Question

What percent of $128$ is $24$ $?$

Answer 1

Hint: To solve this type of question we need to know the concept of percentage. The question requires conversion of percentage into fraction and vice-versa. We will have to use the concept of reciprocal.

Complete step by step solution:
The question asks for what percentage of $128$ does the number give $24$. Let the known percentage be $x\%$, mathematically it would be written as
$x\%\times 128=24$
Now we will calculate the value of $x$. Since $x$ is a percentage, so it will be divided by $100$ to change the percentage into fraction, on doing this we get:
$x\%=\dfrac{x}{100}$
So on substituting the percentage with the fraction, the equation becomes :
$\dfrac{x}{100}\times 128=24$
To find the value of $x$ we will bring the denominator of L.H.S to the numerator in R.H.S, while the numerator of R.H.S. to the denominator in L.H.S.. On doing so we get,
$\Rightarrow \dfrac{24\times 100}{128}$
On multiplying the numerator terms together
$\Rightarrow \dfrac{2400}{128}$
For calculating further, we would divide the numerator and denominator by a common factor, this results in, on dividing the numerator and denominator by $4$, we get
Further on dividing the fraction with $4$ we get,
$\Rightarrow \dfrac{150}{8}$
Again on dividing the fraction with $2$ we get,
$\Rightarrow \dfrac{75}{4}$
On converting the fraction into a decimal we get,
$\Rightarrow 18.75$
The value of $x$ is $18.75$.

$\therefore 24$ is $18.75\%$ of $128.$

Note: Let us check whether the answer we got is correct or not. For this we would perform the particular task, Let's check what will be $18.75\%$ of $128$, which mathematically could be written as
$\Rightarrow 18.75\%\times 128$
On converting the percentage to fraction we get
$\Rightarrow \dfrac{18.75}{100}\times 128$
On multiplying the numerator terms together
$\Rightarrow \dfrac{2400}{100}$
On calculating we get $24$. This shows that the number $24$ is $18.75\%$ of $128.$
This is the way we can check, whether the solution is correct or not.