Civil Service Exam (Subprofessional) Numerical Ability — Word Problems — Speed/Distance/Age, Discount & InterestCheat Sheet
Word Problems — Speed/Distance/Age, Discount & Interest cheat sheet for Civil Service Exam (Subprofessional) aspirants. If you could only take one sheet of paper into your review session, this is what it would look like. Civil Service Commission (CSC)'s most-tested concepts, all in one place.
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 Word Problems — Speed/Distance/Age, Discount & Interest appears in position 6th 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.
Word Problems — Speed/Distance/Age, Discount & Interest - Cheat sheet
Your last-minute revision companion for mastering word problems in speed, distance, time, age, discount, and interest calculations — essential for CSE, UPCAT, and other entrance exams.
Sections
Formulas
Formula
Speed = Distance ÷ Time
Meaning
Speed (km/h or m/s), Distance (km or m), Time (hours or seconds)
Watch Out
Check units! Convert km/h to m/s by multiplying by 5/18
When To Use
When finding how fast something moves
Formula
Distance = Speed × Time
Meaning
Distance (km or m), Speed (km/h or m/s), Time (hours or seconds)
Watch Out
Ensure speed and time units match (hours with hours, seconds with seconds)
When To Use
When finding how far something traveled
Formula
Time = Distance ÷ Speed
Meaning
Time (hours or seconds), Distance (km or m), Speed (km/h or m/s)
Watch Out
Convert minutes to hours by dividing by 60, not multiplying
When To Use
When finding how long a journey takes
Formula
Average Speed = Total Distance ÷ Total Time
Meaning
For round trips or multiple segments
Watch Out
Never just average the two speeds — must use total distance over total time
When To Use
When different speeds are used for different parts of journey
Common Values
Value
5 km/h
Symbol
v
Quantity
Walking speed
Value
10-15 km/h
Symbol
v
Quantity
Running speed
Value
40-60 km/h
Symbol
v
Quantity
Car speed (city)
Section Title
Speed, Distance, and Time
Important Facts
- 1 km/h = 5/18 m/s (multiply by 5/18)
- 1 m/s = 18/5 km/h (multiply by 18/5)
- 1 hour = 60 minutes = 3600 seconds
- When solving round trips, calculate time for each segment separately
- Speed is always positive in physics problems
Key Definitions
Term
Speed
Example
60 km/h means 60 km in 1 hour
Definition
Distance covered per unit time
Term
Average Speed
Example
100 km in 2 hours = 50 km/h average
Definition
Total distance divided by total time for entire journey
Diagrams To Know
- Speed-Distance-Time triangle
- Unit conversion charts
Formulas
Formula
Present Age = x, Age after n years = x + n
Meaning
x = current age, n = number of years in future
Watch Out
Add for future ages, subtract for past ages
When To Use
When dealing with future ages
Formula
Present Age = x, Age n years ago = x - n
Meaning
x = current age, n = number of years in past
Watch Out
Don't mix up past and future — ago means subtract
When To Use
When dealing with past ages
Formula
Ratio Ages: a:b = ax:bx
Meaning
Ages in ratio a:b are ax and bx where x is common factor
Watch Out
Both ages must use same multiplier x
When To Use
When ages are given in ratio form
Section Title
Age Problems
Important Facts
- Set up equations for each time period mentioned
- Use same variable for same person across all time periods
- Age difference between two people remains constant over time
- If A is n years older than B now, A will always be n years older than B
- Check your answer by substituting back into original conditions
Key Definitions
Term
Present Age
Example
If John is 20 now, his present age is 20
Definition
Current age at the time of solving
Term
Age Ratio
Example
3:2 means first person is 1.5 times older
Definition
Proportion of one age to another
Diagrams To Know
- Age timeline showing past, present, and future
- Age relationship tables
Formulas
Formula
Discount = List Price - Selling Price
Meaning
Discount (amount saved), List Price (original price), Selling Price (final price)
Watch Out
List price is always higher than selling price
When To Use
When finding the peso amount of discount
Formula
Discount % = (Discount ÷ List Price) × 100
Meaning
Discount % (percentage), Discount (peso amount), List Price (original price)
Watch Out
Divide by list price, not selling price
When To Use
When finding percentage discount
Formula
Selling Price = List Price × (100% - Discount%)
Meaning
Alternative way to find selling price directly
Watch Out
Convert percentage to decimal (20% = 0.20)
When To Use
When discount percentage is given
Formula
Discount Amount = List Price × Discount Rate
Meaning
Direct calculation of discount in pesos
Watch Out
Convert percentage to decimal before multiplying
When To Use
When discount rate is given as percentage
Common Values
Value
10%, 15%, 20%, 25%, 50%
Symbol
d%
Quantity
Common discount rates
Section Title
Discount Problems
Important Facts
- Discount is always calculated from the original list price
- Selling Price = List Price - Discount Amount
- A 20% discount means you pay 80% of the original price
- Trade discount is for retailers, not end customers
- Quantity discount applies when buying in bulk
Key Definitions
Term
List Price
Example
₱1,500 marked on price tag
Definition
Original marked price before any discount
Term
Selling Price
Example
₱1,200 after 20% discount
Definition
Final price after discount is applied
Term
Discount Rate
Example
20% off means 0.20 discount rate
Definition
Percentage reduction from list price
Diagrams To Know
- Price breakdown showing list price, discount, and selling price
- Percentage circle showing discount portion
Formulas
Formula
I = PRT
Meaning
Interest (₱), Principal (₱), Rate (decimal), Time (years)
Watch Out
Convert percentage rate to decimal (5% = 0.05)
When To Use
Basic simple interest calculation
Formula
P = I ÷ (RT)
Meaning
Finding principal when interest, rate, and time are known
Watch Out
Time must be in years, convert months by dividing by 12
When To Use
When principal is unknown
Formula
R = I ÷ (PT)
Meaning
Finding rate when interest, principal, and time are known
Watch Out
Result will be in decimal form, multiply by 100 for percentage
When To Use
When interest rate is unknown
Formula
T = I ÷ (PR)
Meaning
Finding time when interest, principal, and rate are known
Watch Out
Result will be in years, multiply by 12 for months
When To Use
When time period is unknown
Formula
F = P + I or F = P(1 + RT)
Meaning
Future Value (maturity value), Principal, Interest or combined formula
Watch Out
Don't forget to add principal to interest for total amount
When To Use
When finding total amount after interest
Common Values
Value
0.5% - 2% annually
Symbol
r
Quantity
Typical savings rates
Value
5% - 15% annually
Symbol
r
Quantity
Typical loan rates
Section Title
Simple Interest
Important Facts
- Simple interest is calculated only on the original principal
- Time must be converted to years (months ÷ 12)
- Rate must be in decimal form for calculations
- Interest earned each year is the same in simple interest
- Maturity value = Principal + Total Interest
Key Definitions
Term
Principal
Example
₱10,000 initial deposit
Definition
Original amount invested or borrowed
Term
Simple Interest
Example
₱500 interest on ₱10,000 at 5% for 1 year
Definition
Interest calculated only on principal amount
Term
Maturity Value
Example
₱10,500 after 1 year (₱10,000 + ₱500)
Definition
Principal plus accumulated interest
Term
Interest Rate
Example
5% per year means 0.05 in calculations
Definition
Annual percentage charged or earned
Diagrams To Know
- Simple interest timeline showing constant interest per year
- Principal-Interest-Maturity value breakdown
Formulas
Formula
F = P(1 + r)^t
Meaning
Future Value, Principal, Rate (decimal), Time (years)
Watch Out
Use parentheses correctly, calculate (1 + r) first, then raise to power t
When To Use
Finding maturity value with compound interest
Formula
P = F ÷ (1 + r)^t
Meaning
Finding principal when future value is known
Watch Out
This is the reverse of compound interest formula
When To Use
Present value calculations
Formula
Ic = F - P
Meaning
Compound Interest = Future Value - Principal
Watch Out
Don't confuse with simple interest calculation
When To Use
Finding the interest earned
Section Title
Compound Interest
Important Facts
- Compound interest grows faster than simple interest
- Interest is calculated on increasing principal each year
- Future value includes both principal and all accumulated interest
- Rate must be in decimal form (5% = 0.05)
- Time must be in years for annual compounding
Key Definitions
Term
Compound Interest
Example
Interest earns interest each year
Definition
Interest calculated on principal plus accumulated interest
Term
Compounding
Example
Year 1: ₱100 becomes ₱105, Year 2: ₱105 becomes ₱110.25
Definition
Process where interest is added to principal for next calculation
Diagrams To Know
- Compound vs simple interest growth comparison
- Year-by-year compound interest breakdown
Must Remember
- Speed = Distance ÷ Time (remember the triangle: cover what you're solving for)
- Average speed = Total distance ÷ Total time (never average the speeds directly)
- Age difference between people stays constant over time
- Discount % = (Discount amount ÷ List price) × 100
- Simple Interest: I = PRT (P = principal, R = rate as decimal, T = time in years)
- Compound Interest: F = P(1 + r)^t (don't forget the exponent)
- Convert months to years by dividing by 12
- Convert percentage to decimal by dividing by 100
- Always check units match before calculating
- Selling price = List price - Discount amount
Last Minute Tips
- Draw timelines for age problems to visualize relationships clearly
- For speed problems, write D-S-T in a triangle and cover what you're solving for
- In discount problems, identify which price is the 'base' for percentage calculations
- For compound interest, use calculator for (1 + r)^t — don't try to do large exponents mentally
- Always substitute your answer back into the original problem to verify it makes sense
Comparison Tables
Rows
Values
- Principal only
- Principal + accumulated interest
Property
Interest calculated on
Values
- I = PRT
- F = P(1 + r)^t
Property
Formula
Values
- Linear (constant)
- Exponential (accelerating)
Property
Growth pattern
Values
- Same each year
- Increases each year
Property
Interest per year
Columns
- Feature
- Simple Interest
- Compound Interest
Table Title
Simple vs Compound Interest
Rows
Values
- ÷ 12
- × 1
- × 30
Property
Months
Values
- ÷ 365
- ÷ 30
- × 1
Property
Days
Values
- × 1
- × 12
- × 365
Property
Years
Columns
- Unit
- Convert to Years
- Convert to Months
- Convert to Days
Table Title
Time Conversions
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