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How to Find Percentage of a Number?

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  • Last Updated : 07 Feb, 2022

A percentage is defined as the proportion of a certain thing. It can be the proportion of a number, proportion of liquids, proportion of items, etc. In mathematics, it is represented as a fraction of a hundred or 1/100. The method of using percentage is very common in every field, such as tax percentage, discount percentage on products, percentage of humidity in the air, and percentage composition of substances in mixtures. Thus, knowledge of calculating percentages helps in mathematics and also helps in solving the percentage value of products and many items in day-to-day life.  

Percentage of a Number

The percentage symbol is ‘%.’ It is also used to represent the average percentage of students in a class, data representation, profit percentage, loss percentage, interest, etc.

The range of percentages lies between 0 and 100. It can be 0.5%, 10%, 40%, 70%, 80%, 92%, 99%, and maximum up to 100%. 100% of a number is the same as the number.

For example,

100 percentages of 10 means

100% of 10

100 × 1/100 × 10

= 10

Hence proved, that 100% of a number is the same as the number itself.  

Note: Percentage equal to the number divided by 100

For example,

20%

20 % = 20/100

Thus, 20% is represented as a fraction of 20/100.

Suppose the percentage of a number N is to be calculated, it will be represented as:

P% of N

P/100 × N

Or

(P × N)/100

Where,

P is the percent  

N is the number

% is equal to 1/100

For example,

10% of 20

It is equal to 2

Thus, to find the percentage value of a number, we need to simply multiply the number with the percentage value and divide it by 100.  

Steps to find the percentage of a number

Let’s consider an example to find 10% of 500.

Step 1: Substitute 1/100 instead of the % symbol

10 × 1/100 of 500

Step 2: Substitute multiply symbol (×) instead of ‘of’

10 × 1/100 × 500

Step 3: Solve the above-formed equation

10 × 500/100

5000/100

= 50

Thus, 10% of 500 is 50.

Increase in the percentage of a number

Let’s consider an example.

10% increase of the number 50

The formula is given by:

Number + percentage of the same number

50 + 10% of 50

= 50 + 10 × 1/100× 50

= 50 + 500/100

= 50 + 5

= 55

Steps to find the increase in the percentage of a number

Example:  Find15% increase of 200.

Step 1: Form an equation using the formula

The formula is given by:

Number + percentage of the same number

= 200 + 15% of 200

Step 2: Substitute 1/100 instead of the % symbol

15× 1/100 of 200

Step 3: Substitute multiply symbol (×) instead of ‘of’

15 × 1/100 × 200

Step 4: Solve the above-formed equation

15× 200/100

3000/100

= 30

Step 4: Add the number

200 + 30

= 230

Thus, a 15% increase of 200 is 230.

Direct formula

(100 + increase percentage value)% × number

(100 + 15)% × 200

(115)% × 200

115 × 1/100 × 200

= 230

Decrease in percentage of a number

Let’s consider an example.

10% decrease of the number 50

The formula is given by:

Number – the percentage of the same number

50 – 10% of 50

= 50 – 10 × 1/100 × 50

= 50 – 500/100

= 50 – 5

= 45

Steps to find the increase in the percentage of a number

Example: Find a 45% decrease of 300.

Step 1: Form an equation using the formula

The formula is given by:

Number – the percentage of the same number

= 300 – 45% of 300

Step 2: Substitute 1/100 instead of the % symbol

45× 1/100 of 300

Step 3: Substitute multiply symbol (×) instead of ‘of’

45 × 1/100 × 300

Step 4: Solve the above-formed equation

45× 300/100

135000/100

= 135

Step 5: Subtract the number

300 – 135

= 165

Thus, a 45% decrease of 300 is 165.

Direct formula

(100 – decrease percentage value)% × number

(100 – 45)% × 300

(55)% × 300

55 ×1/100 × 300

= 165

Sample Problems

Question 1: Find 20% of 80?

Solution:  

20 × 1/100 × 80

= (20 × 80)/100

= 1600/100

16

Thus, 20% of 80 equals to 16.  

Question 2: Find 50% of 200?

Solution:  

50 × 1/100 × 200

= (50 × 200)/100

= 10000/100

= 100

Or

50/100 × 200

= (1/2) × 200

= 0.5 × 200

= 100

Thus, 50% of 200 equals to 100.

Question 3: Find 10% of 50?

Solution:  

10 × 1/100 × 50

= (10 × 50)/100

= 500/100

= 5

Thus, 10% of 50 equals to 5.

Question 4: Find 0.5% of 5?

Solution:  

0.5 × 1/100 × 5

= (0.5 × 5)/100

= 2.5/100

= 0.025

Thus, 0.5% of 5 equals to 0.025.

Question 5: Find 80% of 600?

Solution:  

80 × 1/100 × 600

= (80 × 600)/100

= 48000/100

= 480

Thus, 80% of 600 equals to 480.

Question 6: Find a 22% increase of 50.

Solution

The formula to find the percentage increase of a number is given by:

(100 + increase percentage value)% × number

(100 + 22)% × 50

(122)% × 50

122 × 1/100 × 50

= 61

Question 7: Find 70% decrease of 150.

Solution

The formula to find the percentage decrease of a number is given by:

(100 – decrease percentage value)% × number

(100 – 70)% × 150

(30)% × 150

30 × 1/100 × 150

= 45

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