To Get Percentage Formula from our best teachers. You can learn everything related to Percentage formulas like % increase & decrease and % difference. The Percentage is a fraction that has 100 as its denominator. In other words, Percentage is the relation between the part and the whole, where the whole is always taken as 100. The phrase “percentage” was derived from a Latin word “per centum,” which means “by the hundred.”
What is the Percentage?
In mathematics, Percentage is a number or a ratio in which the whole value is always expressed by 100.
For example, If we have to calculate the percent of a number, then we have to divided the number by the whole and multiply by 100.
Percentages are also called the dimensionless number because it has no dimension.
Examples of Percentages
There are some examples of percentages are given below:
- 10% is equal to a 1/10 fraction
- 20% is equivalent to ⅕ fraction
- 25% is equivalent to ¼ fraction
- 50% is equivalent to ½ fraction
- 75% is equivalent to ¾ fraction
- 90% is equal to a 9/10 fraction
Percentage Formula
To determine the percentage of any number, we have to divide the given value by the total value after then multiply the resultant by 100.
Let’s see the formulas of percentages:
Percentage formula = (Given Value/Total value) × 100
Example: 3/5 × 100 = 0.6 × 100 = 60 per cent
Percentage Difference Formula
If we have two values, then we need this formula; the formula is given below:
Percentage difference= N1- N2 /[N1+n2/2] * 100
For example, if 10 and 20 are two (2) different values, then the percentage (%) difference between them will be:
% difference between 10 and 20 is –
Percentage difference= 10- 20 /[10+20/2] * 100
Therefore, the Percentage difference = 200
Percentage Increase and Decrease
The percentage increase is equal to subtracting the Given number from a resultant number, dividing by the Given number, and multiplying by 100.
Percentage (%) increase = [(resultant number – Given number)/Given number] x 100
where,
increase in number = Resultant number – Given number.
Similarly, a percentage decrease equals subtracting a Resultant number from the Given number, dividing by the Given number, and multiplying by 100.
Percentage (%) decrease = [(Given number – Resultant number)/Given number] x 100
Where decrease in number = Given number – Resultant number
So, if the answer is negative, there is a percentage decrease.
Some Examples
Two quantities are generally expressed based on their ratios. Here, let us understand the concepts of percentages through a few examples much better.
Example:
Let a bag contain 4 kg of apples and 5 kg of grapes. Find the percentage occupied by each and the ratio of quantities present.
Solution:
In a bag, The number of apples and grapes can compare in terms of their ratio, i.e., 4:5.
The actual interpretation of % can be understood as follows:
The exact quantity can represent the percentage occupied, which can be done as given below.
Total quantity present = 4+5 kg = 9 kg
The ratio of apples (in terms of total quantity) = 4/9
=4/9×100/100
From the given definition of (%), it is the ratio that is represented or expressed per 100,
(1/100) = 1%
Thus, Percentage of Apples = (4/9) × 100 = 44.4%
Percentage of Grapes = (5/9) × 100 = 55.5%
Converting Fractions to Percentage
A fraction can represented by a/b
Then multiplying and dividing the fraction by 100, we have
a/b * 100/100
[ a/b * 100] 1/100 ——-(i)
From the definition of percentage, we have the following;
(1/100) = 1%
Thus, equation (i) can written as:
(a/b) × 100%
Therefore, a fraction can convert to a percentage simply by multiplying the fraction by 100.
Difference between Percentage and Percent
The words percentage and percent are closely related, but they have many differences.
A specific number accompanies the percent ( or symbol %).
For example, More than 70 percent (%) of the participants responded positively to the sacrifice.
The percentage is represented without a number.
For example, The percentage of the population influenced by malaria is between 60% and 65%.
Ratios, Fractions, Decimals, and Percents are interrelated individually.
Some Percentage Examples:
Example 1:
Find the number if 18% of 50% of a number is 6.
Solution:
Let X be the required number.
Therefore, as per the given question,
(18/100) × (50/100) × X = 6
So, X = (6× 100 × 100) / (18 × 50)
= 66.67%
Example 2:
What percentage of 3/8 is 1/25?
Solution:
Let X% of 3/8 be 1/25.
∴ [(3/8) / 100] × X = 1/25
⇒ X = (1/25) × (8/3) × 100
= 10.67%
Example 3:
Which number is 40% less than 90?
Solution:
Required number = 40% of 90
= (90 x 40)/100
= 36
Therefore, the number 36 is 40% less than 90.
Example 4:
The sum of (15% of 14.2) and (20% of 1.40) is equal to what value?
Solution:
As per the given question,
Sum = (15% of 14.2) + (20% of 1.40)
= (14.2 × 15)/100 + (1.40 × 20)/100
= 2.13 + 0.28
Sum = 2.14 ( Answer )
Extra Questions Related to Percentage
Question 1:
A fruit seller had some apples. He sells 50% apples and still has 520 apples. Initially, he had how many apples?
Solution:
Let he had N apples, originally.
Now, as per the given question, we have the following;
(100 – 50)% of N = 520
⇒ (50/100) × N = 520
⇒ N = (520 × 100/50) = 1040
Question 2:
What is 50 % of 90?
Solution:
50 % of 90
= 50/100 × 90
= (50 × 90)/100
=45 ( Answer )
Question 3:
In a class of 40 students, 50 % are girls. Find the number of girls and number of boys in the class.
Solution:
Number of girls in the class = 50 % of 40
= 50/100 × 40
= 2000/100
Number of girls in the class = 20
Number of boys in the class = Total number of students in the class – Number of girls
= 40 – 20
= 20 ( Answer )
Solved Examples of Percentage
Question 4:
Ram scored 444 out of 500 marks, and his elder brother Balram scored 682 marks out of 700 marks. Who scored the percentage better?
Solution:
Percentage of marks scored by Ram = (444/500 × 100) %
= (44400/500) %
= (444/5) %
Therefore, marks scored by Ram = 88.8 %
Percentage of marks scored by Balram = (682/700 × 100) %
= (68200/700) %
= (682/7) %
Therefore, marks scored by Balram = 97.42 %
Hence, the percentage marks scored by Balram are better.
Question 5:
In the final exam of class IX (nine), there were 60 students, and 20 % of students failed. How many students passed class IX?
Solution:
Percentage of students passed to class IX = 100 % – 20 % = 80 %
80 % of the 60
= 80/100 × 60
= 4800/100
Percentage of students passed to class IX = 48
Therefore, 48 students passed class IX.
Question 6:
Varsha gets 92 % marks in examinations. If these are 460 marks, find the maximum marks.
Solution:
Let the maximum marks be m
Then 92 % of m = 460
⇒ 92/100 × m = 460
⇒ m = (460 × 100)/92
or, m = 46000/92
Therefore, m = 500
Therefore, the maximum marks in the examinations are 500.
Practice Problems Related to Percentage Formula:
Now, you can solve these problems by yourself; the list of some issues is given below:
- In the final exam of class X, there were 120 students 15 % of students failed. How many students passed class X?
- In a class of 75 students, 40 % are girls. Find the number of girls and number of boys in the class.
- If 38 % of 78 % of a number is 9, find the number.
- A fruit seller had some apples. He sells 45% of Mangoes and still has 350 Grapes. Initially, he had how many Grapes?
- The sum of (25% of 38.6) and (40% of 2.80) is equal to what value?
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