A number when increased by $20\%$ becomes 72. What will it become if it is decreased by $10\%$?

Hint: To obtain the answer of the given question we will use percentage concept. Firstly we will let our number be any variable then we will add $20\%$ of the number to the number and put it equal to 72 and get the number. Then we will subtract $10\%$ of that number by the number and get the desired answer.

Complete step-by-step solution:
We have been given that when the number is increased by $20\%$ becomes 72.
Let the number be $x$
We will increase the number by $20\%$ as follows:
$\begin{align}
  & x+\left( 20\%\times x \right) \\
 & = x+\dfrac{20}{100}\times x \\
 & = x+\dfrac{x}{5} \\
 & = \dfrac{5x+x}{5} \\
 & = \dfrac{6x}{5} \\
\end{align}$
It is given that above value is equal to 72 so,
$\begin{align}
  & \dfrac{6x}{5}=72 \\
 & \Rightarrow x=72\times \dfrac{5}{6} \\
 & \Rightarrow x=60 \\
\end{align}$
So we got our number as 60.
Now we have to find what it will become when it decreases by $10\%$.
So we will proceed as follows:
$\begin{align}
  & 60-\left( 10\%\times 60 \right) \\
 &= 60-\dfrac{10}{100}\times 60 \\
 &= 60-6 \\
 &= 54 \\
\end{align}$
We got our answer as 54.
Hence when the number is decreased by $10\%$ it becomes 54.

Note: Percentage is used to find a portion among the given values. It is a number or ratio that can be expressed as a fraction of 100. To calculate the percentage of a number, divide the number by a whole and multiply the obtained fraction by 100. We can also say that percentage means, a part per hundred. It is represented by $''\%''$ or “per”. It is a dimensionless number as it doesn’t have any dimension. The percentage can never be negative; it can only be denoted as percentage increased or decreased.