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 – How to Find Percentage of a Number?

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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