Answer

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**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.

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