Question

The \[20\% \] of \[20\] is equal to \[50\% \] of what number?

Answer 1

Hint: To find \[20\% \] of \[20\] is equal to \[50\% \] of what number, we have to first find what is \[20\% \] of \[20\]. A percentage is a number expressed as a fraction of \[100\% \]. We will assume that the unknown number is \[x\]. Then we will find \[50\% \] of \[x\] then we will equate it to the value we got by calculating \[20\% \] of to find the value of \[x\].

Complete step-by-step answer:
As we know, if there is a number say \[a\] and we have asked to find \[m\% \] of \[a\]. Then it is equal to \[\dfrac{m}{{100}} \times a\].
In the same way, \[20\% \] of \[20\] will be the following:
\[ \Rightarrow \dfrac{{20}}{{100}} \times 20 = 4\]
Let us assume that the unknown number is \[x\].
Now, we have to find \[50\% \] of \[x\] in the same way we calculated \[20\% \] of \[20\].
It will be the following:
\[ \Rightarrow \dfrac{{50}}{{100}} \times x = \dfrac{{50x}}{{100}}\]
Now, we will equate \[20\% \] of \[20\] and \[50\% \] of \[x\] as it is already mentioned in the question that they are equal.
We have \[20\% \] of \[20\] as \[4\] and \[50\% \] of \[x\] as \[\dfrac{{50x}}{{100}}\].
On equating \[50\% \] of \[x\] and \[20\% \] of \[20\], we get
\[ \Rightarrow \dfrac{{50x}}{{100}} = 4\]
On simplifying the left hand side of the above equation we get
\[ \Rightarrow \dfrac{x}{2} = 4\]
Multiplying \[2\] on both the sides of the equation, we get
\[ \Rightarrow x = 8\]
Hence, we get the unknown number \[x\] as \[8\].
Therefore, \[20\% \] of \[20\] is equal to \[50\% \] of \[8\].
So, the correct answer is “ \[8\]”.

Note: A percentage is a number or ratio expressed as a fraction of \[100\]. It is often denoted using the percent sign i.e., \['\% '\] . Whenever we face such type of problem of finding the percentage of a given number then we need to know that \[p\] percent of \[q\] can be written as \[\dfrac{p}{{100}} \times q\].