In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign “%”. Did you know that **percentage** plays a very important role in our day-to-day life? If not then I will tell you how.

Understanding the financial aspects of everyday life is important. Much of what we buy in the shops has a 10% Goods and Services Tax (GST) included in the price.

## Real-Life Examples

- The percentage is used for the comparative study of any topic. The topic may be related to Health, Geography, etc.
- With the help of percentages, the large data can be analyzed in less time with great accuracy.
- In a time of the election, percentage plays a very important role.
- The largest use of percentage is in the sector of business like profit or loss and many other things are related to percentage too.
- It is useful for the government to make some decisions like reservations, different schemes for many people.
- It is a very effective medium to represent numerical data most simply.
- It also gives information about the increase in civilization, urbanization, and the increase in production of any industry.

## Problems on Percentages

**Example 1:** 80 is what percent of 64?

- 75%
- 85%
- 120%
- 125%

**Explanation**: Let x percent of 64 be 80

64 * x/100 = 80 => x = (80*100)/64 => x = 125

Hence, 80 is 125% of 64

**Answer: **D.125%

**Example 2:** If A got 80 marks and B got 60 marks, then what percent of A’s mark is B’s mark?

- 60%
- 65%
- 75%
- 80%

**Explanation**: A’s marks = 80; B’s marks = 60.

Let x% of A = B => x/100 * 80 = 60

=> x = (60 * 100)/80 = 75

B’s marks is 75% of A’s marks

**Answer-)** C. 75%

## Percentage in Math

In every percentage problem, there are three possible unknowns or variables

- Percentage
- Part
- Base

To solve any percentage problem, you need to identify these variables.

## Examples

**Example 1:** 70% of 30 is 21

70 is the percentage.

30 is the base.

21 is the part.

**Example 2:** 6 is 50% of 12

6 is the part.

50 is the percent.

12 is the base.

## Percentage Tricks

Did you know that there is a trick to calculate percentages? I will tell you how to calculate it.

So, here’s the formula with a solved problem for you.

**x % of y = y % of x**

**Example: **Prove that 10% of 30 is equal to 30% of 10.

**Solution: **10% of 30 = 3

30% of 10 = 3

Therefore they are equal i.e. x % of y = y % of x holds.

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