Question

12.5 is $25\mathrm{\%}$ of what number ?

Answer 1

Hint: In the given question, we are required to calculate the number whose $25\mathrm{\%}$ corresponds to a specific number given to us in the problem. We must remember the formula for finding a specific percentage of a number as: $Percentage={\displaystyle \frac{Part}{Whole}}\times 100\mathrm{\%}$. Percentage of a number corresponds to the share or share in the whole thing.

Complete step by step answer:
In this specific question, we are required to find the number whose $25\mathrm{\%}$ corresponds to $12.5$.
So, we find that specific number by using the formula for percentage as $Percentage={\displaystyle \frac{Part}{Whole}}\times 100\mathrm{\%}$.
Let us assume the total number to be x.
So, the whole corresponds to the number x and the part corresponds to the number $12.5$ in this case. Also, the percentage is given to us as $25\mathrm{\%}$. So, we substitute these known values in the above mentioned formula. So, we get,
$\Rightarrow 25\mathrm{\%}={\displaystyle \frac{12.5}{x}}\times 100\mathrm{\%}$
Now, we have to find the value of x in the above equation.
We use the method of transposition to shift the terms in the equation and find the value of the variable. Shifting the variable to the left side of equation and constants to the right side of the equation, we get,
$\Rightarrow x={\displaystyle \frac{12.5}{25\mathrm{\%}}}\times 100\mathrm{\%}$
Simplifying the calculations, we get,
$\Rightarrow x={\displaystyle \frac{1250}{25}}$
Simplifying the calculations by cancelling common factors in numerator and denominator, we get,
$\Rightarrow x=50$
So, the value of x is $50$.
Hence, $12.5$ is $25\mathrm{\%}$ of $50$.

Note:
The percentage formula $Percentage={\displaystyle \frac{Part}{Whole}}\times 100\mathrm{\%}$ can be used to find any parameter in the equation given the other parameters. In these questions we should focus on what these words mean. Percentage is unitless quantity. When we find percent of two quantities then both should have the same unit.