Chapters
In this article, we will discuss what is a percentage and how to calculate it. So, let us get started.
Percentage
A ratio or a number that depicts a part or fraction of 100 is known as a percentage. We often use the word percent to describe the percentage and denote it by the symbol %.
When we use the word percent, we actually mean value of something per hundred. For example, 25 percent is equal to and 100 percent is equal to .
A percentage can be represented as a fraction or a decimal number. For instance, 78% is equal to 0.78 or .
How to calculate the percentage
We multiply the numeric value of the ratio by 100 to get a percentage. For example, suppose there are a total of 30 marbles in a basket. John gets 10 of them and his younger sister gets 20 of them. What percentage of marbles both of them have?
Well, first we need to find out the ratio. The ratio of marbles John have is . Now, we will multiply this ratio by 100 to get the percentage of marbles he gets.
=
=
Hence, John gets 33.33% of the total marbles.
To calculate the percentage of marbles his younger sister gets, we will simply subtract 33.33% from 100%.
=
In the next section of the article, we will solve a couple of examples related to percentage.
Example 1
The cost of a motorbike was \5000
Percent discount = 25%
Discount (in dollars) =
= 12505000 - \3750
Example 2
The price of an apartment last year was \85000
Percent increase in the price = 15%
Increase in the price by dollars =
= \85000 + \97750
Example 3
The cost of the furniture was \1200 this month. Calculate the percent decrease in the cost of the furniture.
Solution
The cost of the furniture last month = \1200
Percent decrease in the cost =
=
Hence, there is 20% reduction in the price of the furniture this month.
Example 4
There are 50 students in the class. 17 out of 50 students like mathematics, 23 students like computer science, and the rest of the students like physics. What percentage of students like mathematics, computer science, and physics?
Solution
Total students in the class = 50
Number of students who like mathematics = 17
Percentage of students who like mathematics =
=
Number of students who like computer science = 23
Percentage of students who like computer science =
=
Number of students who like physics =
Percentage of students who like physics = .
Example 5
There are 200 students in a college. 56 out of 200 students like to play football, 85 students like basketball, and the rest of the students like both football and basketball. What percentage of students like football, basketball, and both the games?
Solution
Total students in a college = 200
Number of students who like football = 56
Percentage of students who like football =
=
Number of students who like basketball = 85
Percentage of students who like basketball =
=
Number of students who like both the games =
Percentage of students who like both the games = .
Example 6
The total pocket money of Sarah, John, and Alice are \800, and \150 more than the previous month.
a) How much pocket money did Sarah get this month?
b) How much pocket money did John get this month?
c) Calculate the percent increase in the pocket money of Alice this month?
Solution
This question has three parts. We will solve each part separately one by one.
Part a
Total pocket money Sarah got last month = \\
= 560560 this month.
Part b
Total pocket money John received last month = \\
= 600600 this month.
Part c
Total pocket money of Alice last month = \600 + \750
Percent increase in the pocket money =
Example 7
Out of 120 questions in a test, John gets 75% correct. How many questions did he answer incorrectly in the test?
Solution
Total questions in a test = 120
Percentage of correct answers = 75%
Number of questions answered correctly =
Hence, he answered 90 questions correctly
Number of questions he answered incorrectly = Total number of questions - Number of questions answered correctly
= 120 - 90 = 30
Hence, John answered 30 questions incorrectly.
Example 8
Out of 250 questions in an exam, John attempts 80% of the total questions. Out of the attempted questions, 150 of his answers are correct, and the remaining are wrong.
a) How many questions did he attempt and missed in the exam?
b) What percentage of total questions, did he answer correctly?
c) What percentage of total questions did he answer incorrectly?
Solution
This question has 3 parts. We will solve each part separately.
Part a
Total questions in an exam = 250
Percentage of questions John attempted = 80%
Number of questions he attempted = questions
Hence, he attempted 200 questions in the exam.
Number of questions missed in the exam = Total questions - Number of questions attempted
= 250 - 200 = 50 questions
Hence, he missed 50 questions in the exam.
Part b
Number of correct answers = 150
Total number of questions in the exam = 250
Percentage of correct answers =
Part c
Number of incorrect answers = 200 - 150 = 50
Total number of questions in the exam = 250
Percentage of incorrect answers =
Example 9
In a college, 30% of the total teachers teach physics. If the number of teachers in a college who teach physics is 45, then how many total teachers are there in a college?
Solution
Number of teachers who teach physics = 45
Percentage of teachers who teach physics = 30%
In other words, we can say that the number of physics teachers is 0.30 times the total number of teachers. The formula can be written as:
Number of physics teachers = Total number of teachers x 0.30
We can derive the formula for the total number of teachers from the above formula like this:
Total number of teachers =
Total number of teachers in the college =
Hence, the total number of teachers in a college is 150.
Example 10
In a class, 40% of the total students enrolled for the extra class. If the number of students who enrolled for an extra class is 24, then how many total students are there in a class?
Solution
Number of students who enrolled for the extra class= 24
Percentage of students who got enrolled for an extra class = 40%
In other words, we can say that the number of students who enrolled themselves for an extra class is 0.40 times the total number of students in the class
Number of students who got enrolled = Total number of students in a class x 0.40
We can derive the formula for the total number of teachers from the above formula like this:
Total number of students in the class =
Total number of students in a class =
Hence, the total number of students in the class is 60.