Question

A number X is increased by 20%, then it is decreased by 30%. What is the net change in the number?​

Answer 1

A number $\displaystyle\sf {X}$ is increased by its 20%. Then new number is,

$\displaystyle\sf{\longrightarrow X_1=\dfrac {(100+20)X}{100}}$

$\displaystyle\sf{\longrightarrow X_1=\dfrac {6X}{5}\quad\quad\dots(1)}$

Now this number is decreased by 30%. Then new number is,

$\displaystyle\sf{\longrightarrow X_2=\dfrac {(100-30)X_1}{100}}$

$\displaystyle\sf{\longrightarrow X_2=\dfrac {7X_1}{10}}$

From (1),

$\displaystyle\sf{\longrightarrow X_2=\dfrac {7}{10}\times\dfrac {6X}{5}}$

$\displaystyle\sf{\longrightarrow X_2=\dfrac {21X}{25}\quad\quad\dots(2)}$

Then, net change in the number $\displaystyle\sf {X}$ expressed as percentage is,

$\displaystyle\sf{\longrightarrow \delta X=\dfrac {X_2-X}{X}\times 100}$

$\displaystyle\sf{\longrightarrow \delta X=\dfrac {\dfrac {21X}{25}-X}{X}\times 100}$

$\displaystyle\sf{\longrightarrow \delta X=\dfrac {-4}{25}\times 100}$

$\displaystyle\sf {\longrightarrow\underline {\underline {\delta X=-16\%}}}$

I.e., the number $\displaystyle\sf {X}$ is decreased by 16% overall.