Percentage

1. What is Percentage?

Percentage is a way of expressing a number as a fraction of 100. It is used to compare quantities, analyze data, and measure increase or decrease in values. The symbol '%' means "per hundred."

Way of Expressing a Fraction of 100

Used to Compare Quantities

Measures Increase or Decrease

Symbol '%' Means "Per Hundred"

Simple Definition: Percentage means a part or share of 100. If we say "40%," it means 40 out of 100.

Examples:

40% = 40/100 = 0.4

75% of 200 = (75/100) × 200 = 150

20% increase on ₹500 = ₹500 + (20% of 500) = ₹600

2. Important Concepts & Formulas

Concept	Formula / Description	Example
Basic Formula	Percentage = (Value / Total) × 100	(25/200)×100 = 12.5%
Finding Value	Value = (Percentage × Total) / 100	20% of 400 = 80
Percentage Increase	Increase = ((New – Old) / Old) × 100	(120–100)/100 ×100 = 20%
Percentage Decrease	Decrease = ((Old – New) / Old) × 100	(100–80)/100 ×100 = 20%
Converting Fraction to %	Multiply fraction by 100	¾ ×100 = 75%
Converting % to Fraction	Divide by 100	25% = 25/100 = 1/4
Successive Change	Net % = A + B + (AB/100)	+10% and +20% ⇒ 10 + 20 + (10×20)/100 = 32%

3. Step-by-Step Method for Solving

Step	Description
Step 1:	Identify what "%" is being calculated (of what number).
Step 2:	Convert % into a fraction (÷100).
Step 3:	Apply formula (increase, decrease, or comparison).
Step 4:	Simplify using BODMAS to get the final value.

4. Real-Life Analogy

Think of percentage like marks in an exam

80 out of 100

→ That's 80%

40 out of 50

→ That's also 80%

So percentage helps compare results easily, even when totals differ.

5. Common Delhi Police / SSC Exam Facts

Percentage-based questions are very frequent in the Arithmetic section

Always check if question is about increase, decrease, or part of total

Successive % increase/decrease is a common SSC-style trick

Shortcut tip: x% of y = y% of x (use for simplification)

Common conversions help in mental math

Common Fraction-Percentage Conversions

½ = 50%

⅓ = 33.33%

¼ = 25%

⅕ = 20%

⅙ = 16.66%

⅛ = 12.5%

⅒ = 10%

6. Practice Questions (Exam-Type)

No.	Question	Solution	Answer
1	Find 25% of 240	(25/100)×240 = 60	60
2	20% of a number is 50. Find the number.	(20/100)×x = 50 → x = 250	250
3	A number increased from 80 to 100. Find % increase.	(20/80)×100 = 25%	25%
4	If price decreased from ₹500 to ₹400, find % decrease.	(100/500)×100 = 20%	20%
5	Two successive discounts of 10% and 20%. Find net discount.	10 + 20 - (10×20)/100 = 28%	28%

7. Quick Recap

Concept	Summary
Percentage	Value expressed per hundred
Main Formula	(Value / Total) × 100
Increase / Decrease	Change ÷ Original × 100
Successive Change	A + B + (AB/100)
Exam Tip	Learn common fraction–percentage conversions

You've completed Percentage Concepts!

Courage Tip: Remember the key formulas for percentage calculations, and practice identifying whether a problem requires finding percentage, value, or change. Master the successive change formula for Delhi Police exam.