Question

Find the number whose $24\%$ is $30$.

Answer 1

Hint: To solve this question, we will assume the number. Then, we will use the formula of percentage and substitute the corresponding values in the formula. After that we will simplify the formula to get the required answer.

Complete step by step solution:
Let’s consider that the number is $x$.
So, it can be said that the $24\%$ of $x$ is $30$.
Now, we will write it into mathematical terms as:
$\Rightarrow x\times 24\%=30$
We can write the percentage in to fraction of hundred as:
$\Rightarrow \%=\dfrac{1}{100}$
So, we can write the equation as:
$\Rightarrow x\times 24\times \dfrac{1}{100}=30$
Here, we will multiply with $100$ both sides of the above step as:
$\Rightarrow x\times 24\times \dfrac{1}{100}\times 100=30\times 100$
Now, we will cancel out the equal like terms and will get $3000$ after multiplying $30$ and $100$ as:
$\Rightarrow x\times 24=3000$
Here, we will divide by $24$ both sides of the above step as:
$\Rightarrow \dfrac{x\times 24}{24}=\dfrac{3000}{24}$
Again we will cancel out the equal like term as:
$\Rightarrow x=\dfrac{3000}{24}$
Now, simplify the above fraction into simplest form as:
$\Rightarrow x=125$
Hence, the number is $125$.

Note: We can check whether the solution is correct or not in the following way. Here, we will try to find out $24\%$ of $125$ as:
$\Rightarrow 125\times 24\%$
Now, we will simplify the above step.
$\begin{align}
  & \Rightarrow 125\times \dfrac{24}{100} \\
 & \Rightarrow 5\times \dfrac{24}{4} \\
 & \Rightarrow 5\times 6 \\
 & \Rightarrow 30 \\
\end{align}$
Since, we have given $30$ in the question. Hence, the solution is correct.