Question

\[8\] is what percent of \[40?\]

Answer 1

Hint: In mathematics, percentage is a number or ratio that can be expressed as a fraction of \[100\].
To solve this question, we will let that \[8\] is \[x\] percentage of \[40\]. Then we will set an equation with this information and solve the equation to get the value of \[x\].

Complete step by step answer:
In the question we are asked to find what percent of \[40\] is \[8\]. So, we let \[x\] percent of \[40\] is \[8\].
So, we have;
\[x\% {\text{ of 40 = 8}}\]
Mathematically,
\[ \Rightarrow \dfrac{x}{{100}} \times 40 = 8\]
Now we will shift \[40,100\], to the RHS, we get;
\[ \Rightarrow x = \dfrac{{8 \times 100}}{{40}}\]
On solving we get;
\[ \Rightarrow x = \dfrac{{100}}{5}\]
Further on dividing we get;
\[ \Rightarrow x = 20\]
Hence, \[8\] is \[20\% \] of \[40\].

Additional details:
\[100\% \] of a number is the number itself.
We can also prove this result.
Suppose the number is \[x\].
Now, according to the formula we have;
\[100\% {\text{ of }}x = x \times \dfrac{{100}}{{100}}\]
On simplification we get:
\[ \Rightarrow 100\% {\text{ of }}x = x\]

Note:
The capability of representing any number or quantity on the basis of \[100\] is called percentage.
For example:
\[x\% = \dfrac{x}{{100}}\]
One point to note here is that, while calculating the percentage, the same units should be used. For example; if the question is like ten paisa is what percent of one rupee. So here we see that paisa and rupee are not the same units. So, we will convert either paise to rupee or rupee to paisa and then find the percentage.
Another point to note is that we can also solve things like suppose someone has got \[8\] marks out of \[40\] and we need to calculate the percentage. So, we can calculate as;
\[ = \dfrac{8}{{40}} \times 100\]