Civil Service Exam (Subprofessional) Numerical Ability — Ratio, Proportion & PercentageRevision Notes
Final-week revision notes for Ratio, Proportion & Percentage. If you have already studied the full chapter, this page is your go-to refresher before sitting the Civil Service Exam (Subprofessional). Compact, high-yield, and aligned with what Civil Service Commission (CSC) tests in the Numerical Ability subtest.
Exam context
On the Civil Service Exam (Subprofessional) 2026, the Numerical Ability subtest carries a "~25% weightage" weight in Civil Service Commission (CSC)'s pattern. Ratio, Proportion & Percentage lands at position 4th out of 9 in the standard review order. Target score is 80%, and roughly 17 items come from Numerical Ability on a typical Civil Service Exam (Subprofessional) paper.
Ratio, Proportion & Percentage - Revision notes
Ratio, Proportion, and Percentage are fundamental mathematical concepts frequently tested in Philippine entrance exams (UPCAT, CSE, LET, NLE, NMAT, ACET, USTET). These topics involve relationships between quantities, equal ratios, and parts of a whole expressed as fractions of 100. Mastering these concepts is essential for solving word problems in business, statistics, and everyday applications.
Sections
Formulas
Example
5 : x = 3 : 9, so 5 × 9 = 3 × x, therefore x = 15
Formula
a : b = c : d if and only if ad = bc
Variables
a, b, c, d are real numbers where b ≠ 0 and d ≠ 0
Application
Cross-multiplication to verify equal ratios or solve for unknown terms
Example
In ratio 2:3:5 with total 100, parts are 20, 30, 50
Formula
Total parts = sum of all ratio terms
Variables
For ratio a:b:c, total parts = a + b + c
Application
Finding actual quantities when given total and ratio
Exam Tips
- Always check if ratios need to be simplified
- Draw diagrams for complex ratio problems
- Verify answers using cross-multiplication
- Pay attention to the order of quantities mentioned
Key Points
- A ratio compares two or more quantities using division
- Ratios can be written as a:b, a/b, or a to b
- Simplify ratios by dividing by the greatest common factor (GCF)
- Cross-multiplication is used to check if ratios are equal
- Ratios show relative size, not absolute quantities
Definitions
Term
Ratio
Definition
A comparison between two or more quantities expressed as a fraction or using colon notation
Importance
Foundation for proportion problems and percentage calculations
Term
Terms of a Ratio
Definition
The individual numbers being compared in a ratio
Importance
Understanding which quantities are being related
Section Title
Ratio Fundamentals
Common Mistakes
- Confusing the order of terms in a ratio
- Not simplifying ratios to lowest terms
- Mixing up cross-multiplication setup
- Adding ratios incorrectly instead of finding equivalent ratios
Formulas
Example
If 5 liters serve 12 guests, then x liters serve 120 guests: 5/12 = x/120
Formula
If a/b = c/d, then ad = bc
Variables
a, b, c, d are proportional quantities
Application
Solving for unknown values in proportion problems
Example
Distance = speed × time (constant speed)
Formula
Direct Proportion: y = kx
Variables
y varies directly with x, k is the constant of proportionality
Application
Problems where quantities increase or decrease together
Exam Tips
- Identify what quantities are being compared
- Set up proportion carefully with correct units
- Always check if your answer makes logical sense
- Practice with different types of word problems
Key Points
- Proportion states that two ratios are equal
- Used in direct and inverse variation problems
- Essential for scaling, unit conversion, and rate problems
- Cross-multiplication is the primary solving method
- Can involve three or more quantities in continued proportion
Definitions
Term
Proportion
Definition
A statement that two ratios are equal, written as a:b = c:d
Importance
Fundamental for solving ratio-based word problems
Term
Mean Proportional
Definition
The middle term in a proportion a:b = b:c, where b is the mean proportional
Importance
Used in geometric sequences and scaling problems
Section Title
Proportion Applications
Common Mistakes
- Setting up incorrect proportions from word problems
- Forgetting to check units when setting up ratios
- Incorrectly identifying which quantities are related
- Not simplifying the final answer
Formulas
Example
150 females out of 250 total: (150/250) × 100% = 60%
Formula
Percentage = (Part/Base) × 100%
Variables
Part = portion being considered, Base = total amount
Application
Finding what percent one quantity is of another
Example
40% of 500: (40/100) × 500 = 200
Formula
Part = (Rate/100) × Base
Variables
Rate = percentage as a number, Base = total amount
Application
Finding the actual amount when percentage and total are known
Example
200 is 40% of what number: 200 ÷ 0.40 = 500
Formula
Base = Part ÷ (Rate/100)
Variables
Part = actual amount, Rate = percentage
Application
Finding the total when part and percentage are known
Exam Tips
- Identify whether you're finding rate, base, or percentage
- Convert percentages to decimals before calculating
- Double-check by using a different method
- Pay attention to what the question is asking for
Key Points
- Percentage means 'per hundred' or parts out of 100
- Three main types: finding percentage, finding base, finding rate
- Formula: Percentage = (Part/Whole) × 100%
- Converting between fractions, decimals, and percentages
- Applications in business, statistics, and everyday situations
Definitions
Term
Percentage
Definition
A fraction expressed as parts per hundred, denoted with % symbol
Importance
Universal way to express proportions and changes
Term
Base
Definition
The reference quantity or total amount in percentage problems
Importance
The denominator in percentage calculations
Term
Rate
Definition
The percentage number without the % symbol
Importance
Used in calculations after converting from percentage form
Section Title
Percentage Calculations
Common Mistakes
- Confusing which quantity is the base (total)
- Forgetting to convert percentage to decimal
- Using wrong formula for the problem type
- Not expressing final answer in requested format
Formulas
Example
₱2,050 with 30% discount: ₱2,050 × 0.70 = ₱1,435
Formula
Sale Price = Original Price × (1 - Discount Rate)
Variables
Discount Rate as decimal (e.g., 20% = 0.20)
Application
Finding final price after discount
Example
Bought at ₱400, sold at ₱500: (500-400)/400 × 100% = 25%
Formula
Profit Rate = (Selling Price - Cost Price)/Cost Price × 100%
Variables
Selling Price = final sale amount, Cost Price = original cost
Application
Calculating profit or loss percentage
Example
Paid ₱13,600 at 15% discount: ₱13,600 ÷ 0.85 = ₱16,000
Formula
Original Price = Sale Price ÷ (1 - Discount Rate)
Variables
Sale Price = discounted price, Discount Rate as decimal
Application
Finding original price when sale price and discount are known
Exam Tips
- Read carefully whether tax is added before or after discount
- Always verify if the calculation makes economic sense
- Practice multi-step problems combining discounts and taxes
- Remember Philippine VAT rate is typically 12%
Key Points
- Discount = Original Price × Discount Rate
- Sale Price = Original Price - Discount
- Tax Amount = Price × Tax Rate
- Total Cost = Price + Tax
- Profit/Loss calculations using percentages
Definitions
Term
Discount
Definition
Reduction in price, usually expressed as percentage of original price
Importance
Common in retail and business calculations
Term
Value Added Tax (VAT)
Definition
Tax added to the price of goods and services, typically 12% in Philippines
Importance
Essential for business and consumer calculations
Section Title
Business Applications
Common Mistakes
- Adding discount instead of subtracting
- Forgetting to add tax after calculating discount
- Using wrong base for profit/loss calculations
- Confusing marked price with selling price
Formulas
Example
Population growing 5% yearly for 3 years
Formula
Final Value = Initial Value × (1 + Rate)^n for growth
Variables
Rate as decimal, n = number of periods
Application
Compound growth problems
Example
Price changed from ₱80 to ₱100: (100-80)/80 × 100% = 25%
Formula
Percentage Change = (New Value - Old Value)/Old Value × 100%
Variables
Positive for increase, negative for decrease
Application
Measuring relative change between two values
Exam Tips
- Break complex problems into smaller steps
- Keep track of what percentage refers to what base
- Use estimation to check if answers are reasonable
- Practice problems with multiple percentage operations
Key Points
- Compound percentage changes
- Mixture and alligation problems
- Population growth and depreciation
- Multiple ratio comparisons
- Percentage increase and decrease calculations
Definitions
Term
Depreciation
Definition
Decrease in value over time, often expressed as percentage
Importance
Important for asset valuation and business accounting
Term
Compound Growth
Definition
Growth calculated on both original amount and previously accumulated growth
Importance
Models real-world population and investment growth
Section Title
Advanced Applications
Common Mistakes
- Treating compound changes as simple addition
- Using wrong base for percentage change calculations
- Confusing appreciation with depreciation
- Not accounting for time periods in growth problems
Connections
- Ratios form the foundation for understanding proportions and percentages
- Percentage problems often require setting up proportions to solve
- Business applications combine multiple concepts: discounts, taxes, and profit calculations
- Proportion concepts are essential for unit conversion and scaling problems
- These topics connect to algebra through cross-multiplication and equation solving
- Statistical analysis frequently uses percentage and ratio comparisons
Exam Strategy
Focus on identifying problem types quickly. Practice the three main percentage formulas until they become automatic. For ratio problems, always simplify and check using cross-multiplication. In business problems, read carefully to determine the sequence of operations (discount first, then tax, etc.). Time management is crucial - don't spend too long on complex multi-step problems. Always verify that your answers make logical sense in context.
Quick Review Questions
If 150 out of 250 female students live in rural areas, what percentage live in rural areas?
150 ÷ 250 = 0.6 = 60%. Divide the part (150) by the whole (250) and multiply by 100%.
Find x in the proportion 5:x = 3:9
Cross multiply: 5 × 9 = 3 × x, so 45 = 3x, therefore x = 15.
A refrigerator costs ₱15,000. If there's a 30% discount, how much is saved?
Discount = 30% of ₱15,000 = 0.30 × ₱15,000 = ₱4,500.
800 is 25% of what number?
Base = Part ÷ Rate = 800 ÷ 0.25 = 3,200.
If books are in ratio 2:3 and there are 18 red books, how many violet books are there?
Set up proportion: 2:3 = 18:x. Cross multiply: 2x = 54, so x = 27.
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