Question

What is $30\%$ of $75$ $?$

Answer 1

Hint: To solve this question we should know the concept of percentage. We need to convert the percentage into fraction. The fraction then will be multiplied to the number so as to find a certain percentage of that number. To change the percentage into fraction we will divide the number with $100$.

Complete step by step solution:
This question asks us to find the value of $30\%$ of the number, $75$. To find the value we will have to change the percentage into fraction. For doing so we will divide the percentage value by $100$ and remove the percentage sign from it. So mathematically it will be represented by
$\Rightarrow 30\%=\dfrac{30}{100}$
Now, we will find the number which will be $\dfrac{30}{100}$ of the number, $75$$.$ On writing this mathematically we get:
$\Rightarrow \dfrac{30}{100}$ of $75$
$\Rightarrow \dfrac{30}{100}\times 75$
On multiplying the numerator term together and denominator together, we get:
$\Rightarrow \dfrac{2250}{100}$
On dividing the numerator and denominator with the common factor we get
$\Rightarrow 22.5$

$\therefore $ The value of $30\%$ of $75$ is $22.5$

Note: For converting the percentage into fraction we divide the number by $100$ and not by any other number, because percentage is a ratio of fraction of $100$ .
We can check whether $30\%$ of $75$ is $22.5$ or not. For this we will assume the number whose $30\%$ is $22.5$, to be $x$ . So on formulating it we get,
$\Rightarrow 30\%\times x=22.5$
On converting the percentage into fraction
$\Rightarrow \dfrac{30}{100}\times x=22.5$
Taking the fraction, $\dfrac{30}{100}$ from L.H.S. to R.H.S. The fraction gets reciprocal which means the numerator changes to denominator and vice-versa. Thus we get:
$\Rightarrow x=22.5\times \dfrac{100}{30}$
On calculating we get:
$\Rightarrow \dfrac{2250}{30}$
$\Rightarrow 75$
Since the value of $x$ comes to $75$ , which is the same as the given question. So we got the correct answer.