Ratio, Proportion & Percentage - Exam Answer Templates
Proper answer writing is crucial for scoring maximum marks in Ratio, Proportion & Percentage questions. These templates show you exactly how to structure your answers for different mark allocations, what key phrases to include, and how to avoid common mistakes that cost valuable marks in competitive exams like UPCAT, CSE, LET, and other Philippine entrance tests.
Answer templates
Express the ratio 15:25 in its simplest form.
Examiner tip
Always check if your answer can be simplified further
Model answer
15:25 = 15÷5 : 25÷5 = 3:5
Answer structure
- Find the common factor and divide both terms by it [1 mark]
Scoring breakdown
Criteria
Correct simplification by finding GCD and dividing both terms
Common mark deductions
- Not finding the highest common factor
- Arithmetic errors in division
Key phrases to include
- GCD
- simplest form
- divide by common factor
Find the value of x if 4:x = 12:15
Examiner tip
Always verify your answer by substituting back into the original proportion
Model answer
Given: 4:x = 12:15
Cross-multiplying: 4 × 15 = 12 × x
60 = 12x
x = 60 ÷ 12 = 5
Answer structure
- Line 1: Write the given proportion [0.5 marks]
- Line 2: Cross-multiply correctly [1 mark]
- Line 3: Solve for x with correct arithmetic [0.5 marks]
Scoring breakdown
Criteria
Correct cross-multiplication setup
Criteria
Correct solving and final answer
Common mark deductions
- Wrong cross-multiplication
- Arithmetic errors
- Not showing steps
Key phrases to include
- cross-multiply
- given proportion
- solve for x
What percentage of 250 is 75?
Examiner tip
Always include the % sign in your final answer for percentage questions
Model answer
To find: What percentage of 250 is 75?
Formula: Percentage = (Part/Whole) × 100%
Percentage = (75/250) × 100%
Percentage = 0.3 × 100% = 30%
Answer structure
- Line 1: State the formula for finding percentage [1 mark]
- Line 2: Substitute values and calculate [1 mark]
Scoring breakdown
Criteria
Correct formula identification and setup
Criteria
Correct calculation and final answer with % sign
Common mark deductions
- Forgetting the % sign
- Wrong formula
- Calculation errors
Key phrases to include
- percentage formula
- part/whole
- multiply by 100%
A shirt costs ₱800 after a 20% discount. What was the original price?
Examiner tip
Remember that after a 20% discount, you pay 80% of the original price
Model answer
Given: Sale price = ₱800, Discount = 20%
Let original price = x
After 20% discount, selling price = 80% of original price
0.80x = 800
x = 800 ÷ 0.80 = ₱1,000
Therefore, the original price was ₱1,000.
Answer structure
- Line 1: Identify given information [0.5 marks]
- Line 2: Set up equation using discount relationship [1 mark]
- Line 3: Solve for original price [1 mark]
- Line 4: State final answer clearly [0.5 marks]
Scoring breakdown
Criteria
Correct understanding that sale price = 80% of original
Criteria
Correct equation setup: 0.80x = 800
Criteria
Correct calculation and final answer
Common mark deductions
- Wrong percentage calculation
- Not understanding discount concept
- Missing currency symbol
Key phrases to include
- original price
- after discount
- let x be
- therefore
In a school of 800 students, 320 are boys. What percentage are girls?
Examiner tip
Always find the actual number before calculating percentage
Model answer
Total students = 800
Boys = 320
Girls = 800 - 320 = 480
Percentage of girls = (480/800) × 100% = 60%
Answer structure
- Line 1: Find number of girls by subtraction [1 mark]
- Line 2: Calculate percentage using formula [1 mark]
Scoring breakdown
Criteria
Correct calculation of number of girls
Criteria
Correct percentage calculation
Common mark deductions
- Not finding girls first
- Wrong subtraction
- Missing % sign
Key phrases to include
- total students
- number of girls
- percentage formula
If 5 notebooks cost ₱125, how much will 8 notebooks cost?
Examiner tip
Make sure the ratio maintains the same order (notebooks to cost)
Model answer
Given: 5 notebooks cost ₱125
Using proportion: 5:125 = 8:x
Cross-multiplying: 5x = 125 × 8
5x = 1000
x = ₱200
Answer structure
- Line 1: Set up proportion correctly [1 mark]
- Line 2: Cross-multiply and solve [1 mark]
Scoring breakdown
Criteria
Correct proportion setup
Criteria
Correct cross-multiplication and answer
Common mark deductions
- Wrong proportion setup
- Arithmetic errors
- Missing currency symbol
Key phrases to include
- proportion
- cross-multiply
- given
A car travels 240 km in 4 hours. At the same speed, how far will it travel in 7 hours?
Examiner tip
Always include proper units (km, hours, km/hr) in your answer
Model answer
Given: Distance = 240 km in 4 hours
Speed = 240 ÷ 4 = 60 km/hr
Distance in 7 hours = Speed × Time
Distance = 60 × 7 = 420 km
Therefore, the car will travel 420 km in 7 hours.
Answer structure
- Line 1: Calculate speed from given data [1 mark]
- Line 2: Use speed to find distance in 7 hours [1 mark]
- Line 3: State final answer clearly [1 mark]
Scoring breakdown
Criteria
Correct speed calculation
Criteria
Correct use of distance formula
Criteria
Correct final answer with proper unit
Common mark deductions
- Not calculating speed first
- Wrong formula
- Missing units
Key phrases to include
- speed
- distance formula
- same speed
- therefore
The ratio of boys to girls in a class is 3:4. If there are 21 boys, find the number of girls and total students.
Examiner tip
Always verify your answer by checking if the ratio is maintained
Model answer
Given: Boys:Girls = 3:4, Number of boys = 21
Let the common factor be x
Then boys = 3x and girls = 4x
Since boys = 21: 3x = 21
x = 7
Number of girls = 4x = 4 × 7 = 28
Total students = 21 + 28 = 49
Answer structure
- Line 1: Set up the ratio with common factor [1 mark]
- Line 2: Find the common factor using given information [1 mark]
- Line 3: Calculate girls and total students [1 mark]
Scoring breakdown
Criteria
Correct setup with common factor x
Criteria
Correct calculation of x = 7
Criteria
Correct final answers for girls and total
Common mark deductions
- Not using common factor method
- Arithmetic errors
- Forgetting to find total
Key phrases to include
- common factor
- let x be
- ratio
- total students
A shopkeeper marks an item 40% above cost price and gives a discount of 15%. If he makes a profit of ₱85, find the cost price.
Examiner tip
Break down the problem step by step and clearly show the relationship between cost, marked, and selling prices
Model answer
Let the cost price = ₱x
Marked price = Cost price + 40% of cost price
Marked price = x + 0.40x = 1.40x
Selling price = Marked price - 15% discount
Selling price = 1.40x - (0.15 × 1.40x)
Selling price = 1.40x - 0.21x = 1.19x
Profit = Selling price - Cost price
85 = 1.19x - x
85 = 0.19x
x = 85 ÷ 0.19 = ₱447.37
Therefore, the cost price is ₱447.37
Answer structure
- Line 1: Define variable for cost price [0.5 marks]
- Line 2: Express marked price in terms of cost price [1 mark]
- Line 3: Express selling price after discount [1.5 marks]
- Line 4: Set up profit equation [1 mark]
- Line 5: Solve for cost price [1 mark]
Scoring breakdown
Criteria
Correct marked price calculation
Criteria
Correct selling price after discount
Criteria
Correct profit equation setup
Criteria
Correct final calculation and answer
Common mark deductions
- Wrong percentage calculations
- Not showing all steps
- Arithmetic errors
- Wrong profit formula
Key phrases to include
- let cost price be
- marked price
- selling price
- profit equation
In a mixture of 60 liters, the ratio of milk to water is 2:1. How much water should be added to make the ratio 1:1?
Examiner tip
Remember that when adding water, only the water quantity changes, milk remains constant
Model answer
Given: Total mixture = 60 liters, Milk:Water = 2:1
Let the common factor be x
Milk = 2x, Water = x
Total = 2x + x = 3x = 60
x = 20
Initial milk = 2 × 20 = 40 liters
Initial water = 1 × 20 = 20 liters
For ratio 1:1, milk = water
Since milk remains 40 liters, water should also be 40 liters
Water to be added = 40 - 20 = 20 liters
Therefore, 20 liters of water should be added.
Answer structure
- Line 1: Find initial quantities using ratio [2 marks]
- Line 2: Determine required water for 1:1 ratio [1 mark]
- Line 3: Calculate additional water needed [1 mark]
- Line 4: State final answer [1 mark]
Scoring breakdown
Criteria
Correct calculation of initial milk and water quantities
Criteria
Understanding that for 1:1 ratio, milk = water
Criteria
Correct calculation of additional water
Criteria
Clear final answer
Common mark deductions
- Wrong initial calculation
- Not understanding final ratio requirement
- Arithmetic errors
Key phrases to include
- common factor
- initial quantities
- ratio 1:1
- additional water
Express 0.375 as a percentage.
Examiner tip
To convert decimal to percentage, multiply by 100 and add % sign
Model answer
0.375 × 100% = 37.5%
Answer structure
- Multiply decimal by 100 and add % sign [1 mark]
Scoring breakdown
Criteria
Correct conversion to percentage
Common mark deductions
- Forgetting % sign
- Wrong multiplication
Key phrases to include
- multiply by 100
- percentage
If 24% of a number is 96, find the number.
Examiner tip
Convert percentage to decimal before setting up the equation
Model answer
Let the number be x
24% of x = 96
0.24x = 96
x = 96 ÷ 0.24 = 400
Therefore, the number is 400.
Answer structure
- Line 1: Set up equation with unknown [1 mark]
- Line 2: Solve for the unknown [1 mark]
Scoring breakdown
Criteria
Correct equation setup: 0.24x = 96
Criteria
Correct calculation and final answer
Common mark deductions
- Wrong percentage conversion
- Division errors
- Not stating final answer clearly
Key phrases to include
- let the number be
- 24% of x
- therefore
The population of a city increased from 50,000 to 65,000. Find the percentage increase.
Examiner tip
Percentage increase = (Actual increase / Original value) × 100%
Model answer
Initial population = 50,000
Final population = 65,000
Increase = 65,000 - 50,000 = 15,000
Percentage increase = (Increase/Initial) × 100%
Percentage increase = (15,000/50,000) × 100% = 30%
Therefore, the percentage increase is 30%.
Answer structure
- Line 1: Find the actual increase [1 mark]
- Line 2: Apply percentage increase formula [1 mark]
- Line 3: Calculate and state final answer [1 mark]
Scoring breakdown
Criteria
Correct calculation of increase = 15,000
Criteria
Correct formula for percentage increase
Criteria
Correct final calculation and answer
Common mark deductions
- Wrong subtraction
- Using wrong formula
- Missing % sign
Key phrases to include
- increase
- percentage increase formula
- initial population
Three numbers are in the ratio 2:3:5. If their sum is 200, find the numbers.
Examiner tip
Always verify that your answers maintain the given ratio
Model answer
Given: Numbers are in ratio 2:3:5, Sum = 200
Let the numbers be 2x, 3x, and 5x
Sum = 2x + 3x + 5x = 10x = 200
x = 200 ÷ 10 = 20
First number = 2x = 2 × 20 = 40
Second number = 3x = 3 × 20 = 60
Third number = 5x = 5 × 20 = 100
Therefore, the numbers are 40, 60, and 100.
Answer structure
- Line 1: Express numbers in terms of common factor [1 mark]
- Line 2: Find common factor using sum condition [1 mark]
- Line 3: Calculate all three numbers [1 mark]
Scoring breakdown
Criteria
Correct setup with 2x, 3x, 5x
Criteria
Correct calculation of x = 20
Criteria
Correct final values of all three numbers
Common mark deductions
- Wrong setup
- Arithmetic errors
- Not finding all numbers
Key phrases to include
- let the numbers be
- common factor
- sum condition
A student scores 85% in an exam of 120 marks. How many marks did the student lose?
Examiner tip
Always double-check that marks scored + marks lost = total marks
Model answer
Total marks = 120
Marks scored = 85% of 120 = 0.85 × 120 = 102
Marks lost = Total marks - Marks scored
Marks lost = 120 - 102 = 18
Therefore, the student lost 18 marks.
Answer structure
- Line 1: Calculate marks scored using percentage [1 mark]
- Line 2: Find marks lost by subtraction [1 mark]
Scoring breakdown
Criteria
Correct calculation of marks scored = 102
Criteria
Correct calculation of marks lost = 18
Common mark deductions
- Wrong percentage calculation
- Subtraction errors
- Not clearly stating final answer
Key phrases to include
- marks scored
- marks lost
- 85% of 120
Mark wise strategy
Direct application of formula or simple calculation. No need for detailed explanation.
Do
- Show the key calculation step
- Include proper units/symbols
- Write answer clearly
Don't
- Over-explain simple concepts
- Skip the calculation step
- Forget units or % signs
Show formula/method and calculation. Brief explanation may earn partial marks.
Do
- State the formula used
- Show substitution of values
- Calculate step-by-step
Don't
- Jump to final answer
- Use wrong formula
- Make arithmetic errors
Include problem interpretation, method selection, detailed calculation, and clear conclusion.
Do
- Identify given information
- Show all calculation steps
- State final answer clearly
- Use proper mathematical language
Don't
- Skip intermediate steps
- Use unclear notation
- Forget to conclude properly
Comprehensive solution with clear problem understanding, systematic approach, detailed working, and verification if possible.
Do
- Define variables clearly
- Show complete working
- Explain each major step
- Verify answer makes sense
- Present solution logically
Don't
- Rush through steps
- Use shortcuts without explanation
- Make computational errors
- Present disorganized working
General answer writing tips
- Always write the formula or relationship first before substituting values
- Show all steps clearly - examiners award marks for correct method even if final answer is wrong
- Use proper mathematical notation and include units where applicable
- For percentage problems, clearly indicate whether you're finding rate, base, or percentage
- Cross-multiply correctly in proportion problems and show the calculation
- Round final answers appropriately and check if they make practical sense
- Label your final answer clearly and box it when possible
- For word problems, identify what is given and what is being asked before solving
Diagrams
Ratio Proportion and Percentage Concepts
Comprehensive mind map showing all major concepts in Ratio, Proportion, and Percentage with their key components and applications
Problem Solving Strategy for Percentage Questions
Step-by-step flowchart for solving percentage problems by first identifying what is being asked, then applying the appropriate formula
Cross Multiplication Method for Proportion
Systematic approach to solving proportion problems using cross multiplication, with verification step
Discount and Tax Calculation Process
State diagram showing the sequence of price transformations in complex discount and tax problems