}$
Increased number $= x + \frac{2 x}{5}$
$= \frac{5 x + 2 x}{5} = \frac{7 x}{5}$
The resulting number decreased by $40 %$
Decrease in the number $= 40 % o f \frac{7 x}{5}$
$= \frac{2}{5} \times \frac{7 x}{5} = \frac{14 x}{25}$
New number $= \frac{7 x}{5} - \frac{14 x}{25}$
$= \frac{35 x - 14 x}{25}$
$= \frac{21 x}{25}$
The net decrease $= x - \frac{21 x}{25}$
$= \frac{25 x - 21 x}{25} = \frac{4 x}{25}$
Net % decrease $= \frac{\frac{4 x}{25}}{x} \times 100$
$= \frac{4 x}{25} \times \frac{1}{x} \times 100 = 4 \times 4 = 16 %$
Hence, the net percent decrease $= 16 %$

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