Question

If $45\%$ of a number is $36$ What is the number?

Answer 1

Hint: Here we have to find the number whose $45\%$ is $36$ . Firstly we will write the formula for finding the percentage of a number and let the number as $x$. Then we will substitute all the given values and the value we have left in the formula and change the percentage sign into $\dfrac{1}{100}$ . Finally we will simplify the equation and get our desired answer.


Complete step by step answer:
We have been given that $45\%$ of a number is $36$ .
So let the number be $x$ .
As we know that formula for finding the percentage of a number is given as follows:
$P\%$ of Number $=X$…..$\left( 1 \right)$
From our statement we know the values as follows
$P\%=45\%$ , $X=36$ and the number is $x$
Substitute the above value in equation (1) as follows:
$\Rightarrow 45\%\times x=36$
As we can write $45\%=\dfrac{45}{100}$ by the definition of percentage we get,
$\Rightarrow \dfrac{45}{100}\times x=36$
$\Rightarrow x=\dfrac{36\times 100}{45}$
Simplifying further we get,
$\Rightarrow x=\dfrac{4\times 100}{5}$
$\Rightarrow x=4\times 20$
So we get,
$x=80$
So we get the number as $80$ .
Hence $45\%$ of $80$ is $36$ .

Note: Percentage is any number that can be expressed as a fraction of $100$ . It has no dimension and therefore it is known as dimensionless number. Percentage can be represented in decimal as well as fraction form. Always Remember to change the percentage symbol into the number which is $45\%=\dfrac{45}{100}$ as we want a number as our answer. We can cross check our answer by simplify finding $45\%$ of $80$ as follows and see whether we get $36$ as our answer which is mentioned in the question:
$\Rightarrow 45\%\times 80$
$\Rightarrow \dfrac{45}{100}\times 80$
Simplify further we get,
$\Rightarrow \dfrac{45}{10}\times 8$
$\Rightarrow 36$
We got the value as $36$ so our answer is correct.