Question

What percent of $180$ is $35$ $?$

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 answer:
The question asks for what percentage of $180$ does the number give $35$. Let the known percentage be $x\%$, mathematically it would be written as
$x\%\times 180=35$
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 :
$\dfrac{x}{100}\times 180=35$
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,
$\Rightarrow \dfrac{35\times 100}{180}$
On multiplying the numerator terms together
$\Rightarrow \dfrac{3500}{180}$
For calculating further, we would divide the numerator and denominator by a common factor, this results in, on dividing the numerator and denominator by $10$, we get
Further on dividing the fraction with $10$ we get,
$\Rightarrow \dfrac{350}{18}$
Again on dividing the fraction with $2$ we get,
$\Rightarrow \dfrac{175}{9}$
On converting the fraction into a decimal we get,
$\Rightarrow 19.44$
The value of $x$ is $19.44$.

$\therefore 35$ is $19.44\%$ of $180$.

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 $19.44\%$ of $180$, which mathematically could be written as
$\Rightarrow 19.44\%\times 180$
On converting the percentage to fraction we get
$\Rightarrow \dfrac{19.44}{100}\times 180$
On multiplying the numerator terms together
$\Rightarrow \dfrac{3499.2}{100}$
$\Rightarrow 34.992\approx 35$
On calculating we get $35$. This shows that the number $35$ is $19.44\%$ of $180$.
This is the way we can check, whether the solution is correct or not.