Clear Concept of Percentage

In this article, we will cover all basic concepts related to percentage, which is a function of mathematics. By covering each concept in brief, this article will help you perform great in quantitative aptitude and data interpretation sections of many competitive exams.  

A number or a ratio that can be expressed as a fraction of 100 is defined as a percentage in the field of mathematics. In order to find the percentage of a particular number, we simply need to divide it by the whole and then multiply it by 100. The official symbol of percentage is %.  

Example of some percentage are

10 % of 200 = 10/200 X 100 = 5 

20% of 100 = 20/100 X 100 = 20 

Percentages can also be expressed using the fractional form or decimal form. The percentage is known to be a dimensionless number. Examples of decimal form percentages are 0.25%, 0.5%, etc.  

Percentage formula 

In order to determine the value of the percentage, we simply need to divide the given value by the whole value and then multiply it by 100. So, the formula of percentage becomes: 

Let’s say that Y is a given percentage of another number, Z. 

So, Y% of Z = Y/Z X 100 % 

Let’s take an example: 

Question: what is 20% of 400? 

Let’s assume 20% of 400 is X 

20/100 X 400 = x 

= 80 is 20% of 400.  

Percentage change

2 types of changes that happen to a quantity when modifications are introduced are: 

• Change in percentage 

• Change in actual value 

The percentage of change can be calculated by:  

Actual change/ original value X 100 

Percentage increase and decrease

Percentage increase: it can be calculated by subtracting the original number from the new and changed number and then dividing it by the original number X 100.  

Increase % = [new number – original number] / original number X 100 

Percentage decrease: it can be calculated by subtracting the new and changed number from the original number, further dividing it by the original number, and then multiplying it by 100.  

Decrease % = [original number – new number] / original number X 100 

The relationship between percentage and ratio 

If the denominator of the percentage remains constant, we can derive a direct relationship between the numerator of the ratio and the ratio itself. When the numerator is increased to a certain percentage, then the ratio itself is raised to a certain percentage.  

Some percentage questions as examples

Question: What number would be 30% less than 120? 

Answer:  Applying percentage formula, we get: 

The number we are looking for is 60% of 120 

Putting them into the equation, we have  

60 X 120 / 100 = 72 is the required number 

Question: A company owner had a lot of cars to sell. They sell 20 % of the cars and still have 200 cars left. How many cars did the company owner have originally? 

Answer: We can suppose that the company owner had Z number of cars originally. 

According to the question, 

[100 – 20] % of Z = 200 

Then applying the percentage formula:  

80 / 100 Z = 200 

Z = 200 X 100 / 80 

= 250 cars, the owner of the company had 250 cars originally 

There is no need to memorize the formulas related to percentages. In order to master problems where they ask about how to find percentages, you need practice and effort. Thorough knowledge of the concept of percentages can help you in sections such as profit loss analysis, compound interest, and other interest problems. In order to efficiently learn any concept of math, one needs to have a lot of practice. Practice is everything in mathematics so keep practicing problems on how to find percentages.   

Conclusion 

We covered the basic definition of various concepts linked to percentages and looked at some problems and how to solve them. We also covered the various mathematical formulas linked to finding percentages. These tips and formulas would help you solve percentage problems in various competitive exams.