Question

\[40\% \] of what number is \[30\]?

Answer 1

Hint:In mathematics, percentage is a number or ratio that can be expressed as a fraction of a hundred. To solve this question, we will consider that \[40\% \] of a number \[x\] is equal to \[30\]. Then with this information we will set up a mathematical equation. Further we will solve the equation to obtain the value of \[x\].

Complete step by step answer:
Let,
\[40\% \] of a number \[x\] is equal to \[30\].
Then we can represent it mathematically as;
\[\dfrac{{40}}{{100}} \times x = 30\]
Now we will shift the fraction from the LHS to RHS. So, we get;
\[ \Rightarrow x = 30 \times \dfrac{{100}}{{40}}\]
On calculating we get;
\[ \Rightarrow x = 75\]
So, \[40\% \] of \[75\] is equal to \[30\].

Additional information:
\[100\% \] 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 suppose in some other question we have been given that \[50\% \] of a number is equal to \[30\], and asked to find that number. Then in that case we can simply find the number by multiplying \[30\] by \[2\]. This is because \[50\% \] of a number is the same as dividing the number by \[2\].