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# If $32\%$ of a number is $8$ , find the number.

Last updated date: 19th Jul 2024
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Hint: For calculating the number, let’s assume that the number is $x$. Then, we will use the question as a condition to create an equation. After that we will do necessary calculation and will simplify the equation to get the required number.

Since, we already have the given percentage and percentage value in number as $32\%$ and $8$ respectively.
So, let’s suppose that the number is $x$.
Here, the condition given in the question is $32\%$ of a number$x$ is $8$. We can write the conditions in mathematical expression as:
$\Rightarrow x\times 32\%=8$
We can write percentage in terms of fraction one by hundred as:
$1\%=\dfrac{1}{100}$
So, the equation of condition will be as:
$\Rightarrow x\times \dfrac{32}{100}=8$
Now, we will do multiplication with $100$ both sides of above step as:
$\Rightarrow x\times \dfrac{32}{100}\times 100=8\times 100$
Here, equal like terms will be canceled out and multiplication of $8$ and $100$ will be $800$ as:
$\Rightarrow x\times 32=800$
Now, we will divide by $32$ each side of the above step as:
$\Rightarrow \dfrac{x\times 32}{32}=\dfrac{800}{32}$
After division, equal like terms will be canceled out and we will have $25$ by division of $800$ and $32$ as:
$\Rightarrow x=25$
Hence, the required number is $25$.

Note: We can check that the solution is correct or not by using the equation of condition mentioned in the solution as:
$\Rightarrow x\times 32\%=8$
Here, we will substitute $25$ for $x$ as:
$\Rightarrow 25\times 32\%=8$
Now, we will solve the left hand side of the above equation as:
$\Rightarrow 25\times 32\%$
Here, we can convert the percentage into fraction to make calculation easy as:
$\Rightarrow 25\times \dfrac{32}{100}$
Now, we will do the multiplication of numerator as:
\begin{align} & \Rightarrow \dfrac{25\times 32}{100} \\ & \Rightarrow \dfrac{800}{100} \\ \end{align}
After dividing, we will have:
$\Rightarrow 8$
And this is equal to the right hand side. Therefore, the solution is correct.