Question

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

Answer 1

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.

Complete step by step answer:
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.