Civil Service Exam (Subprofessional) Numerical Ability — Word Problems — Speed/Distance/Age, Discount & InterestSlides
The slide format strips Word Problems — Speed/Distance/Age, Discount & Interest to the visuals that Civil Service Exam (Subprofessional) reviewers remember best. Civil Service Commission (CSC)'s 2026 Numerical Ability papers reward reviewers who recognise the structure of a concept before they parse the item text; these slides train that recognition.
Exam context
Civil Service Commission (CSC) runs the Career Service Examination — Subprofessional Level on Bi-annual — March and August 2026. Its Numerical Ability section sits under a "~25% weightage" weighting, and Word Problems — Speed/Distance/Age, Discount & Interest is the 6th chapter in the 9-chapter Civil Service Exam (Subprofessional) Numerical Ability rotation. The Civil Service Exam (Subprofessional) passing mark is 80%, and the most recent 2026 paper drew about 17 questions from Numerical Ability.
Word Problems — Speed/Distance/Age, Discount & Interest - Slides
This comprehensive chapter covers essential word problem types commonly encountered in Philippine examinations including UPCAT, CSE, and other standardized tests. Students will master problem-solving techniques for speed-distance-time relationships, age problems, discount calculations, and simple interest computations. These skills are fundamental for numerical ability sections and practical life applications.
Slides
Chapter Overview: Word Problems in Numerical Ability
Word problems test your ability to translate real-world situations into mathematical equations. These problem types frequently appear in entrance exams and civil service tests, requiring both mathematical skills and logical reasoning.
Notes
Start with overview to show how all topics connect
Topic
Chapter Introduction
Slide Id
S1
Visual Type
mermaid
Image Prompt
Slide Number
1
Mermaid Diagram
Code
mindmap root((Word Problems)) Speed Distance Time Distance Formula Speed Formula Time Formula Average Speed Age Problems Present Age Past Relationships Future Relationships Age Ratios Discount Problems List Price Selling Price Discount Rate Trade Discount Simple Interest Principal Rate Time Interest Earned
Type
mermaid_mindmap
Description
Mind map showing the four main categories of word problems and their key components
Speed, Distance, and Time Fundamentals
The relationship between speed, distance, and time forms the foundation for solving motion problems. These three quantities are interconnected, and knowing any two allows you to find the third using basic formulas.
Notes
Essential foundation formulas that students must memorize
Topic
Speed-Distance-Time Basics
Slide Id
S2
Visual Type
mermaid
Image Prompt
Slide Number
2
Mermaid Diagram
Code
flowchart TD A[Given Information] --> B{What to Find?} B -->|Distance| C[Distance = Speed × Time] B -->|Speed| D[Speed = Distance ÷ Time] B -->|Time| E[Time = Distance ÷ Speed] C --> F[Check Units] D --> F E --> F F --> G[Final Answer]
Type
mermaid_flowchart
Description
Decision flowchart for choosing the correct speed-distance-time formula
Unit Conversion in Speed Problems
Unit conversion is crucial in speed problems as different units are often mixed. Converting to consistent units prevents calculation errors and ensures accurate answers.
Notes
Critical skill for avoiding errors in speed problems
Topic
Unit Conversion
Slide Id
S3
Visual Type
mermaid
Image Prompt
Slide Number
3
Mermaid Diagram
Code
flowchart LR A[km/h] -->|×5/18| B[m/s] B -->|×18/5| A C[Hours] -->|×60| D[Minutes] D -->|×60| E[Seconds] E -->|÷60| D D -->|÷60| C F[km] -->|×1000| G[m] G -->|×100| H[cm]
Type
mermaid_flowchart
Description
Unit conversion relationships for speed, time, and distance
Average Speed Problems
Average speed problems require careful calculation of total distance and total time. Students often make the mistake of averaging the speeds directly, which gives incorrect results.
Notes
Emphasize this is NOT arithmetic mean of speeds
Topic
Average Speed
Slide Id
S4
Visual Type
mermaid
Image Prompt
Slide Number
4
Mermaid Diagram
Code
flowchart TD A[Multi-segment Journey] --> B[Calculate Each Segment Time] B --> C[Add All Distances] B --> D[Add All Times] C --> E[Total Distance] D --> F[Total Time] E --> G[Average Speed = Total Distance ÷ Total Time] F --> G G --> H[Final Answer]
Type
mermaid_flowchart
Description
Step-by-step process for calculating average speed in multi-segment journeys
Solving Speed-Distance-Time Word Problems
A systematic approach ensures accuracy in speed problems. Following these steps helps organize information and prevents common calculation errors.
Notes
Systematic approach prevents errors
Topic
Problem-Solving Method
Slide Id
S5
Visual Type
mermaid
Image Prompt
Slide Number
5
Mermaid Diagram
Code
flowchart TD A[Read Problem Carefully] --> B[Identify Given Values] B --> C[Identify What to Find] C --> D{Check Units} D -->|Different| E[Convert Units] D -->|Same| F[Choose Formula] E --> F F --> G[Substitute Values] G --> H[Calculate Answer] H --> I[Check Units and Reasonableness] I --> J[Write Final Answer]
Type
mermaid_flowchart
Description
Problem-solving flowchart for speed-distance-time word problems
Age Problems: Basic Concepts
Age problems test logical thinking about how ages change over time while maintaining constant relationships. Understanding that age differences never change is crucial for solving these problems.
Notes
Emphasize that age differences never change
Topic
Age Problem Fundamentals
Slide Id
S6
Visual Type
mermaid
Image Prompt
Slide Number
6
Mermaid Diagram
Code
timeline title Age Relationship Over Time 5 Years Ago : Maria 15, Juan 10 : Difference = 5 Present : Maria 20, Juan 15 : Difference = 5 In 5 Years : Maria 25, Juan 20 : Difference = 5 In 10 Years : Maria 30, Juan 25 : Difference = 5
Type
mermaid_timeline
Description
Timeline showing how age difference remains constant over time
Setting Up Age Problem Equations
Age problems require careful translation of word statements into algebraic equations. Using variables and expressing relationships mathematically is key to finding solutions.
Notes
Show systematic approach to variable assignment
Topic
Age Problem Setup
Slide Id
S7
Visual Type
mermaid
Image Prompt
Slide Number
7
Mermaid Diagram
Code
flowchart TD A[Read Problem Statement] --> B[Assign Variable to One Age] B --> C[Express Other Ages in Terms of Variable] C --> D{Time Reference} D -->|Present| E[Use Current Expressions] D -->|Past| F[Subtract Years from Current Ages] D -->|Future| G[Add Years to Current Ages] E --> H[Set Up Equation from Given Relationship] F --> H G --> H H --> I[Solve for Variable] I --> J[Find All Required Ages]
Type
mermaid_flowchart
Description
Process for setting up and solving age problem equations
Age Problem Examples and Solutions
This example demonstrates the complete process of solving age problems, from variable assignment through equation setup to final solution verification.
Notes
Complete worked example with verification
Topic
Age Problem Example
Slide Id
S8
Visual Type
mermaid
Image Prompt
Slide Number
8
Mermaid Diagram
Code
flowchart TD A[Father is 4 times son's age] --> B[Let x = son's age] B --> C[Father's age = 4x] C --> D[In 20 years condition] D --> E[Son = x + 20, Father = 4x + 20] E --> F[Father will be twice son's age] F --> G[4x + 20 = 2 times x + 20] G --> H[4x + 20 = 2x + 40] H --> I[2x = 20] I --> J[x = 10 years]
Type
mermaid_flowchart
Description
Step-by-step solution of age problem example
Discount Problems: Business Mathematics Basics
Discount problems are common in business mathematics and consumer situations. Understanding the relationship between list price, discount, and selling price is essential for solving these problems.
Notes
Foundation concepts for discount calculations
Topic
Discount Fundamentals
Slide Id
S9
Visual Type
mermaid
Image Prompt
Slide Number
9
Mermaid Diagram
Code
flowchart LR A[List Price ₱500] --> B[Discount Rate 20%] B --> C[Calculate Discount Amount] C --> D[₱500 × 0.20 = ₱100] A --> E[Subtract Discount] D --> E E --> F[Selling Price = ₱500 - ₱100 = ₱400]
Type
mermaid_flowchart
Description
Calculation flow for finding selling price after discount
Discount Formulas and Calculations
These formulas provide different approaches to solve discount problems depending on what information is given and what needs to be found.
Notes
Different formulas for different problem types
Topic
Discount Formulas
Slide Id
S10
Visual Type
mermaid
Image Prompt
Slide Number
10
Mermaid Diagram
Code
flowchart TD A{What to Find?} --> B[Selling Price] A --> C[Discount Rate] A --> D[List Price] B --> E[SP = LP × 1 - Rate] C --> F[Rate = Discount ÷ LP × 100] D --> G[LP = SP ÷ 1 - Rate] E --> H[Calculate] F --> H G --> H
Type
mermaid_flowchart
Description
Decision tree for choosing appropriate discount formula
Types of Discounts
Different types of discounts serve various business purposes. Understanding these types helps in solving real-world discount problems and business situations.
Notes
Important to distinguish between discount types
Topic
Discount Types
Slide Id
S11
Visual Type
mermaid
Image Prompt
Slide Number
11
Mermaid Diagram
Code
mindmap root((Discount Types)) Trade Discount Distributor to Retailer Business to Business Not for End Customer Quantity Discount Bulk Purchases Volume Based Economies of Scale Promotional Discount New Products Stock Clearance Marketing Strategy Seasonal Discount Holiday Sales End of Season Time Limited
Type
mermaid_mindmap
Description
Mind map showing different types of discounts and their characteristics
Simple Interest: Basic Concepts
Simple interest is the most basic form of interest calculation, used in many loans and investments. Unlike compound interest, it doesn't earn interest on previously earned interest.
Notes
Emphasize interest only on principal, not on interest
Topic
Simple Interest Basics
Slide Id
S12
Visual Type
mermaid
Image Prompt
Slide Number
12
Mermaid Diagram
Code
flowchart LR A[Principal ₱10000] --> B[Rate 8% per year] B --> C[Time 3 years] C --> D[Simple Interest Calculation] D --> E[Interest = P × R × T] E --> F[Only on Original Principal]
Type
mermaid_flowchart
Description
Components of simple interest calculation
Simple Interest Formulas and Applications
These formulas allow calculation of any unknown component when the other three are given. The maturity value represents the total amount to be received or paid.
Notes
Students need to identify what's given and what to find
Topic
Simple Interest Formulas
Slide Id
S13
Visual Type
mermaid
Image Prompt
Slide Number
13
Mermaid Diagram
Code
flowchart TD A{What to Find?} --> B[Interest I] A --> C[Principal P] A --> D[Rate R] A --> E[Time T] A --> F[Maturity Value F] B --> G[I = P × R × T] C --> H[P = I ÷ R × T] D --> I[R = I ÷ P × T] E --> J[T = I ÷ P × R] F --> K[F = P + I or P × 1 + RT]
Type
mermaid_flowchart
Description
Decision tree for choosing appropriate simple interest formula
Time Conversion in Interest Problems
Time conversion is critical in interest problems because the standard formula assumes annual rates and time in years. Incorrect time conversion leads to wrong answers.
Notes
Critical step often overlooked by students
Topic
Time Conversion
Slide Id
S14
Visual Type
mermaid
Image Prompt
Slide Number
14
Mermaid Diagram
Code
flowchart TD A[Time Given] --> B{Units?} B -->|Months| C[Divide by 12] B -->|Days| D[Divide by 365] B -->|Quarters| E[Divide by 4] B -->|Years| F[Use as is] C --> G[Time in Years] D --> G E --> G F --> G G --> H[Apply I = PRT Formula]
Type
mermaid_flowchart
Description
Time conversion process for simple interest calculations
Problem-Solving Strategies and Tips
Successful problem-solving requires systematic approach and careful attention to details. These strategies help avoid common errors and improve accuracy in examinations.
Notes
Emphasize systematic approach for exam success
Topic
Problem-Solving Strategy
Slide Id
S15
Visual Type
mermaid
Image Prompt
Slide Number
15
Mermaid Diagram
Code
flowchart TD A[Read Problem Carefully] --> B[Identify Problem Type] B --> C[List Given Information] C --> D[Identify What to Find] D --> E[Check Units] E --> F[Choose Appropriate Formula] F --> G[Substitute and Calculate] G --> H[Verify Answer] H --> I{Reasonable?} I -->|Yes| J[Final Answer] I -->|No| K[Check Calculations] K --> G
Type
mermaid_flowchart
Description
Universal problem-solving strategy for all word problem types
References
- Civil Service Institute Civil Service Complete Exam Reviewer - Numerical Ability Section
- NEW CURRICULUM CIVIL SERVICE 2026 EDITION - Word Problems Chapter
- NCV CIVIL SERVICE - Worded Problems Practice Materials
- Philippine Civil Service Commission Examination Guidelines
In summary
Mastering word problems in speed/distance/time, age, discount, and simple interest requires understanding fundamental formulas, systematic problem-solving approaches, and consistent practice. These problem types are essential for success in Philippine entrance examinations and civil service tests. Remember to always identify what is given and what to find, convert units appropriately, and verify that your answers are reasonable. Regular practice with varied problem types will build confidence and speed in examinations.
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