# Percentage Formula

The quant and reasoning section of the competitive exam, checks the ability of the students by testing their logical, quantitative, and critical problem-solving skills, which are essential in the business and management world. Percentage is used widely in our daily lives, from calculating the marks of the students to discount on footwear or eatables. Even in your smartphone, the battery shows with the sign of the percentage. In this article, we will delve deeper to know the percentage formula, along with sample questions related to percentage for better understanding of students.

Understanding the Concept: Percentage

Percentage is used to find the share in terms of 100. The percentage formula is given as-

 Percentage = (Value ⁄ Total Value) × 100

For better understanding, let’s understand the application of percentage formula, through an example:

Example: Find 75% of 10.

Solution: =75/100 10

= 7.5

Questions of Percentage framed in the Competitive Examination

Given below is a list of type of questions framed in the quantitative section in a competitive exam from percentage, including: how to calculate the percentage of a value, calculating percentage change, turning decimals into fractions, and calculating compound interest.

Ques 1: Express ⅝ as percentage.

Solution1: 520= 55/205

= 25/100 = 25%

Percentage Formula: Question related to Percent Change

 Percent Change= (Amount of Change/Starting Amount) 100

Ques2: The price of refurbished sofa changes from Rs 2,000 to Rs 2,500 and you have to calculate the percent increase.

Solution 2: Change of the amount= Rs 2,500 – Rs 2,000 = Rs 500

Now as given in the question, the starting price of the refurbished sofa was Rs 2,000. So,

Percent change = (500/2000)100 = 25%

Percentage Formula: Question related to Percentage Error-

 % Error = Error/ Real Value 100

Ques 3: Neha measures the length of her textbook as 15cm. If the length is actually 12cm, what is the percentage error in Neha’s calculation?

Ans 3: Given,

Length of the textbook measured by Neha = 15cm

Actual length of the textbook = 12cm

% Error = Error / Real Value100

= (15-12/12)100

= 3/12100

= 25%

Percentage Formula: Question related to Original Value-

 Original Value = New Value / 100 + % change 100

Ques 4: Sukhdev buys a stamp collection and makes a 45% profit by selling it for Rs 3,500. Find the cost of the collection. It is the original value we wish to find, so the above formula is used.

Ans 4: Given,

Profit earned by Sukhdev by selling stamp collection = 45%

Sale Price = Rs 3,500

Original Value = (New Value/100 + %change)100

= (3,500/100+35)100

= 25.925 %

Percentage Formula: Question related to Percentage Increases and Interest-

 New Value = 100 + % increase / 100 Original Value

Ques 5: Rs 5,00,000 is put in a bank where there is 8% per annum interest. Work out the amount in the bank after 1 year.

Ans 5:  Given,

Amount deposit in the bank = Rs 5,00,000

Rate of Interest = 8%

New Value = 100 + % increase / 100 Original Value

=  (100 + 8/ 100) 5,00,000

= 108/100 5,00,000

= Rs 5,40,000

Hence, the article has listed down some of the important percentage formulas, which are generally used by students in solving percentage related questions in competitive exams.

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#### About the Author

##### Piyush Bhartiya

Piyush values education and has studied from the top institutes of IIT Roorkee, IIM Bangalore, KTH Sweden and Tsinghua University in China. Post completing his MBA, he has worked with the world’s # 1 consulting firm, The Boston Consulting Group and focused on building sales and marketing verticals for top MNCs and Indian business houses.