Question

What percentage of $75$ is $15$?

Answer 1

Hint: First of all, we need to assume the required percentage to be $x\%$. Then since the percentage is equivalent to the fraction $\dfrac{1}{100}$, the unknown percentage can be expressed in the form of a fraction as $\dfrac{x}{100}$. According to the question, we can say that $x\%$ of $75$ is equal to $15$ so that we can write the equation $\dfrac{75x}{100}=15$. On solving this equation, we will obtain the value for x and hence the required percentage.

Complete step by step solution:
Let the required percentage be equal to $x\%$. According to the information given in the question, the unknown percentage of $75$ is equal to $15$. Since we assumed the percentage to be $x\%$, we can say that $x\%$ of $75$ is equal to $15$. Now, we know that the percentage of a number is equivalent to the fraction $\dfrac{1}{100}$ so that we can replace the percentage $\%$ symbol by the fraction $\dfrac{1}{100}$ to write the unknown percentage as
$\begin{align}
  & \Rightarrow x\times \dfrac{1}{100} \\
 & \Rightarrow \dfrac{x}{100} \\
\end{align}$
Now, since $x\%$ of $75$ is equal to $15$, we can write the below equation.
$\begin{align}
  & \Rightarrow \dfrac{x}{100}\times 75=15 \\
 & \Rightarrow \dfrac{75x}{100}=15 \\
\end{align}$
Multiplying both the sides of the above equation by $100$, we get
$\begin{align}
  & \Rightarrow \dfrac{75x}{100}\times 100=15\times 100 \\
 & \Rightarrow 75x=1500 \\
\end{align}$
Finally, dividing both the sides of the above equation by $75$, we get
$\begin{align}
  & \Rightarrow \dfrac{75x}{75}=\dfrac{1500}{75} \\
 & \Rightarrow x=20 \\
\end{align}$

Hence, $20\%$ of $75$ is $15$.

Note: Do not forget to use the percentage $\left( \% \right)$ symbol while writing the final answer. The term “of” indicates the operation of the multiplication in mathematics which is the reason why we multiplied the fraction $\dfrac{x}{100}$ by $75$ which was equal to $15$.