Civil Service Exam (Subprofessional) Numerical Ability — Word Problems — Speed/Distance/Age, Discount & InterestRevision Notes

Formulas

Exam Tips

• Always identify what is given and what needs to be found
• Create a table for complex problems with multiple speeds or times
• Remember: Distance has units like km, m; Speed has units like km/hr, m/s; Time has units like hr, min
• For average speed problems, never add the speeds - always use total distance ÷ total time

Key Points

• Speed is the distance traveled per unit time (Speed = Distance ÷ Time)
• Distance is the total path covered (Distance = Speed × Time)
• Time is the duration of travel (Time = Distance ÷ Speed)
• Average speed = Total distance ÷ Total time (for round trips or multiple segments)
• Unit conversions: 1 km/hr = 5/18 m/s, 1 m/s = 18/5 km/hr
• For problems with two different speeds, create a table with distance, speed, and time for each segment

Definitions

Section Title

Speed, Distance, and Time Problems

Common Mistakes

• Adding speeds instead of using the average speed formula for round trips
• Forgetting to convert units (hours to minutes, km/hr to m/s)
• Not creating a systematic table for multi-segment journeys
• Confusing distance with displacement in physics contexts

Formulas

Exam Tips

• Create a table with columns for each person and rows for different time periods
• Clearly define your variable (usually the present age of one person)
• Check your final answer by substituting back into the original problem
• Age problems often have two equations that need to be solved simultaneously

Key Points

• Age problems involve relationships between people's ages at different times
• Present age, past age (n years ago), and future age (n years later) are key concepts
• If present age is x, then: Past age = x - n, Future age = x + n
• Age ratios: If ages are in ratio a:b, then ages are ax and bx
• Set up equations based on the given relationships between ages
• Use variables to represent unknown ages and solve systematically

Definitions

Section Title

Age Word Problems

Common Mistakes

• Confusing past and future age calculations (adding instead of subtracting)
• Not maintaining consistency in time periods across all people in the problem
• Forgetting to check if the solution makes logical sense (negative ages, etc.)
• Setting up incorrect equations from complex word relationships

Formulas

Exam Tips

• Always identify which values are given: list price, selling price, discount amount, or discount %
• Remember: Discount % is always calculated based on the list price, not selling price
• Check if your discount percentage makes sense (should be less than 100%)
• Practice both methods: direct calculation and using (100% - discount%) approach

Key Points

• Discount is the reduction in the original price of an item
• List price (marked price) is the original tagged price
• Selling price is the actual price paid after discount
• Discount can be expressed as amount (₱) or percentage (%)
• Types: Trade discount, quantity discount, promotional discount
• Alternative calculation: Selling price = List price × (100% - Discount%)

Definitions

Section Title

Discount Problems

Common Mistakes

• Confusing discount amount with discount percentage
• Using selling price instead of list price in percentage calculations
• Forgetting to convert percentage to decimal form in calculations
• Not distinguishing between different types of discounts in complex problems

Formulas

Exam Tips

• Always convert percentage to decimal and time to years before calculating
• For simple interest: I = Prt, then F = P + I
• For compound interest: F = P(1 + r)ᵗ, then I = F - P
• Remember: Simple interest grows linearly, compound interest grows exponentially
• Check units: P and F in pesos, r as decimal, t in years, I in pesos

Key Points

• Simple interest is calculated only on the principal amount
• Compound interest is calculated on principal plus accumulated interest
• Principal (P) is the original amount borrowed or invested
• Rate (r) is the annual interest rate (convert % to decimal)
• Time (t) must be expressed in years
• Maturity/Future value is the total amount after interest
• Simple interest: I = Prt, Future value: F = P + I or F = P(1 + rt)
• Compound interest: F = P(1 + r)ᵗ, Interest: I = F - P

Definitions

Section Title

Interest Problems (Simple and Compound)

Common Mistakes

• Forgetting to convert percentage rates to decimal form (divide by 100)
• Not converting months to years (divide months by 12)
• Using simple interest formula when compound interest is required
• Confusing interest amount with total maturity value
• Incorrect calculation of compound interest exponents