Percentage Formula

Percentage Formula (Basic, Change & Tricks)

The Percentage Formula is an essential mathematical tool used to express a number or a ratio as a fraction of 100. Derived from the Latin phrase "per centum" (meaning "by the hundred"), percentages are crucial for school arithmetic in CBSE Class 7 and 8, calculating exam marks, and cracking quantitative aptitude sections in competitive exams like Bank PO, SSC, and UPSC CSAT.

Class: 7 & 8
Topic: Comparing Quantities
Exams: CBSE · SSC · Bank PO · CSAT

What is a Percentage?

A percentage is simply a fraction with 100 as its denominator. It is denoted by the symbol %. For instance, if a student secures 85% marks in an exam, it means they scored 85 marks out of every 100 marks allocated. Percentages allow us to normalize and compare different datasets easily.

✓ Conceptual Link
To convert any fraction or decimal into a percentage, simply multiply it by 100. To remove the percentage sign, divide the number by 100.

1. Basic Percentage Formula

The fundamental percentage formula computes the ratio of a specific value relative to a total whole value, scaled out of 100.

Fundamental Equation
Percentage (%) = [Part ValueTotal Value] × 100

2. Marks Percentage Formula

This specialized version is heavily searched by students across Indian school boards (CBSE, ICSE, State Boards) to evaluate overall performance across report card aggregates.

Marks Evaluation Equation
Marks Percentage = [Total Marks ObtainedMaximum Total Marks] × 100

3. Percentage Change Formula (Increase & Decrease)

When comparing values across growth tracking systems, data analysis problems require evaluating relative change based on an initial baseline value.

Percentage Increase Formula:
Percentage Increase = [New Value − Original ValueOriginal Value] × 100
Percentage Decrease Formula:
Percentage Decrease = [Original Value − New ValueOriginal Value] × 100

Master Reference Table of Percentage Formulas

Calculation Intent Mathematical Expression Key Context
Basic Percentage (Value / Total) × 100 Standard structural evaluations
Find Value from % Value = (Percentage × Total) / 100 Finding exact share parameters
Percentage Increase (Change / Original Value) × 100 Evaluating upward price/growth scales
Percentage Decrease (Change / Original Value) × 100 Evaluating depreciation or discounts

Competitive Exam Shortcuts (Aptitude Tricks)

When preparing for Bank, SSC, or placement tests, long fractional calculations eat up time. Use these conversion shortcuts:

💡 The Commutative Trick: x% of y = y% of x
Struggling to calculate 16% of 50 in your head? Flip it! 50% of 16 is incredibly easy to process mentally: half of 16 is 8. Both equations yield the exact same answer.
🚀 Successive Percentage Trick
If a value increases by x% and then increases by y%, the net total percentage change is given directly by:
Net Change = x + y + [xy100] %
(Note: Use a negative sign for any percentage decreases/discounts)

Solved Structural Examples

Example 1: Basic Score Evaluation

Ananya secured 440 marks out of a total maximum of 500 in her term-end CBSE Class 10 board evaluation. Calculate her total marks percentage.

Given: Obtained = 440, Total Maximum = 500
Calculation:
Percentage = (440 / 500) × 100
Percentage = 0.88 × 100 = 88%
Answer: Marks Percentage = 88%
Example 2: Percentage Increase Calculation

The price of a physics textbook increased from ₹400 to ₹460. Find the percentage increase in the price of the book.

Given: Original Price = ₹400, New Price = ₹460
Absolute Change = 460 − 400 = ₹60

Calculation:
Percentage Increase = (Absolute Change / Original Price) × 100
Percentage Increase = (60 / 400) × 100
Percentage Increase = 15%
Answer: Price Increased by 15%

Example 3: Working Backwards to Find Total

A student needs 33% marks to pass an entrance test. He gets 125 marks and fails by 40 marks. What are the maximum marks for the test?

Analysis:
The student scored 125 marks but fell short by 40 marks.
Passing Marks Required = 125 + 40 = 165 marks.
According to the problem, these 165 marks represent exactly 33% of the absolute total value.

Calculation:
33% of Total Maximum Marks = 165
Total Maximum Marks = (165 × 100) / 33
Total Maximum Marks = 5 × 100 = 500 marks.
Answer: Maximum Total Marks = 500

Frequently Asked Questions (FAQs)

What is the basic formula to find a percentage?
The structural formula is: Percentage = (Part Value / Total Whole Value) × 100. For example, if you get 40 out of 50 in a test, your percentage is (40/50) × 100 = 80%.
How do I compute my overall marks percentage?
Add up the marks obtained across all your individual subjects to get your aggregate score. Then, divide this by the sum of the maximum possible marks across those same subjects and multiply the final fraction by 100.
What is the difference between percentage increase and percentage decrease?
Both formulas evaluate the ratio of the absolute change relative to the original baseline value. The only difference is whether the value has moved upward (Increase) or downward (Decrease) relative to that initial starting number.
Why do we always divide by the original value in growth tracking?
Because percentage growth or decline must always show how much a value changed relative to where it started. Dividing by the new value instead of the original value is the most common mistake made by students in exams.

FAQs (Frequently Asked Questions)

The rate of change is the rate of change from the old value to the new value. Calculated using the following formula: % change = (difference between old and new value/old value) x 100%

Here are some practical examples of percentages.

Cell phone or laptop battery percentage. Percentage of nutrients contained in the food package. The composition of oxygen, carbon dioxide, nitrogen, etc. in the air. Percentage of performance on a test.

Yes, if the value is greater than the total, the percentage would exceed 100 There is a possibility.

To convert a percentage to a decimal, omit the per cent sign (%), divide by 100, and write the resulting fraction in decimal form.