Percentage Increase Formula

In basic mathematics many times we have to compute the percentage value of some term. It is needed to give the referential value in the form of ratio involving the 100 as a standard base. For example, showing marks a student in his final result, we need to compute the percentage marks. As we can see that the percentage value is very important to provide a comparative study of some data.  In this article, the student will learn the concept of percentage with percentage increase formula and relevant examples. Let us begin learning!

Percentage Increase Formula

What is Percentage?

Percent basically means “for every 100” or “out of 100.” The % symbol is used in mathematics for percentage as a quick way to write a fraction with a denominator of 100.  As an example, instead of saying that “it rained 14 days out of every 100,” we can say “it rained 14% of the time.”

If we divide our pizza into 100 little pieces, then each piece will represent 1 percent of the pizza. This is another way to consider percentages. We can take a whole of something and divide it into 100 little pieces and then figure out the portion. If we want a quarter of the pizza, we will see that it will require 25 little pieces out of 100, or 25 percent of the pizza.

Thus data representation using percentage is very useful and informative. It is giving a solid base in data analysis and decision making. We can guide our students to take the opportunity to explain the importance and relevance of percentage calculations. Some real life-related terms are a pay rise, allowance rise, interest rate, discounts on sale items, etc.

The Formula for Calculating Percentages

The formulas for calculating percentages value is used with fraction value.

So, to convert the fraction to a percentage value the formula is given as:

Percentage = \(\frac{Concerned value}{ total value }\) × 100

Also, to find a concern value we have to multiply percentage value with total value and then divide it by 100 and hence reduce the fraction if required. The formula is given as:

Concerned value =  \(\frac{Total value × Percentage }{ 100}\)

For example, if 12 people out of a total of 25 were female. Then find the percentage of females among them.

Here percentage will be \(\frac {12} {25}\) × 100

i.e. the percentage female is 48%

The Formula for Percentage Increase

The percentage increase formula is the ratio of the value increased to the original value and further multiplied by 100. It is expressed in terms of percentage. If there is an increase in the value of any value, then there is an increase in percentage.

Thus to calculate the percentage increase we will follow two steps:

Step-1: Work out for the difference i.e. increase between the two numbers we are comparing.

i.e. Increase = New Number – Original Number

Step-2:  Divide the increase by the original number and multiply the answer by 100.

i.e. % increase = \(\frac{Increase} {Original\; Number}\) × 100

Solved Examples

Q.1: What is the percentage change in the rent of the house if on the month of January it was Rs. 10,000 and in the month of March it is Rs. 15,000?

Solution: We can see here that there is an increase in the value of rent.  Therefore the percentage increase will be given as:

So, Increase in percentage = \(\frac {Increased Value} { Original Value}\) × 100

Thus increased value = 15000 – 10000 = 5000

Original Value = 10000

\(\frac {5000} { 10000}\)

= 33.33 %

Hence, there is a 33.33 %  net increase in the value of rent.