### Percentages

# Definition of Percentage

Percentage is defined as a given part or amount in every hundred. Percentages are fractions that have 100 as the denominator. Simply put, it is the relation between the part and the whole, where the value of the whole is always taken as 100.

It is represented by the symbol "%".

The term "percentage" was adapted from the Latin word "per centum" meaning "by the hundred".

For example, if Anita scored 40% marks in his math test, it means that she scored 40 marks out of 100. It is written as 40/100 in the fraction form and 40:100 (simplified to 4:10) in terms of ratio.

**RELEVANCE OF PERCENTAGES**

In instances where we want to figure out how much of something we have left or have given away, there are a few ways to approach such a problem.

- Taking a wild guess is one way, however, it’s not an accurate method.
- Fractions, on the other hand, are a much better way. However, sometimes it’s not much better than a guess.

In arithmetic, percentages are always preferred. This is mostly because they can be converted into decimals and used in equations with ease.

Note: To find the percentage of something, it’s important to have a measurement.

For example, if there are ten chips in a package, that’s a measurement. If someone were to eat five of those chips, fifty percent would be gone. This percentage could be converted into a decimal of .5 if someone wanted an accurate description of how many chips were left.

**CALCULATING PERCENTAGES**

In this section, we will see, how to calculate the percentage

Calculating percentage means that we have to find the share of a whole, with respect to 100.

There are two ways to find a percentage:

- By using the unitary method.
- By changing the denominator of the fraction to 100.

It should be kept in mind that the second method for calculating the percentage is not used in situations where the denominator is not a factor of 100. For such cases, we use the unitary method.

Points to keep in mind:

While solving percentage word problems, it’s best to convert the statement into numbers.

For example, the problem may ask to find sixteen percent of 400.

Firstly, sixteen percent needs to be converted into decimal.

This can be done by moving the decimal point over two places, making %16 into .16 (for this problem, to convert the decimal back to percent form it can be multiplied by 100)

The two numbers will then be multiplied. The problem would look like this, (.16)(400) = 64.

Hence, sixteen percent of 400 is 64.

**FORMULA TO CALCULATE PERCENTAGE/ PERCENTAGE CALCULATOR FORMULA**

The percentage formula is used to find the share of a whole in terms of 100. By using this formula, you can represent a number as a fraction of 100.

**Percentage= (Value/Total Value)×100**

**INCREASE OR DECREASE PERCENTAGE**

In some cases, it may be necessary to find the difference between two numbers and identify if it is a case of increase or decrease percentage.

For example; If one week a business has 200 soldier toys on hand and in next week, they have 50, the store owner might want to know what percentage of their stock was sold in that week.

First, the two numbers need to be compared. The two numbers will have a difference that needs to be found. 200 minus 50 leaves a difference of 150.

The difference will then need to be divided by the original number, 150 / 200 = .75.

In the next step, the answer should be multiplied by one hundred for an answer of %75. This means %75 of the store’s soldier toys stock was sold.

**Method to Calculate Percentage Increase**

Percentage increase refers to the change in the value, when it is increased over a period of time.

For example, population increase, increase in the number of covid patients, etc.

Percentage increase can be calculated by using the following formula:

**Percentage Increase= (Increased Value-Original value)/Original value × 100**

**Method to Calculate Percentage Decrease**

Percentage decrease refers to the change in the value when it is decreased over a period of time.

For example, decrease in the level of rainfall, decrease in the number of Covid patients, etc.

Percentage decrease can be calculated by using the following formula:

**Percentage Decrease= (Original value-Decreased Value)/Original Value × 100**

**PERCENTAGE BY RATIO**

In this section we will see how to find percentage by ratio

The ratio is defined as the relation between the quantities of two or more objects and it indicates the amount of one object contained in the other.

The general form of representing a ratio of two quantities say x and y is **x : y**

where,

x = Antecedent

y = Consequent

The ratio formula is used while comparing the relationship between two numbers or quantities.

For example, there are times when you could be given a ratio, such as 20 out of 50 and asked to find the percentage.

This can be done by dividing the numerator by the denominator, or 20 / 50.

The answer of .40 can then be converted to percentage by multiplying by 100.

Thus, with the ratio of 20 out of 50, 14 would be 40%

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### Examples

## Q1 . Calculate 20% of 80.

## Solution:

Let 20% of 80 = X

20/100 * 80 = X

X = 16

## Q2. In a class of 50 students, 30 % are girls. Find the number of girls and number of boys in the class?

## Solution:

Solution:

Number of girls in the class = 30 % of 50

= 30/100 × 50

= 1500/100

= 15

Number of boys in the class = Total number of students in the class – Number of girls

= 50 – 15

= 35

## Q3.Raj scored 340 marks out of 400 marks and his elder brother Raghu scored 560 marks out of 600 marks. Who scored percentage is better?

## Solution:

This is a question on how to calculate percentage of marks

Percentage of marks scored by Raj = (340/400 × 100) %

= (34000/400) %

= (340/4) %

= 85 %

Percentage of marks scored by Raghu = (560/600 × 100) %

= (56000/600) %

= (560/6) %

= 93.33 %

Hence, the percentage marks scored by Raghu is better than that scored by Raj

## Q4.The sum of (16% of 24) and (10% of 42) is equal to what value?

## Solution:

Sum = (16% of 24) + (10% of 42)

Required value = (24 × 16)/100 + (42 × 10)/100

Required value = 3.84 + 4.2

Therefore, required value = 8.04

## Q5.A fruit seller had some mangoes. He sells 40% mangoes and still has 480 mangoes. Originally, he had how many mangoes?

## Solution:

Let he had N mangoes, originally.

Now as per the given question,

(100 – 40)% of N = 480

⇒ (60/100)x N = 480

⇒ N = (480 x 100/60) = 800

## Q6.Out of two numbers, 40% of the greater number is equal to 60% of the smaller. If the sum of the numbers is 200, then the greater number is?

## Solution:

Let us assume, greater number be X.

∴ Smaller number = 200 – X

According to the question,

(40 x X)/100 = 60(200 – X)/100

⇒ 2X = 3 × 200 – 3X

⇒ 5X = 3 × 200

⇒ X = 120

## Q8.In final exam of a class, there are 120 students, out of which 10 % students failed. How many students passed the final exam?

## Solution:

Percentage of students who passed the exam= 100 % – 10 % = 90 %

90 % of 120

= 90/100 × 120

= 10800/100

= 108

Therefore, 108 students passed the final class exam.

## Q9.Rita gets 90 % marks in examinations. If these are 475 marks, find the maximum marks.

## Solution:

Let the maximum marks be m

Then 95 % of m = 475

⇒ 95/100 × m = 475

⇒ m = (475 × 100)/95

⇒ m = 475000/95

⇒ m = 500

Therefore, maximum marks in the examinations are 500.

## Q10. Let a bag contain 4 kg of apples and 6kg of grapes. Find the ratio of quantities present, and percentage occupied by each.

## Solution:

The number of apples and grapes in a bag can be compared in terms of their ratio, i.e. 4:6, which can be simplified to 2:3.

The same quantity can be represented in terms of percentage occupied, which is given as:

Total quantity present = 10 kg

Ratio of apples (in terms of total quantity) = 4:10, simplified to 2:5

From the definition of percentage, the ratio can be expressed per hundred,

(2/5)x 100

Hence, Percentage of Apples = 2/5×100=40

Percentage of Grapes = 60

## Q11.Ashu got a 10% hike in his salary. His current salary is Rs 70,000. Calculate his revised salary after the hike.

## Solution:

Ashu’s current salary = Rs70,000

10% hike in the salary means: 10% of 70,000= 10/100 × 70,000

10 × 700 = Rs 7000

Ashu’s pay hike is Rs 7000.

Hence, his new salary will be Rs70,000 + Rs7000 = Rs77,000.

∴ Ashu’s salary after the hike will be Rs 77,000.

## Q12. In a class of 70 students, 49 are girls and the remaining are boys. Using the ratio formula, find the ratio of the total number of boys to the number of girls.

## Solution:

Total number of students = 70

Number of girls = 49

Number of boys = Total number of students – Number of girls

= 21

Using ratio formula,

The ratio of number of boys to the number of girls = Number of boys: Number of girls = 21:49, which can be simplified to 3:7

### Practice Questions

## Percentage Practice Questions

### Related Study Materials

### FAQ

### What do you mean by percentage?

A percentage is a value or ratio that shows a fraction of 100.

### What is the unit for percentage?

Percent means per 100. It does not have any unit.

### What is the symbol of percentage?

Percentage is termed as per cent, is denoted by ‘%’ symbol.

### What is the percentage formula?

The formula to calculate percentage of a number out of another number is:

Percentage = (Original number/Another number) x 100

### What is the percentage of 75 out of 150?

(75/150) x 100 = 50%

### What is 30% of 120?

30% of 120

= 30/100 x 120

= 36

### 60% of 40 is 24. Explain this statement.

60 is the percentage.

40 is the base.

24 is the part.

### 25% of 400 is 50. Explain this statement.

25 is the percent.

400 is the base.

100 is the part.

### 26 is 50% of 52. Explain this statement.

26 is the part.

50 is the percent.

52 is the base.

### What is profit percentage formula?

When the percentage formula is used to find profits earned, it is known as the profit percentage formula.

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