Infographics: Percentage

 Page 1


Percentage
A comprehensive guide to understanding and solving percentage problems in competitive 
exams
What is Percentage?
A way to express a 
number as a fraction of 
100. The symbol % 
represents "per hundred"
Formula: (Part/Whole) × 
100
Why Important for SSC 
CGL?
Percentages appear in 
multiple question types: 
profit/loss, interest 
calculations, data 
interpretation, and 
mixture problems
Key to Success
Master common fraction-
to-percentage 
conversions and practice 
reverse percentage 
calculations for faster 
problem-solving
Essential Percentage Conversions
Memorizing these common fractions and their percentage equivalents will significantly 
speed up your calculations during the exam.
Basic Fractions
1/2 = 50%
1/3 = 33.33%
1/4 = 25%
1/5 = 20%
1/6 = 16.67%
1/8 = 12.5%
1/10 = 10%
Common Multiples
3/4 = 75%
2/3 = 66.67%
3/5 = 60%
5/6 = 83.33%
7/8 = 87 .5%
1/20 = 5%
1/25 = 4%
Core Formulas & Techniques
Percentage Change
Formula: [(New Value - 
Old Value) / |Old Value|] 
× 100
Use this to calculate 
percentage increase or 
decrease between two 
values
Reverse Percentage
Formula: Original Value 
= Final Value / (1 ± 
Percentage/100)
Find the original amount 
when you know the final 
value and percentage 
change
Decimal Conversion
To Decimal: Divide 
percentage by 100
To Fraction: Write over 
100 and simplify
Example: 25% = 0.25 = 
1/4
Problem Type 1: Mixtures & Alligations
Understanding how percentages change when substances are mixed or diluted is crucial for 
solving alligation problems in SSC CGL.
01
Identify Initial Composition
Determine the percentage of each 
component in the original mixture
02
Calculate Quantities
Find the actual amount of each substance 
using the percentage and total volume
03
Apply Changes
Add or remove substances and recalculate 
the new percentages
04
Solve for Unknown
Set up equations based on the final 
percentage requirements
Example Problem: Milk & Water Mixture
A 60L mixture contains 80% milk. How much water must be added to reduce milk 
percentage to 60%?
Solution: Initial water = 20% of 60L = 12L. Let x = water added. New mixture = 
(60+x)L with 48L milk (unchanged). For 60% milk: 48/(60+x) = 0.6 ³ 48 = 36 + 0.6x 
³ x = 20L
Problem Type 2: Ratios & Fractions
When fractions undergo percentage changes, both numerator and denominator transform. 
Understanding this relationship is key to solving complex fraction problems.
Key Concept: If numerator increases by a% and denominator decreases by b%, the new 
fraction becomes: (Original Numerator × (1 + a/100)) / (Original Denominator × (1 - b/100))
Example Question
Numerator increases by 50%, denominator decreases by 10%. New fraction = 4/5. Find 
original?
Answer: Setting up: (x × 1.5)/(y × 0.9) = 4/5 ³ 1.5x/0.9y = 4/5 ³ x/y = 12/25
Problem Type 3: Income, Salary & Expenditure
Income & Salary
Total money received 
regularly from work or 
investments. Form the basis 
for percentage calculations
Expenditure
Money spent on various 
needs and wants. Usually 
expressed as a percentage 
of total income
Savings
Income minus Expenditure. If 
expenditure = x%, then 
savings = (100-x)% of 
income
Quick Tip for SSC CGL
If someone spends x% of salary, they save (100-x)%. If savings amount is given, use: 
Salary = Savings / ((100-x)/100)
Problem Type 4: Population Growth & Decline
Population problems involve successive percentage changes over multiple time periods. 
The key is to apply each percentage change sequentially, not additively.
Initial Population
Start with the base population figure (P )
Year 1 Change
Apply first percentage: P¡ = P  × (1 ± 
r¡/100)
Year 2 Change
Apply second percentage: P¢ = P¡ × (1 ± 
r¢/100)
Final Result
Combine: P¢ = P  × (1±r¡/100) × (1±r¢/100)
Example: Population = 3000. Year 1: -4%, Year 2: +5%. Final = 3000 × 0.96 × 1.05 = 
3024
Problem Type 5: Profit & Loss
Fundamental Concepts
Cost Price (CP): Amount paid to acquire 
goods
Selling Price (SP): Amount received 
from selling goods
Profit: SP - CP (when SP > CP)
Loss: CP - SP (when CP > SP)
Profit % = (Profit/CP) × 100
Loss % = (Loss/CP) × 100
Key Formulas
When Profit % is given:
SP = CP × (1 + Profit%/100)
When Loss % is given:
SP = CP × (1 - Loss%/100)
Reverse calculation:
CP = SP / (1 ± Profit or Loss %/100)
Problem Setup
CP of 20 chairs = SP of x 
tables. Profit = 25%. Find 
x.
Apply Formula
Profit% = (SP/CP) × 100 = 
1.25 = 20/x
Solve
x = 20/1.25 = 16 tables
Advanced Tips & Shortcuts
Shortcut 1: Double 
Percentage
If 20% of a = b, then b% 
of 20 = ?
Solution: (20/100) × a = 
b, so (b/100) × 20 = 
(20a/100) × (20/100) = 
4% of a
Shortcut 2: Successive 
Changes
Two successive changes 
of a% and b%: Net 
change = a + b + 
(ab/100)%
Example: +10% then 
+20% = 10 + 20 + 
(10×20/100) = 32% 
increase
Shortcut 3: Percentage 
Points
Difference between 
percentages vs. 
percentage of a 
percentage
From 40% to 50% is 10 
percentage points but 
25% increase
Exam Strategy for SSC CGL
1
Identify Question Type
Quickly recognize whether it's 
mixture, profit/loss, population, 
or salary-based problem
2
Apply Relevant Formula
Use the appropriate formula or 
shortcut for that specific 
problem type
3
Work with Fractions
Convert percentages to 
fractions when possible for 
easier mental calculation
4
Verify Answer
Do a quick reasonability check - 
does the answer make logical 
sense?
Practice Makes Perfect
15
Minutes Daily
Dedicate focused time to 
percentage problems each 
day
50
Problems Weekly
Solve diverse percentage 
questions to build speed and 
accuracy
90%
Target Accuracy
Aim for high accuracy 
through consistent practice 
and formula revision
Remember: Percentage problems in SSC CGL are designed to test both your 
mathematical ability and time management. Master the shortcuts, memorize common 
conversions, and practice regularly to excel in this crucial topic.