Word Problems — Speed/Distance/Age, Discount & Interest - Exam Answer Templates
Proper answer writing is crucial for scoring maximum marks in Numerical Ability word problems. These templates show you exactly how to structure your answers for different mark values. Follow the step-by-step approach, use correct formulas, and show all calculations clearly to avoid mark deductions. Remember that word problems require both mathematical accuracy and clear presentation of your solution process.
Answer templates
A shopkeeper marks an item at ₱2,500 and offers a discount of 15%. Find the selling price.
Examiner tip
Always show the discount amount calculation separately before finding selling price
Model answer
Given: Marked Price = ₱2,500, Discount = 15%
Discount Amount = 15% of ₱2,500 = 0.15 × 2,500 = ₱375
Selling Price = Marked Price - Discount Amount = ₱2,500 - ₱375 = ₱2,125
Answer structure
- Line 1: Write given values and identify what to find [0.5 marks]
- Line 2: Calculate discount amount using percentage [1 mark]
- Line 3: Calculate selling price and state final answer [0.5 marks]
Scoring breakdown
Criteria
Correct calculation of discount amount
Criteria
Correct final selling price with proper units
Common mark deductions
- Not showing discount calculation step
- Incorrect percentage calculation
- Missing peso sign in answer
Key phrases to include
- Given
- Discount Amount
- Selling Price
- ₱
Find the simple interest on ₱8,000 at 6% per annum for 3 years.
Examiner tip
Always write the formula first, then substitute - this shows understanding
Model answer
Given: Principal (P) = ₱8,000, Rate (R) = 6% per annum, Time (T) = 3 years
Using Simple Interest formula: I = PRT/100
I = (8,000 × 6 × 3)/100 = 144,000/100 = ₱1,440
Answer structure
- Line 1: Write given values clearly [0.5 marks]
- Line 2: State the simple interest formula [0.5 marks]
- Line 3: Substitute values and calculate [1 mark]
Scoring breakdown
Criteria
Correct use of simple interest formula
Criteria
Accurate calculation and final answer
Common mark deductions
- Using wrong formula
- Calculation errors
- Not converting percentage properly
Key phrases to include
- Simple Interest formula
- I = PRT/100
- ₱
A car travels 240 km in 4 hours. What is its speed in km/h?
Examiner tip
For 1-mark questions, write formula and answer in one clean line
Model answer
Speed = Distance/Time = 240 km ÷ 4 hours = 60 km/h
Answer structure
- Single line: Apply speed formula and calculate [1 mark]
Scoring breakdown
Criteria
Correct application of speed formula with right answer and units
Common mark deductions
- Missing units
- Wrong formula
- Calculation error
Key phrases to include
- Speed =
- Distance/Time
- km/h
Ram is 3 times as old as his son. If the sum of their ages is 48 years, find their present ages.
Examiner tip
Always verify your answer by checking if it satisfies the original condition
Model answer
Let son's present age = x years
Then Ram's present age = 3x years
Given: Sum of their ages = 48 years
So, x + 3x = 48
4x = 48
x = 12
Therefore, Son's age = 12 years, Ram's age = 3 × 12 = 36 years
Answer structure
- Line 1: Define variable for unknown age [0.5 marks]
- Line 2-3: Set up equation based on given condition [1 mark]
- Line 4-5: Solve the equation [1 mark]
- Line 6: State both ages clearly [0.5 marks]
Scoring breakdown
Criteria
Correct variable assignment and equation setup
Criteria
Accurate solution of linear equation
Criteria
Both ages stated correctly with verification
Common mark deductions
- Not defining variables clearly
- Setting up wrong equation
- Not stating both final ages
Key phrases to include
- Let
- present age
- years
- Therefore
A train covers 300 km in 5 hours. On its return journey, it covers the same distance in 6 hours. Find the average speed for the entire journey.
Examiner tip
Remember: average speed is NOT the average of individual speeds - use total distance/total time
Model answer
Given: Distance each way = 300 km, Time for first journey = 5 hours, Time for return journey = 6 hours
Total distance covered = 300 + 300 = 600 km
Total time taken = 5 + 6 = 11 hours
Average speed = Total distance/Total time = 600/11 = 54.55 km/h (approximately)
Answer structure
- Line 1: Write all given information [0.5 marks]
- Line 2: Calculate total distance [0.5 marks]
- Line 3: Calculate total time [0.5 marks]
- Line 4: Apply average speed formula and calculate [1.5 marks]
Scoring breakdown
Criteria
Correct calculation of total distance and time
Criteria
Proper use of average speed formula
Criteria
Accurate final calculation with appropriate rounding
Common mark deductions
- Adding speeds instead of using distance/time
- Not considering return journey
- Incorrect formula usage
Key phrases to include
- Average speed
- Total distance
- Total time
- km/h
Find the compound interest on ₱5,000 at 8% per annum for 2 years.
Examiner tip
Show the exponential calculation step-by-step to avoid errors
Model answer
Given: Principal (P) = ₱5,000, Rate (R) = 8% per annum, Time (T) = 2 years
Using compound interest formula: A = P(1 + R/100)^T
A = 5,000(1 + 8/100)² = 5,000(1.08)² = 5,000 × 1.1664 = ₱5,832
Compound Interest = A - P = ₱5,832 - ₱5,000 = ₱832
Answer structure
- Line 1: Write given values [0.5 marks]
- Line 2: State compound interest formula [0.5 marks]
- Line 3: Calculate amount [1.5 marks]
- Line 4: Find compound interest by subtracting principal [0.5 marks]
Scoring breakdown
Criteria
Correct compound interest formula
Criteria
Accurate calculation of amount
Criteria
Correct final compound interest
Common mark deductions
- Using simple interest formula
- Calculation errors in exponents
- Not subtracting principal from amount
Key phrases to include
- Compound interest formula
- A = P(1 + R/100)^T
- Amount
- Compound Interest
The present age of a father is 42 years and his son is 14 years. After how many years will the father be twice as old as his son?
Examiner tip
Verify your answer by substituting back: Father will be 56, son will be 28, and 56 = 2 × 28 ✓
Model answer
Given: Father's present age = 42 years, Son's present age = 14 years
Let after x years, father will be twice as old as his son
Father's age after x years = 42 + x
Son's age after x years = 14 + x
According to condition: 42 + x = 2(14 + x)
42 + x = 28 + 2x
42 - 28 = 2x - x
14 = x
Therefore, after 14 years, the father will be twice as old as his son.
Answer structure
- Line 1: Write given information [0.5 marks]
- Line 2-3: Express ages after x years [0.5 marks]
- Line 4: Set up equation based on condition [1 mark]
- Line 5-7: Solve the equation [1 mark]
Scoring breakdown
Criteria
Correct setup of equation with variable
Criteria
Accurate solution of linear equation
Criteria
Clear statement of final answer
Common mark deductions
- Wrong equation setup
- Algebraic errors
- Not clearly stating the final answer
Key phrases to include
- Let
- after x years
- According to condition
- Therefore
What principal will amount to ₱8,800 in 3 years at 10% simple interest per annum?
Examiner tip
Remember that Amount = Principal + Interest, so derive the combined formula
Model answer
Given: Amount (A) = ₱8,800, Time (T) = 3 years, Rate (R) = 10% per annum
Using A = P + I and I = PRT/100
A = P + PRT/100 = P(1 + RT/100)
₱8,800 = P(1 + 10×3/100) = P(1 + 0.3) = 1.3P
P = ₱8,800 ÷ 1.3 = ₱6,769.23 (approximately)
Answer structure
- Line 1: Write given values [0.5 marks]
- Line 2-3: Use amount formula with simple interest [1 mark]
- Line 4: Calculate principal [0.5 marks]
Scoring breakdown
Criteria
Correct use of amount and simple interest relationship
Criteria
Accurate calculation of principal
Common mark deductions
- Using wrong formula
- Not combining amount and interest formulas properly
Key phrases to include
- Amount
- Principal
- Simple interest
- A = P + I
A cyclist covers 60 km in 4 hours. How much time will he take to cover 105 km at the same speed?
Examiner tip
Find speed first, then use it to calculate the required time
Model answer
Given: Distance₁ = 60 km, Time₁ = 4 hours, Distance₂ = 105 km
Speed = Distance₁/Time₁ = 60/4 = 15 km/h
Time₂ = Distance₂/Speed = 105/15 = 7 hours
Answer structure
- Line 1: Write given information [0.5 marks]
- Line 2: Calculate speed from first journey [0.75 marks]
- Line 3: Calculate time for second journey [0.75 marks]
Scoring breakdown
Criteria
Correct calculation of speed
Criteria
Correct application of speed to find time
Common mark deductions
- Not calculating speed first
- Direct proportion errors
Key phrases to include
- Speed =
- Distance/Time
- km/h
- hours
Find the rate of discount if the marked price is ₱5,000 and selling price is ₱4,250.
Examiner tip
Use the formula: Discount% = (Discount Amount/Marked Price) × 100
Model answer
Discount% = [(MP - SP)/MP] × 100 = [(5,000 - 4,250)/5,000] × 100 = (750/5,000) × 100 = 15%
Answer structure
- Single line: Apply discount percentage formula and calculate [1 mark]
Scoring breakdown
Criteria
Correct discount percentage formula and accurate calculation
Common mark deductions
- Wrong formula
- Calculation errors
- Missing percentage sign
Key phrases to include
- Discount%
- MP - SP
- %
A sum of money doubles itself in 8 years at simple interest. Find the rate of interest.
Examiner tip
When money 'doubles itself', the interest earned equals the principal amount
Model answer
Given: Amount = 2 × Principal (money doubles), Time = 8 years
Let Principal = P, then Amount = 2P
Simple Interest = Amount - Principal = 2P - P = P
Using I = PRT/100
P = P × R × 8/100
Canceling P from both sides: 1 = R × 8/100
R = 100/8 = 12.5%
Therefore, the rate of interest is 12.5% per annum.
Answer structure
- Line 1: Interpret 'doubles itself' condition [0.5 marks]
- Line 2-3: Calculate simple interest [0.5 marks]
- Line 4-6: Apply simple interest formula and solve for rate [1.5 marks]
- Line 7: State final answer [0.5 marks]
Scoring breakdown
Criteria
Understanding that doubling means A = 2P and I = P
Criteria
Correct application of simple interest formula
Criteria
Accurate calculation of interest rate
Common mark deductions
- Not understanding doubling condition
- Algebraic manipulation errors
Key phrases to include
- doubles itself
- Amount = 2P
- Simple Interest
- per annum
Two cars start from the same point and travel in opposite directions. Car A travels at 60 km/h and Car B at 80 km/h. After how much time will they be 420 km apart?
Examiner tip
For opposite directions, add the speeds; for same direction, subtract the speeds
Model answer
Given: Speed of Car A = 60 km/h, Speed of Car B = 80 km/h, Final distance apart = 420 km
Since cars travel in opposite directions, relative speed = 60 + 80 = 140 km/h
Distance covered by both cars together = 420 km
Time = Distance/Relative Speed = 420/140 = 3 hours
Therefore, they will be 420 km apart after 3 hours.
Answer structure
- Line 1: Write given information [0.5 marks]
- Line 2: Calculate relative speed for opposite directions [1 mark]
- Line 3-4: Apply time formula and calculate [1 mark]
- Line 5: State final answer [0.5 marks]
Scoring breakdown
Criteria
Understanding relative speed concept for opposite directions
Criteria
Correct calculation of relative speed
Criteria
Accurate time calculation
Common mark deductions
- Not adding speeds for opposite directions
- Using individual speeds instead of relative speed
Key phrases to include
- opposite directions
- relative speed
- Time =
- hours
A shopkeeper bought goods worth ₱8,000. He sold 60% of them at 25% profit and the remaining at 15% loss. Find his overall profit or loss percentage.
Examiner tip
Handle profit and loss parts separately, then combine for overall result
Model answer
Given: Total Cost Price = ₱8,000, 60% sold at 25% profit, 40% sold at 15% loss
Step 1: Calculate cost prices of both parts
CP of 60% goods = 60% of ₱8,000 = 0.6 × 8,000 = ₱4,800
CP of 40% goods = 40% of ₱8,000 = 0.4 × 8,000 = ₱3,200
Step 2: Calculate selling prices
SP of first part = CP + 25% profit = ₱4,800 + 0.25 × 4,800 = ₱4,800 + ₱1,200 = ₱6,000
SP of second part = CP - 15% loss = ₱3,200 - 0.15 × 3,200 = ₱3,200 - ₱480 = ₱2,720
Step 3: Calculate total selling price and profit/loss
Total SP = ₱6,000 + ₱2,720 = ₱8,720
Total CP = ₱8,000
Profit = SP - CP = ₱8,720 - ₱8,000 = ₱720
Step 4: Calculate profit percentage
Profit % = (Profit/CP) × 100 = (720/8,000) × 100 = 9%
Therefore, the shopkeeper has an overall profit of 9%.
Answer structure
- Step 1: Divide total cost into two parts [1 mark]
- Step 2: Calculate selling prices for both parts [2 marks]
- Step 3: Find total selling price and profit [1 mark]
- Step 4: Calculate overall profit percentage [1 mark]
Scoring breakdown
Criteria
Correct division of cost price
Criteria
Accurate calculation of both selling prices
Criteria
Correct total profit calculation
Criteria
Accurate overall profit percentage
Common mark deductions
- Not calculating parts separately
- Mixing up profit and loss calculations
- Incorrect percentage calculations
Key phrases to include
- Cost Price
- Selling Price
- Profit
- Loss
- Overall
- Therefore
At what rate percent per annum will ₱2,000 amount to ₱2,420 in 3 years at simple interest?
Examiner tip
Always find the interest amount first, then use the formula to find the unknown
Model answer
Given: Principal = ₱2,000, Amount = ₱2,420, Time = 3 years
Simple Interest = Amount - Principal = ₱2,420 - ₱2,000 = ₱420
Using I = PRT/100: 420 = (2,000 × R × 3)/100
420 = 6,000R/100 = 60R
R = 420/60 = 7%
Therefore, the rate is 7% per annum.
Answer structure
- Line 1: Write given values and find simple interest [0.5 marks]
- Line 2-4: Apply simple interest formula and solve for rate [1.5 marks]
Scoring breakdown
Criteria
Correct calculation of simple interest from amount
Criteria
Accurate solution for interest rate
Common mark deductions
- Not finding interest first
- Algebraic errors in solving for R
Key phrases to include
- Simple Interest
- I = PRT/100
- per annum
- %
Mark wise strategy
Direct formula application with minimal working. Write formula, substitute, and calculate in one smooth flow.
Do
- State formula clearly
- Show key calculation step
- Include proper units
- Write concisely
Don't
- Over-explain simple concepts
- Skip the formula
- Forget units in answer
- Make calculation errors
Show given values, apply formula, calculate step by step, and state final answer clearly.
Do
- List given information
- State relevant formula
- Show calculation steps
- Verify answer makes sense
Don't
- Rush through calculations
- Skip intermediate steps
- Mix up different formulas
- Forget to double-check
Systematic approach with clear steps: identify given, set up equations, solve methodically, and conclude.
Do
- Define variables clearly
- Set up equations properly
- Solve step by step
- State conclusion clearly
- Check answer
Don't
- Jump steps in algebra
- Use unclear variable names
- Make substitution errors
- Leave answer unverified
Break into logical steps, show all working, verify intermediate results, and present comprehensive solution.
Do
- Number steps clearly
- Show all calculations
- Verify each step
- Link steps logically
- Double-check final answer
Don't
- Skip explanation steps
- Make careless errors
- Rush the solution
- Forget to verify
- Use unclear presentation
General answer writing tips
- Always identify what is given and what needs to be found before starting calculations
- Write down the correct formula first, then substitute values
- Show all calculation steps clearly - examiners award marks for process
- Use proper units throughout your solution and in the final answer
- Double-check your answer by substituting back into the original problem
- For discount problems, clearly distinguish between discount amount and selling price
- In interest problems, convert time periods to years if the rate is annual
- For speed problems, ensure consistent units (convert if necessary before calculating)
Diagrams
Word Problems Overview
Mind map showing the four main categories of word problems covered in this chapter with their key subconcepts
Problem Solving Strategy
Step-by-step flowchart showing the systematic approach to solving word problems in numerical ability
Simple vs Compound Interest Decision
Decision flowchart to help students choose between simple and compound interest formulas