Question

80 is $32\mathrm{\%}$ of a certain number, find the number.

Answer 1

Hint: We solve this question by using the concept of percent. We first assume that the certain number is x. Then we convert the given statement into a mathematical form and solve for the value of x. This x gives us the value of the number whose $32\mathrm{\%}$ is 80.

Complete step by step answer:
In order to solve this question, let us first assume the unknown certain number to be x. Now, we are required to convert the given question into a mathematical form. Given, $32\mathrm{\%}$ of a certain number is 80. Here, it represents multiplication in math. Percent symbol means per cent or per hundred. This means that it is a term given by ${\displaystyle \frac{1}{100}}.$ Therefore, $32\mathrm{\%}={\displaystyle \frac{32}{100}}.$ We also know that the certain number is x. Using all this, we convert the above statement to a mathematical form.
$\Rightarrow {\displaystyle \frac{32}{100}}\times x=80$
Now, let us multiply both sides of the equation by 100.
$\Rightarrow 32\times x=80\times 100$
Now we multiply the right-hand side terms and write the number as,
$\Rightarrow 32\times x=8000$
Next, we divide both sides by 32.
$\Rightarrow x={\displaystyle \frac{8000}{32}}$
We know that 32 times 250 gives us 8000. This is done by cancelling the common factor of 32.
$\Rightarrow x=250$
Hence, the number is 250, such that $32\mathrm{\%}$ of 250 is 80.

Note: We need to know the concept of percent in order to solve such sums. We generally assume any unknown value in a question to be x. We can even choose any other letter or a variable. Care must be taken while solving the sum, while converting the given statement to a mathematical form. It is given that $32\mathrm{\%}$ of a number is 80 and not $32\mathrm{\%}$ of 80. Students tend to make a mistake in this so they need to be more careful while solving this.