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

Last updated date: 24th Jul 2024
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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.