Civil Service Exam (Subprofessional) Numerical Ability — Ratio, Proportion & PercentageCheat Sheet
A printable cheat sheet for Ratio, Proportion & Percentage, built for Civil Service Exam (Subprofessional) reviewers who want one go-to reference in the final stretch. Covers formulas, key definitions, common question types, and the Civil Service Commission (CSC)-specific twists you will see on Civil Service Exam (Subprofessional) day.
Exam context
The Career Service Examination — Subprofessional Level is conducted by Civil Service Commission (CSC) and is scheduled for Bi-annual — March and August 2026. The Numerical Ability subtest is marked as "~25% weightage" in the official pattern, and Ratio, Proportion & Percentage appears in position 4th of 9 in the Civil Service Exam (Subprofessional) Numerical Ability review rotation. Passing mark: 80%. Recent Civil Service Exam (Subprofessional) 2026 papers have drawn roughly 17 questions from this subject.
Ratio, Proportion & Percentage - Cheat sheet
Your last-minute revision companion for mastering ratio, proportion, and percentage problems in Philippine entrance exams
Sections
Formulas
Formula
a:b = a/b
Meaning
a and b are quantities being compared, ratio can be expressed as fraction
Watch Out
Always simplify to lowest terms - don't leave ratios like 6:9 instead of 2:3
When To Use
When comparing two quantities in simplest form
Formula
a:b:c = xa:xb:xc
Meaning
x is the common factor, a:b:c represents three-part ratio
Watch Out
Remember that total parts = a+b+c, not just two parts
When To Use
When dealing with three or more quantities in proportion
Section Title
Ratio Fundamentals
Important Facts
- Ratios must be in same units before comparing
- Order matters in ratios - 3:4 ≠ 4:3
- Cross multiplication works: if a:b = c:d, then ad = bc
- Ratios can be written as fractions, decimals, or with colon notation
Key Definitions
Term
Ratio
Example
Boys to girls = 3:4 means 3 boys for every 4 girls
Definition
Comparison of two or more quantities of the same kind
Term
Equivalent Ratios
Example
2:4 = 1:2 = 3:6
Definition
Ratios that express the same relationship when simplified
Diagrams To Know
- Part-to-part vs part-to-whole ratio diagrams
- Ratio distribution charts
Formulas
Formula
a:b = c:d or a/b = c/d
Meaning
Two ratios are equal, forming a proportion
Watch Out
Cross multiply correctly: ad = bc, not ac = bd
When To Use
When two ratios are stated to be equal
Formula
x = (a×d)/b when a:b = c:d and c = x
Meaning
Solving for unknown term in proportion using cross multiplication
Watch Out
Make sure you multiply and divide in correct order
When To Use
When one term in a proportion is unknown
Section Title
Proportion
Important Facts
- Cross multiplication: if a:b = c:d, then ad = bc
- Three terms proportion: a:b = b:c means b² = ac
- Check if ratios are proportional by cross multiplying
- Word problems often hide proportional relationships
Key Definitions
Term
Proportion
Example
5:10 = 3:6 (both equal 1:2)
Definition
Statement that two ratios are equal
Term
Direct Proportion
Example
More workers, more work done (at same rate)
Definition
As one quantity increases, the other increases proportionally
Term
Inverse Proportion
Example
More speed, less time for same distance
Definition
As one quantity increases, the other decreases proportionally
Diagrams To Know
- Cross multiplication diagrams
- Direct vs inverse proportion graphs
Reactions Or Equations
Note
Fundamental property for solving proportion problems
Equation
If a:b = c:d, then ad = bc
Conditions
All terms must be non-zero
Formulas
Formula
Percentage = (Part/Whole) × 100%
Meaning
Part is the portion, Whole is the total, result is percentage
Watch Out
Don't forget to multiply by 100 - decimal 0.25 = 25%
When To Use
Finding what percent one number is of another
Formula
Part = (Percentage/100) × Whole
Meaning
Finding the actual amount when percentage and total are known
Watch Out
Convert percentage to decimal first: 25% = 0.25
When To Use
When calculating percentage of a given amount
Formula
Whole = (Part × 100)/Percentage
Meaning
Finding the total when part and percentage are known
Watch Out
This is the BASE in percentage problems
When To Use
Finding original amount from percentage information
Common Values
Value
50%
Symbol
1/2
Quantity
Half
Value
25%
Symbol
1/4
Quantity
Quarter
Value
75%
Symbol
3/4
Quantity
Three quarters
Section Title
Percentage Basics
Important Facts
- 100% = 1.00 = whole amount
- 50% = 0.5 = half
- 25% = 0.25 = one quarter
- Percent means 'per hundred'
- Converting: multiply by 100 to get %, divide by 100 to get decimal
Key Definitions
Term
Percentage
Example
25% = 25/100 = 0.25
Definition
A fraction expressed as parts per hundred
Term
Base
Example
In '20% of 500', the base is 500
Definition
The original amount or whole quantity (100%)
Term
Rate
Example
In '20% of 500', the rate is 20%
Definition
The percentage itself
Term
Percentage (Amount)
Example
In '20% of 500 = 100', the percentage amount is 100
Definition
The result of percentage calculation
Diagrams To Know
- Percentage circle diagrams
- Part-whole relationship charts
Reactions Or Equations
Note
0.75 × 100 = 75%
Equation
Decimal × 100 = Percentage
Conditions
For conversion between forms
Note
45% ÷ 100 = 0.45
Equation
Percentage ÷ 100 = Decimal
Conditions
For calculation purposes
Formulas
Formula
Discount = Original Price × Discount Rate
Meaning
Amount saved when discount rate is applied to original price
Watch Out
Sale price = Original price - Discount, not just the discount amount
When To Use
Calculating money saved in sales/discounts
Formula
Sale Price = Original Price × (100% - Discount Rate)
Meaning
Final price after discount is applied
Watch Out
Convert to decimal: 30% discount means multiply by 0.70, not 0.30
When To Use
Finding final price after discount
Formula
Tax Amount = Base Price × Tax Rate
Meaning
Additional amount added as tax
Watch Out
Final price = Base price + Tax amount
When To Use
Calculating VAT, sales tax, or other taxes
Formula
Profit % = ((Selling Price - Cost Price)/Cost Price) × 100
Meaning
Percentage profit based on cost price
Watch Out
Loss % uses same formula but result is negative
When To Use
Calculating profit percentage in business problems
Common Values
Value
12%
Symbol
VAT
Quantity
Philippine VAT
Section Title
Percentage Applications
Important Facts
- Philippine VAT rate is typically 12%
- Discount is subtracted, tax is added
- Profit/Loss % is always calculated on Cost Price
- Successive discounts: apply one after another, not add percentages
Key Definitions
Term
Markup
Example
Cost ₱100, 20% markup = Selling price ₱120
Definition
Percentage added to cost price to get selling price
Term
Discount
Example
₱100 item, 20% discount = Pay ₱80
Definition
Percentage reduction from marked price
Term
VAT (Value Added Tax)
Example
₱100 + 12% VAT = ₱112 total
Definition
Tax added to the price of goods and services
Diagrams To Know
- Price breakdown charts
- Tax and discount flow diagrams
Reactions Or Equations
Note
Order matters: usually discount first, then tax
Equation
Final Price = Base × (1 + Tax Rate) × (1 - Discount Rate)
Conditions
When both tax and discount apply
Formulas
Formula
Percentage Change = ((New Value - Old Value)/Old Value) × 100
Meaning
Shows increase or decrease as percentage of original
Watch Out
Negative result means decrease, positive means increase
When To Use
Comparing two values to show change
Formula
New Value = Old Value × (1 + Rate of Change)
Meaning
Calculating new value after percentage increase/decrease
Watch Out
For decrease, use (1 - Rate), for increase use (1 + Rate)
When To Use
Finding final value after percentage change
Section Title
Percentage Change
Important Facts
- Always calculate change based on original value, not new value
- Population growth, inflation are common percentage change problems
- 50% increase then 50% decrease ≠ back to original (ends up at 75% of original)
Key Definitions
Term
Percentage Increase
Example
From ₱100 to ₱120 is 20% increase
Definition
How much a value has grown expressed as percentage of original
Term
Percentage Decrease
Example
From ₱100 to ₱80 is 20% decrease
Definition
How much a value has fallen expressed as percentage of original
Diagrams To Know
- Before and after comparison charts
- Growth/decline trend diagrams
Must Remember
- Base formula: Percentage = (Part/Whole) × 100%
- Cross multiplication: if a:b = c:d, then ad = bc
- Sale Price = Original Price × (100% - Discount%)
- Tax Amount = Base Price × Tax Rate
- Profit% = ((SP - CP)/CP) × 100
- For 30% discount, multiply by 0.70, not 0.30
- Always simplify ratios to lowest terms
- Philippine VAT is 12%
- Percentage change = ((New - Old)/Old) × 100
- In proportions, check your answer by cross multiplication
Last Minute Tips
- For percentage problems, identify if you're finding Base, Rate, or Percentage first
- In ratio word problems, set up the proportion carefully - make sure units match on both sides
- When solving discount problems, remember: you pay (100% - discount%), not the discount%
- For complex percentage problems, work step by step: find the decimal first, then multiply
- Always check if your percentage answer makes sense (can't be negative in most real situations)
Comparison Tables
Rows
Values
- Comparison of quantities
- Equality of two ratios
- Parts per hundred
Property
Definition
Values
- a:b or a/b
- a:b = c:d
- x% or x/100
Property
Format
Values
- 3:4
- 3:4 = 6:8
- 75%
Property
Example
Values
- Comparing quantities
- Solving for unknowns
- Finding parts of whole
Property
Use Case
Columns
- Aspect
- Ratio
- Proportion
- Percentage
Table Title
Ratio vs Proportion vs Percentage
Rows
Values
- Both increase/decrease together
- One increases, other decreases
Property
Relationship
Values
- y = kx (k constant)
- xy = k (k constant)
Property
Formula
Values
- Distance and time at constant speed
- Speed and time for fixed distance
Property
Example
Values
- Straight line through origin
- Hyperbola curve
Property
Graph Shape
Columns
- Aspect
- Direct Proportion
- Inverse Proportion
Table Title
Direct vs Inverse Proportion
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