Question

Find the number if $ 28\% $ of a number is $ 84 $ .

Answer 1

Hint: Here we will use percent formula i.e. $ p\% \times n = \dfrac{p}{{100}} \times n = z $ to find the result. The value of $ p $ and $ z $ is to be substituted in the given formula and the value of the number $ n $ can be calculated.
According to the definition of percentage, one percent is one hundredth of a whole.

Complete step-by-step answer:
The given information
  $ 28 $ percent of a certain number yields $ 84 $ .
We are required to determine the number.
Let the number be $ n $
The formula to be used here is
  $ p\% \times n = \dfrac{p}{{100}} \times n = z $
Therefore,
 $ \dfrac{p}{{100}} \times n = z \cdots \left( 1 \right) $
Here,
  $ p = 28 $ , $ z = 84 $ as given in the question.
Substituting in equation (i), we get
 $ \Rightarrow \dfrac{{28}}{{100}} \times n = 84 \cdots \left( 2 \right) $
Solving equation (2) for we get,
  $
  n = \dfrac{{84 \times 100}}{{28}} \\
  n = 300 \;
   $
Thus, the required number is $ 300 $ as $ 28\% $ of $ 300 $ is $ 84 $ .
So, the correct answer is “ $300$ ”.

Note: The basics and knowledge of percentage is important in solving the problems dealing with percentage. In mathematics the percentage is a number or the ratio that is represented as a fraction of 100. For instance,
  $ a\% $ can be written in the fraction form as $ \dfrac{a}{{100}} $ .In the same way , $ 35\% $ can be written as $ \dfrac{{35}}{{100}} $ .
The value of $ 100\% $ of a quantity is 1 means it represents an entire quantity and the value of $ 50\% $ is $ \dfrac{1}{2} $ or it represents half the quantity.