Question

What percent of 84 is 21?

Answer 1

Hint: To find what percent of 84 is 21. Firstly we will divide 21 by 84 as we have to find the percent of 21 from 84. Then we will simplify the ratio obtained. Next for getting it in percentage we will multiply the obtained value by 100 and add the percentage sign to get the desired answer.

Complete step by step solution:
To obtain what percent of 84 is 21 we will divide 21 by 84 as follows:
$\dfrac{21}{84}$
Now, as we can see that both numerator and denominator have two common factors i.e. 3 and 7
So, we will simplify the above value by dividing the numerator and denominator by 3 and get,
$\begin{align}
  & \Rightarrow \dfrac{\dfrac{21}{3}}{\dfrac{84}{3}} \\
 & \Rightarrow \dfrac{7}{28} \\
\end{align}$
Again on dividing numerator and denominator by 7 we get,
$\begin{align}
  & \Rightarrow \dfrac{\dfrac{7}{7}}{\dfrac{28}{7}} \\
 & \Rightarrow \dfrac{1}{4} \\
\end{align}$
$\therefore \dfrac{21}{84}=\dfrac{1}{4}$…….$\left( 1 \right)$
Now, we will multiply right side of the equation (1) by 100 and get,
$\begin{align}
  & \Rightarrow \dfrac{1}{4}\times 100 \\
 & \Rightarrow 25\% \\
\end{align}$

Hence 21 is $25\%$ of 84.

Note: The percentage term used is a number or we can say ratio which is expressed as a fraction of 100. It is denoted by percent sign $\%$. It doesn’t have any unit of measurement. Percentage means a part per hundred. It can be represented in decimal form; the most common use of percentage is in exams where the percent of the total marks in all subjects is calculated for every student. We can also use a direct method to find the solution. The formula is:
$P\%$ of Number $=X$…..$\left( 2 \right)$
The Number $=84$
$X=21$
Substituting above value in equation (2) we get,
$\begin{align}
  & P\%\times 84=21 \\
 & \dfrac{P}{100}=\dfrac{21}{84} \\
 & P=\dfrac{21}{84}\times 100 \\
 & P=25\% \\
\end{align}$