Percentage

Are you a student who is struggling to find the percentage of your marks? If yes, then you have come to the right place as this article is all about percentage and how to find it. In this article, you can also learn about the increase and decrease formula for the percentage change. 

The Concept of percentage is used to measure the proportion of value in terms of the original value. Percentages are widely used in business for computing the profit or loss percentage of a business. Also, it is used in schools and colleges to represent the marks obtained by the students. Marks of the students can be estimated using a percentage formula. Percentages are generally defined as a ratio of any value to the whole value multiplied by 100. The symbol used to represent the percentage is %.

Percentage Meaning

Percentage means a number or a ratio represented in the form of fractions of 100. It is represented using the percentage sign ‘%’. The abbreviations used to represent the percentage are ‘pct’ or ‘pc’. In other words, the percentage is defined as how much of one quantity is made by another quantity and it is evaluated in terms of 100.

The percentage has no dimensions. It means they are dimensionless numbers. If we say 60% of a number, then it implies 60 percent of its whole. It can even be expressed in both decimal and fraction forms such as 0.56% or 0.87%. In the examination, marks scored by students in any subject are calculated concerning the percentage. For example-Pooja scored 78% of marks in his exam. So, this percentage is calculated in terms of total marks obtained by Pooja in all the subjects to the total maximum marks and then the result will be multiplied by 100.

Percentage Definition

The Percentage is a relative value that indicates the hundredth parts of any quantity. One percent (1%) represents the one hundredth, 2 percent (2%) represents two hundredths, 100% represents the whole, 200% twice the given quantity and so on…

For example - 1 percent of 1000 mangoes is equal to 1/100 of 1000 or 10 mangoes.

Percentage in Math

Each percentage problem has three possible unknown or variables. These unknown or variables are

•     The per cent

•     The part

•     The base

To solve the percentage problem, you need to recognize these unknown variables

For Example

1. 70% of 40 is 28

Here,

70 is the percent

40 is the base

28 is the part

2. 6 is 50% of 12

Here, 

6 is the part

50 is the percent

12 is the base

Basic Percentage Trick

The following trick can be used to calculate the percentage: X % of y= y % of x

Example: Prove 10% of 50 is equal to 50% of 10

Solution : 10% of 50 = 5

50% of 10 = 5

Hence, they are equal i.e. x % of y = y % of x holds salary original fractions.

Percentage Formula

We should know the percentage formulas to calculate the percentages. The basic formula used to calculate the percentage is equal to the ratio of actual value to the total value and multiply it by 100. The formula of the percentages expressed as

Percentage % = \[\frac{\text{(Actual value)}}{\text{Total value}}* 100\]

Percentage Formula in Case of a Fraction

(Numerator/Denominator)∗100

Percentage Change Formula

\[\text{Percentage change} = \frac{\text{(New value - Original value)}}{\text{Original value}} *100\]

Percentage Increases Formula

When the new value is greater than the original value. The percentage change in the value signifies the percentage increase in the original number such that,

Percentage Increase (% Increase) = \[\frac{\text{Increase in value}}{\text{original value}} \times 100 \]

Here, Increase in value = New value – original value.

Percentage Decreases Formula

When the new value is lesser than the original value. The percentage change in the value signifies the percentage decrease in the original number such that,

Percentage Decrease (% Decrease) =\[\frac{\text{Decrease in value}}{\text{original value}} \times 100 \]

Here, Decrease in value = Original value - New value

How to Calculate the Percentage of a Number

Step-by-Step Percentage Change Calculation:

Calculate the difference (increase) between the two figures you're comparing to arrive at a percentage increase:

Increase = Original Number - New Number

Then multiply the result by 100 by dividing the increase by the original number:

Increase by 100 per cent of the original number.

If the response is a negative figure, the percentage change will be negative.

Calculate the difference (reduction) between the two numbers you're comparing.

Original Number - New Number = Decrease

Then multiply the result by 100 by dividing the decrease by the original number.

Decrease Original Number by 100 per cent = Decrease Original Number by 100 per cent

This is a percentage increase if the answer is a negative number

If you want to compute the % rise or reduction of numerous integers, you should use the percentage increase formula. When the percentage rises, it is indicated by a positive value, but when the percentage reduces, is shown by a negative figure.  

We need to use some formula to calculate the percentage of a number. The formula which is to be used is:

P% of a number = X

Where x is the required percentage

If the percentage sign is removed, then the above formula is expressed as

\[ \frac{P}{100} \times \] Number =  X

For example:

Calculate 20 % * of 800

Let 20 % * of 800 = X

\[\frac{20}{100} \times 800 = X \]

X = 160

Solved Example

1. In a class of 70 students, 60% are boys. Find the total number of girls and boys in the class?

Solution: Total number of boys in class = 60% of 70

\[= \frac{60}{100} \times 70 \]

= \[0.6 \times  70\]

= 42

Total number of girls in the class = Total number of students in the class - Number of boys

= 70 - 42

= 28

Hence, the numbers of boys in the class are 42 and the number of girls in the class is 28.

2. What is 70% of 800?

Solution: 70% of 800

\[= \frac{70}{100} \times 800\]

\[= \frac{70 \times 800} {100} \]

\[X = \frac{56000}{100}\]

= 560

3. Ķrita scored 92% marks in examinations. If these are 460 marks, calculate the maximum marks.

Solution: Let maximum marks be X

Then 92% of X= 460

\[\frac{92}{100} \times X = 460\]

\[X = \frac{460 \times 100} {92} \]

\[X = \frac{46000}{92}\]

X = 500

Hence, the maximum marks in the examination are 500.

4.  The annual salary of Karan was increased from Rs. 18, 00,000, to Rs. 22, 00,000. Calculate the percentage increase.

Solution:

Original salary of Karan = Rs. 18, 00,000

Increased salary of Karan = Rs. 22, 00,000

Increase in Salary = Rs. 22,00,000 - 18, 00,000= Rs. 4, 00,000

Hence, the percentage increase in salary = \[\frac{\text{Increase in salary fractions}}{\text{original salary}} \times 100\]

\[\frac{4,00,000}{18,00,000} \times 100 \] = 22.2%

Fun Facts

• The concept of percentage was not developed by any person. The percentage concept originated throughout History. In Ancient Rome, Mathematical calculations were expressed in fractions of 100. This concept later originated in Percentage.

Quiz Time

1. Half percentage is written as a decimal is

1.     0.2

2.     0.02

3.     0.005

4.     0.05

2. 1.14 expressed as a percent of 1.19 is

1. 6

2. 10

3. 60

4. 90

3. What is 30% of 80?

1.     20

2.     24

3.     56

4.     78

What is Meant by the Percentage Change? 

The percentage term can be described as a fundamental Mathematical term that tells us how much a quantity has changed over time or what is its degree of change. The concept of percentage change can be used in finance for a lot of things, but the most common use of this is that it illustrates the price movement of a security. 

Percentage Change in Context

Any quantity that you measure over time can be expressed as a percentage change. Assume you're keeping track of a security's advertised price. If the price has risen, multiply the result by 100 using the formula (New Price - Old Price) / Old Price. If the price dropped, multiply the result by 100 using the method (Old Price - New Price) / Old Price.

This method is used to compare the values of different currencies, as well as to follow the prices of individual stocks and huge market indexes. The prices of various assets at different points in time, as well as the percentage changes over time, will typically be included in balance sheets with comparative financial statements.

Important Points to Remember

• Percentage change denotes a degree of change over time and is used in finance for a variety of purposes, the most common of which is to show a security's price change.

• Any number that may be measured over time can be expressed as a percentage change.