Question

What percent of 84 is 20?

Answer 1

Hint: We need to assume the percentage. We multiply 84 with the percent value to find the value of 20. We find the mathematical form and solve the equation to find the value of the assumed variable.

Complete step by step solution:
We assume that x% of 84 is 20.
The fraction is the respective ratio of two numbers. We find the value of the numerator with respect to the denominator of the fraction.
In case of percentage, we need to convert the denominator of the fraction into 100.
The numerator of the fraction with denominator being 100 will be the solution of the problem.
Therefore, x% can be written as $\dfrac{x}{100}$.
Now x percent of 84 is 20. Forming the mathematical expression, we get $84\times \dfrac{x}{100}=20$.
We now solve the equation to get
$\begin{align}
  & 84\times \dfrac{x}{100}=20 \\
 & \Rightarrow x=20\times \dfrac{100}{84} \\
\end{align}$
We complete the multiplication and get $x=20\times \dfrac{100}{84}=\dfrac{500}{21}$.
Therefore, $\dfrac{500}{21}$% of 84 is 20.

Note: The value of the fraction is actually the unitary value of x out of 100. Therefore, in percentage value we got $\dfrac{500}{21}$ as the percentage. Percentage deals with the ratio out of 100. The ratio value for both fraction and percentage is the same.