Question

number is increased by 40 % then decreased by 40% find the net increase or decrease percent

Answer 1

$$\begin{gathered} Dearstudent, \\ Lettheoriginalnumberbe\text{'}x\text{'} \\ Whenitincreasedby40\%=x+40\%ofx \\ =x+\frac{40}{100}\times x \\ =x+\frac{2x}{5} \\ =\frac{7x}{5} \\ Whenitisdecreased40\%=\frac{7x}{5}-40\%of\frac{7x}{5} \\ =\frac{7x}{5}-\frac{40}{100}\times \frac{7x}{5} \\ =\frac{7x}{5}-\frac{2}{5}\times \frac{7x}{5} \\ =\frac{7x}{5}-\frac{14x}{25} \\ =\frac{35x-14x}{25} \\ =\frac{21x}{25} \\ \%change=\frac{{\displaystyle \frac{21x}{25}}-x}{x}\times 100 \\ =\frac{{\displaystyle \frac{21x-25x}{25}}}{x}\times 100 \\ =\frac{{\displaystyle \frac{-4x}{25}}}{x}\times 100 \\ =\frac{-4x}{25x}\times 100 \\ =-16\% \\ -vesignshowsthenetdecreaseinnumber \\ thusthenetdecrease\%is16\% \\ Regards \end{gathered}$$