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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- Percentage
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- Maths Trick to Find Percentage
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