Percentage: The Latin word “per centum,” which meaning “by the hundred,” is where the word “percentage” originated. Fractions with 100 as the denominator are called percentages. it is the relationship between a component and the whole in which the “whole” is always valued at 100.
Formula for Percentage:
We must divide the value by the entire value and multiply the resulting number by 100 in order to get the percentage.
Formula for percentages = (Value/Total value) × 100
For instance, 3/5 × 100 = 60%
How is the percentage of a number calculated?
such as P% of Number = X, must be used to determine the percentage of a given number. Here, X represents the necessary percentage.
In order to represent the preceding formulas, we must remove the % sign: P/100 * Number = X
For instance, compute 10% of 160.
Assume 10% of 160 equals X.
10/100 * 160 = X
X is equal to 16.
How Can a Fraction Be Converted to a Percent?
All you have to do is multiply the fraction by 100 and lower it to a percent to convert it to a percent. The following examples will help you understand the process of converting a fraction to a percentage. To convert a fraction to a percentage, take the following steps:
Step 1: The fraction should be converted to a decimal number.
Step 2: To get a percent value, multiply the obtained decimal number by 100.
Examples of Fraction to Percent
Convert 3/4 to a percentage, for example.
solution:
Step 1: convert the 3/4 fraction to a decimal.
Step 2: (3/4)×100= 0.75
Step 3: multiply the decimal by 100 to get % (0.75 × 100).
Thus, 75% is the solution.
To express a/b as a percent:
We have, (a/b) ×100
Example : (3/4)×100= 75%
To express x% as a fraction:
We have, x% = x/100
Example : 20% = 20/100 = 1/5
Percentage Formulas 

If the cost of a product rises by R%, the consumption must be decreased in order to prevent an increase in expenditure  $$ [\frac{R}{100+R}\times100]\% $$ 
If the price of a commodity falls by R%, the increase in consumption needs to maintain expenditure is  $$ [\frac{R}{100R}\times100]\% $$ 
Let P be the town’s current population, and let’s say it grows at a rate of R% annually. After n years, the population  $$P [1 +\frac{R}{100}]^n$$ 
Let P be the town’s current population, and let’s say it grows at a rate of R% annually. Population n years ago  $$ [\frac{P}{(1+\frac{R}{100})^n}]$$ 
Let the present value of a machine be x. Suppose it depreciates at the rate of R% per annum. Then Value of the machine after n years  $$ [ x (1 \frac{R}{100})^n] $$ 
Let the present value of a machine be x. Suppose it depreciates at the rate of R% per annum. Then Value of the machine n years ago  $$[\frac{x}{(1\frac{R}{100})^n}]$$ 
If A is R% more than B, then B is less than A by  $$[\frac{R}{100+R}\times100]\%$$ 
If A is R% less than B, then B is more than A by  $$[\frac{R}{100R}\times100]\%$$ 
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Example problems
Q1. A shopkeeper marked his article 50% above the cost price and gives a discount of 20% on it. If he had marked his article 75% above the cost price and gives a discount of 20% on it then find the earlier profit is what percent of the profit earned latter?
 50%
 60%
 33.33%
 40%
 75%
Solution:
Q2. When a person sold an article, his profit percent is 60% of the selling price. If the cost price is increased by 75% and the selling price remains the same, then find decrement in the profit is what percent of the selling price of the article?
 25%
 30%
 40%
 27.5%
 None of these
Solution:
Q3.Each of the following question is followed by two quantities I, and II. You have to determine the value of the quantities using the information provided and compare the quantities to answer as per the instruction set provided below.
(a) Quantity I>Quantity II
(b) Quantity I≥Quantity II
(c) Quantity I<Quantity II
(d) Quantity I≤Quantity II
(e) Quantity I=Quantity II or no relation
Quantity I: By selling 15 apples, a seller gains the selling price of 2 apples. Calculate his gain percentage.
Quantity II: 25% profit is gained when an article is sold for 625 rupees. Calculate the loss % when the same article is sold for 435 rupees.
Solution:
Q4. There are 75% boys out of total students (boys + girls) in a school and 39% of the total students of the school went on a picnic. If 32% of the total boys went on a picnic, then find what percent of total girls went on a picnic?
 60%
 90%
 75%
 80%
 50%
Solution:
Q5. A dishonest shopkeeper makes a cheating of 10% at the time of buying the items & 10% of at the time of selling the items. Find the overall profit percentage if he professes to sell goods at cost price?
 20%
 21 2/9%
 22 1/9%
 22 2/9%
 25%
Solution:
Q6. In 2018, a school has 1200 students and ratio of boys to girls is 11 : 9. If 92% of the total students got passed in 2018 and 95% of the total boys got passed in 2018 then, find the percentage of girls who got passed in 2018?
 85 1/3%
 81 2/3%
 87 2/3%
 89 1/3%
 88 1/3%
Solution:
Q7. If Amar spends 20% of his monthly income on food and 60% of remaining in transport, 10% of remaining in charity and remaining he saves and the total saving of Amar is Rs.43200 in a year. Find the monthly salary of Amar. (In Rs.)
 10000
 20000
 33000
 40700
 12500
Solution:
Q8. The mark price of an article is Rs.24000 if two successive discount of 10% and x% is given and sell for Rs.17280, find the value of x?
 5
 15
 10
 20
 30
Solution:
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Frequently Asked Questions About Percentage:
Q1. What does “percentage” mean?
Ans. A percentage in mathematics is a number or ratio that represents a portion of 100. Percentage denotes a ratio of 100. There are no units on it.
Q2. What does the percentage sign stand for?
Ans. The sign “%” is used to represent percentages. Another name for it is per cent.
Q3. What is the formula for percentages?
Ans. The following formula can be used to get a number’s proportion of another number:
Percentage = (Original number/Another number) x 100
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