Question

9 is 25% of a number. Find the number.

Answer 1

Hint: We will suppose the number to be \[x\]. Now, we need to find this number \[x\] such that \[9\] is given to be \[25\% \] of the number. We will get an equation in terms of \[x\]and then we can solve the equation obtained for \[x\]. We know,
\[1\% \]of \[x\]= \[\dfrac{1}{{100}}\] of \[x\]
Using the above formula,
We can obtain \[25\% \]of \[x\]and then equate the obtained answer to 9, as we are given that \[25\% \]of the number is equal to \[9\].

Complete step-by-step solution:
Let us suppose,
The required number is \[x\].
We now need to find \[25\% \] of the required number.
So,
\[25\% \] of the required number \[ = 25\% \] of \[x\]
 \[ = \dfrac{{25}}{{100}}\]of \[x\]
 \[ = \dfrac{{25}}{{100}} \times x\]
\[ = \dfrac{1}{4} \times x\]
 \[ = \dfrac{x}{4}\]
Therefore, we get \[25\% \] of the required number \[ = \dfrac{x}{4}\] ----(1)
Also, we are given,
\[25\% \] of the required number \[ = 9\] ----(2)
Now, equating (1) and (2), we get,
\[\dfrac{x}{4} = 9\]
\[\Rightarrow x = 9 \times 4\] (cross multiplying)
 \[\Rightarrow x = 36\]
Hence, the required number is \[36\].
Which means,
\[25\% \] of \[36\] \[ = 9\]
So,
\[9\] is \[25\% \] of \[36\].

Note: We need to read the question carefully first and then interpret what we are asked for. Usually, in this type of questions, we are not clear with what we are supposed to find out. Also, we need to be very careful while framing the equation. If we frame the wrong equation, we will definitely get the wrong answer. We need to keep in mind that when we remove percentages, we divide the number by 100.