Infographic: Percentages | Quantitative Aptitude (Quant) - CAT PDF Download

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Infographic: Percentages
The term "per cent" derives from the Latin centum, meaning "per hundred." A percentage expresses 
a number, ratio, fraction, or decimal as a fraction of 100.
Core Formula: To calculate percentage = (Part / Whole) × 100
Converting to Percentages: The Four Methods
1
Numbers
Multiply the 
number by 100.
Example: 4 = 4 × 
100 = 400%
2
Fractions
Multiply fraction 
by 100 to convert; 
divide by 100 to 
reverse.
Example: 3/5 = 
(3/5) × 100 = 60%
3
Ratios
Convert ratio to 
fraction first, then 
multiply by 100.
Example: 2:5 = 
2/5 × 100 = 40%
4
Decimals
Multiply decimal 
by 100 to convert; 
divide by 100 to 
reverse.
Example: 0.773 = 
0.773 × 100 = 
77.3%
Percentage Change: Two Critical Measures
Absolute Value Change
The actual numerical change in quantity.
Example: Sales from ¹5,000 cr to ¹6,000 cr = 
¹1,000 cr absolute change
Percentage Change
Relative change expressed as a percentage.
Formula: (Absolute Change / Original Value) × 
100
Example: (1,000/5,000) × 100 = 20%
Key Formulas: Percentage change of A from B = [(A-B)/B] × 100 | Percentage change from 
A to B = [(B-A)/A] × 100
Percentage Point vs Percentage Change
Percentage Point Change
Direct arithmetic difference between two 
percentages.
Example: From 25% to 30% = 5 
percentage points
Percentage Change
Relative change considering original 
quantity.
Example: From 25% to 30% = (5/25) × 100 
= 20% change
Increase and Decrease Formulas
For Percentage Increase
New Value = Original × (1 + Increase%/100)
% Increase = [(New 3 Original)/Original] × 100
Use original value as base
For Percentage Decrease
New Value = Original × (1 3 Decrease%/100)
% Decrease = [(Original 3 New)/Original] × 100
Always use original as denominator
Product Constancy: The Inverse Relationship
When two quantities multiply to give a constant third quantity, they are inversely proportional. If 
one increases by x%, the other must decrease to maintain constancy.
Expenditure
Price × 
Consumption
Revenue
Rate × Quantity
Distance
Speed × Time
Work
Time × Efficiency
Critical Formula: If price increases by x%, consumption must decrease by [x/(100+x)] × 
100% to maintain constant expenditure.
Example: Sugar price increases by 25%. To maintain expenditure, decrease consumption by 
[25/(100+25)] × 100 = 20%
Relationship: C = A + B
When three quantities relate as C = A + B, and A increases by x% while C remains constant, B must 
change by 3[A×x/(100×B)]%
CAT Application: Savings = Income 3 Expenditure
Example: Person saves 20% of income (¹100). Expenditure increases 10% (¹80 to ¹88), income 
constant. Savings drop from ¹20 to ¹12 = 40% decrease.
Successive Percentage Changes
When multiple percentage changes apply consecutively, use multiplicative formulas4not simple 
addition. Each change applies to the result of the previous change.
Successive Increases
Final = Original × (1 + a/100) 
× (1 + b/100) × (1 + c/100)
Successive 
Decreases
Final = Original × (1 3 a/100) 
× (1 3 b/100) × (1 3 c/100)
Mixed Changes
Final = Original × (1 ± a/100) 
× (1 ± b/100) × (1 ± c/100)
Use + for increase, 3 for 
decrease
Population Growth Application
Population n Years Later
Formula: P × (1 + r/100)n
Where P = current population, r = annual rate, n 
= years
Population n Years Ago
Formula: P / (1 + r/100)n
Reverse the growth to find earlier value
PCG: Percentage Change Graphic
The PCG is a powerful visualisation tool for tracking successive changes and avoiding calculation 
errors. Sketch it on rough paper during CAT for complex problems.
01
Successive Changes
Visually track each percentage 
change step-by-step. Example: 
100 ³ (+20%) ³ 120 ³ (+10%) 
³ 132
02
Product Changes
When two variables change: 
Net % = A + B + (AB/100). 
Example: 10% and 20% 
increases = 32% net increase
03
Product Constancy
Calculate required decrease to 
offset increase. Example: 25% 
price rise needs 20% 
consumption drop
04
A ³ B ³ A Relationships
Find reverse relationship. Example: B is 25% 
more than A means A is 20% less than B
05
Ratio Changes
Track numerator effect (direct) and denominator 
effect (inverse) separately, then combine
EduRev Tip: Consistent practice with shortcuts and smart techniques for solving 
percentages will significantly boost your QA and DI scores. Focus on accuracy first, then 
build speed.