Question

What percent of $18$ is $12$$?$

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 $18$ does the number give $12$. Let the known percentage be $x\%$, mathematically it would be written as
$x\%\times 18=12$
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 :
$\dfrac{x}{100}\times 18=12$
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,
$\Rightarrow \dfrac{12\times 100}{18}$
On multiplying the numerator terms together
$\Rightarrow \dfrac{1200}{18}$
For calculating further, we would divide the numerator and denominator by a common factor, this results in, on dividing the numerator and denominator by $6$, we get
Further on dividing the fraction with $6$ we get,
$\Rightarrow \dfrac{200}{3}$
Again on dividing the fraction, which is numerator and the denominator with $3$ we get,
$\Rightarrow 66\dfrac{2}{3}$
On converting the fraction into a decimal we get,
$\Rightarrow 66.67$
The value of $x$ is $66.67$.
$\therefore 6$ is $66.67\%$ of $18$.

Note: Let us check whether the answer we got is correct or not. For this we would perform the particular task, Let us check what will be $66.67\%$ of $18$, which mathematically could be written as
$\Rightarrow 66.67\%$ $\times 18$
$66.67\%$ in fractional form is $66\dfrac{2}{3}\%=\dfrac{200}{3}\%$
On converting the percentage to fraction we get
$\Rightarrow \dfrac{\dfrac{200}{3}}{100}\times 18$
On multiplying the numerator terms together
$\Rightarrow \dfrac{200}{3\times 100}\times 18$
$\Rightarrow 12$
On calculating we get $12$. This shows that the number $12$ is $66.67\%$ of $18$.
This is the way we can check, whether the solution is correct or not.