Question

If $12\dfrac{1}{2}\%$ of a certain number is $32$. What is $40\%$ of that number?

Answer 1

Hint: To solve this type of question we need to know the concept of percentage. The question requires conversion of percentage into fraction and vice-versa. We will have to use the concept of reciprocal. We will consider an unknown variable, and will then find the $40\%$ of the value of the known.

Complete step by step answer:
The question asks us to find $40\%$ of the unknown number, if for $12\dfrac{1}{2}\%$ of a certain number is $32$. The first step will be consider the unknown number$x$, mathematically it would be written as
$\Rightarrow 12\dfrac{1}{2}\%\times x=32$
Now the percentage will be changed to fraction. So it will be divided by $100$ to change the percentage into fraction, on doing this we get:
$\Rightarrow 12\dfrac{1}{2}\%=\dfrac{25}{2\times 100}$
$\Rightarrow 12\dfrac{1}{2}\%=\dfrac{1}{8}$
So on substituting the percentage with the fraction and cross multiplying to find the value of$x$ the equation becomes:
$\Rightarrow \dfrac{1}{8}\times x=32$
On cross multiplying the we get:
$\Rightarrow x=32\times 8$
$\Rightarrow x=256$
So the unknown number we got is $256$.
The second step is to find $40\%$ of the number. For that we will change the percentage into fraction and then find it. On doing so we get:
$\Rightarrow \dfrac{40}{100}\times 256$
On changing the fraction into the lowest term we get:
$\Rightarrow \dfrac{2}{5}\times 256$
For further calculation we will multiply the numerators and the divide it to denominator:
$\Rightarrow \dfrac{512}{5}$
On calculating we get:
$\Rightarrow 102.4$
$\therefore $ $40\%$ of that number is $102.4$.

Note: Let us check whether the answer we got is correct or not. For this we would perform the particular task, Lets check what will be $12\dfrac{1}{2}\%$ of $256$, which mathematically could be written as
$\Rightarrow 12\dfrac{1}{2}\%\times 256$
On converting the percentage to fraction we get
$\Rightarrow \dfrac{25}{2\times 100}\times 256$
$\Rightarrow \dfrac{1}{8}\times 256$
On multiplying the numerator terms together
$\Rightarrow \dfrac{256}{8}$
On calculating we got $32$. This shows that the number $32$, which is given in the question is $12\dfrac{1}{2}\%$ of $256$. This means the answer we got is correct.
This is the way we can check whether the solution is correct or not.