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The percentage difference formula is derived by dividing the absolute value by the average value which is then multiplied by 100. The percentage is considered to be the part of 100. The topic is considered very important for competitive exams as it consists of the most common questions in the exam.
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Also Read: How to Calculate Percentage
What do you mean by Percentage Difference Formula?
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The percentage difference formula is mainly used for calculating the difference in two numbers which are expressed in percentage. One can easily calculate the percentage by considering the average value as a reference value in order to be clear from confusion during choosing the values at the denominator.
Also read: Isosceles Triangle Theorems
Percentage Difference Formula Calculation
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Let there be two values a and b
To calculate the percentage difference,
So, Percentage Difference = 
|a-b| = the absolute difference value
(a+b)/2 = the average value
The order of numbers will not matter here, the difference in percentage can be found by taking any two values.
Also Read: Ratio to Percentage
Things to Remember
- The difference in two values can be calculated by finding out the average multiplied by 100.
- The formula is used to find out the percentage of any quantity
- The order of the values does not matter for calculating the percentage difference.
- Percentage means part per 100.
Also Read: Relations and Functions
Sample Questions
Ques. If two given values are 30 and 15. Find the percentage difference in between them. (2 Marks)
Solution: a= 30; b=15
So, a-b = 30 -15 = 15
a-b = 15
(a+b) / 2 = 30+15/2 = 45/2 = 22.5
So, using the percentage difference formula = [ | a-b | / ((a+b) / 2) ] x 100
= [15 / 22.5] x 100
= 0.666 x 100
= 66.7 %
Ques. A tower of 30 ft. is increased to 50 ft. Find the difference using the percentage difference formula. (2 Marks)
Solution: Given, initial height, a =30ft.
The final height of the tower, b = 50ft.
The percentage difference = [ 50-30 / ((50+30) / 2) ] x 100
= [20 / 40] x100
= 50%
So, the percentage difference between the initial and final height of the tower is 50%.
Ques. John works 180hrs per month and Susan works 240hrs per month. What will be the percentage difference in between their working hours? (2 Marks)
Solution: Given, initial value, a = 180
Final value, b = 240
Using the percentage formula, we get
Percentage difference = [ |a-b| / ((a+b) / 2) ] x 100
= [ |180-240| / ((180+240) / 2) ] x 100
= [ 60 / 210] x 100
= 600/21
=200/7
= 28.57% ≈ 29%
So, the percentage difference between the working hours of John and Susan is 29 %.
Ques. Calculate the percentage difference between 35 and 53. (2 Marks)
Solution: The two values given are- a= 35 and b = 53
Using the percentage difference formula, we get,
= [ |a-b| /((a+b) / 2) ] x 100
= [ |35 - 53| / ((35+53) / 2) ] x 100
= [18 / 44] x 100
= 40.9%
= 41%
So, the percentage difference is 41%.
Ques. What will be the percentage difference of the population of two cities having 12 million and 13 million respectively? (2 Marks)
Solution: the difference between two given values is –
12,00,000 – 13,00,000 = 1, 00,000
Average = (12,00,000 + 13,00,000) / 2
= 12, 50,000
Percentage difference of the population is
= (1, 00,000 / 12, 50, 000) x 100
= 8%
Ques. What is the percentage difference between the two teams who scored 220 runs and 150 runs respectively? (2 Marks)
Solution: Using the percentage difference formula, we get,
= [ |a-b| / ((a+b) / 2) ] x 100
= [ 220-150 / ((220+150) / 2) ] x 100
= (70 / 185) x 100
= 37.838%
Ques. Calculate the percentage difference between the two values 56 and 30. (2 Marks)
Solution: Percentage difference formula
= [ |a-b| / ((a+b) / 2) ] x 100
= [ 56-30 / ((56+30) / 2) ] x 100
= 26/43 x 100
= 0.60451 x 100
= 60.4651%
Ques. Calculate the percentage difference between the two measurements of 21ml and 22ml. (2 Marks)
Solution: Percentage difference formula
= [ |a-b| / ((a+b) / 2) ] x 100
= [ |21-22| / ((21+22) / 2) ] x 100
= 4.65 %
Ques. Calculate the percentage difference between 990 and 1000. (2 Marks)
Solution: Let the two values be a = 990 and b= 1000.
Using Percentage difference = [ |a-b| / ((a+b) / 2) ] x 100
= [ |990-1000| / ((990+1000) / 2) ] x 100
= 10/995 x 100
= 1.005%
Ques. A shopkeeper sells apples for 40 rupees per kilo and oranges for 80 rupees per kilo. How much percentage difference is there between the two prices? (2 Marks)
Solution: If we find out the average = (40+80) / 2
= 60
If we find the percentage difference = (40/60) x 100
= 0.666667 x 100
= 66.6667%
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