Question

What percent of $15$ is $6$ $?$

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 $15$ does the number give $6$. Let the known percentage be $x\mathrm{\%}$, mathematically it would be written as
$x\mathrm{\%}\times 15=6$
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:
$x\mathrm{\%}={\displaystyle \frac{x}{100}}$
So on substituting the percentage with the fraction, the equation becomes:
${\displaystyle \frac{x}{100}}\times 15=6$
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,
$\Rightarrow {\displaystyle \frac{6\times 100}{15}}$
On multiplying the numerator terms together
$\Rightarrow {\displaystyle \frac{600}{15}}$
For calculating further, we would divide the numerator and denominator by a common factor, this results in, on dividing the numerator and denominator by $5$, we get
Further on dividing the fraction with $5$ we get,
$\Rightarrow {\displaystyle \frac{120}{3}}$
Again on dividing the fraction, which is numerator and the denominator with $3$ we get,
$\Rightarrow 40$
On converting the fraction into a decimal we get,
$\Rightarrow 40$
The value of $x$ is $40$.

$\therefore 6$ is $40\mathrm{\%}$ of $15$.

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 $40\mathrm{\%}$ of $15$, which mathematically could be written as
$\Rightarrow 40\mathrm{\%}\times 15$
On converting the percentage to fraction we get
$\Rightarrow {\displaystyle \frac{40}{100}}\times 15$
On multiplying the numerator terms together
$\Rightarrow {\displaystyle \frac{600}{100}}$
$\Rightarrow 6$
On calculating we get $6$. This shows that the number $6$ is $40\mathrm{\%}$ of $15$.
This is the way we can check, whether the solution is correct or not.