 # Percent Difference Formula

Percent difference formula is obtained by dividing the absolute value of change by the average of the values and then multiplying it with 100. To recall, a “per-cent” means a part per 100. The topic is of extreme importance and forms a major part of questions in most competitive exams. Among the different types of percentage questions, one of the most common question types involves the percentage difference formula. In this article, the percent difference formula is explained with solved example questions.

## Formula to Calculate Percentage Difference

As stated, the percentage difference is be calculated by dividing the absolute value of the change by the average of the values and multiplying by 100.

∴

$$\begin{array}{l}\large Percent\: Difference\, Formula\,\left ( \%D \right ) = \frac{|n_{1}-n_{2}|}{\frac{n_{1}+n_{2}}{2}}\times 100\end{array}$$

Here, n1and nare the two different values.

With this formula, it is possible to determine the difference in percentage between any two values. It should be noted that as the absolute value is taken for the change (or difference) in values, the order of the numbers does not matter.

Important Note:

This formula should not be confused with the percentage increase or decrease which is- [(Difference) ÷ Original Number] × 100. To calculate percentage error, the difference between the approximate and exact value should be divided by the exact value and then multiplied by 100.

### Example Questions Using the Percentage Difference Formula

Some problems related to the percent difference formula are given below for a better understanding of this concept.

Example 1:

A shopkeeper sells mangoes for Rs. 40 per kilos. Another shopkeeper sells the same mangoes for Rs. 60 per kilos. Find out how much is the percentage difference between the selling price of the shopkeepers.

Solution:

According to the formula, first, the difference between their selling price has to be calculated which is = Rs. 20

Now, 20 needs to be divided by the average of the selling prices and multiply by 100.

Average = (40 + 60)/2 = 50.

So, %D = (20 / 50) × 100 = 40%.

Example 2:

Find the percentage difference between the population of two cities having 12 million and 13 million population respectively.

Solution:

Putting the values of 1.2 million and 1.3 million in the above formula, the percent difference can be calculated.

Here, difference = |12,00,000 – 13,00,000| = 1,00,000.

Average = (12,00,000 + 13,00,000) = 12,50,000

%D = (1,00,000/ 12, 50, 000) × 100

So, percent difference = 8%.

Example 3:

In a cricket match, one team scored 220 runs while the other team managed to score 150 runs. What is the percentage difference between their runs?

Solution:

$$\begin{array}{l}\%D = \frac{|220-150|}{\frac{220+150}{2}}\times 100\end{array}$$

=(70/185) × 100

= 37.838%

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