Civil Service Exam (Subprofessional) Numerical Ability — Ratio, Proportion & PercentageExam Answer Templates
Exam-style answer templates for Ratio, Proportion & Percentage — how to answer Civil Service Exam (Subprofessional) Numerical Ability questions when Civil Service Commission (CSC) asks about this chapter. Use these as your mental checklist on exam day.
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 Ratio, Proportion & Percentage is the 4th 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.
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.
Templates
Express the ratio 15:25 in its simplest form.
Marks
1
Topic
Ratio
Difficulty
easy
Template Id
T1
Examiner Tip
Always check if your answer can be simplified further
Model Answer
15:25 = 15÷5 : 25÷5 = 3:5
Question Type
very_short_answer
Answer Structure
- Find the common factor and divide both terms by it [1 mark]
Scoring Breakdown
Marks
1
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
Marks
2
Topic
Proportion
Difficulty
easy
Template Id
T2
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
Question Type
short_answer
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
Marks
1
Criteria
Correct cross-multiplication setup
Marks
1
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?
Marks
2
Topic
Percentage - Finding Rate
Difficulty
easy
Template Id
T3
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%
Question Type
short_answer
Answer Structure
- Line 1: State the formula for finding percentage [1 mark]
- Line 2: Substitute values and calculate [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct formula identification and setup
Marks
1
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?
Marks
3
Topic
Percentage - Finding Base/Original Price
Difficulty
medium
Template Id
T4
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.
Question Type
short_answer
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
Marks
1
Criteria
Correct understanding that sale price = 80% of original
Marks
1
Criteria
Correct equation setup: 0.80x = 800
Marks
1
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?
Marks
2
Topic
Percentage - Finding Rate
Difficulty
easy
Template Id
T5
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%
Question Type
short_answer
Answer Structure
- Line 1: Find number of girls by subtraction [1 mark]
- Line 2: Calculate percentage using formula [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct calculation of number of girls
Marks
1
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?
Marks
2
Topic
Proportion
Difficulty
easy
Template Id
T6
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
Question Type
short_answer
Answer Structure
- Line 1: Set up proportion correctly [1 mark]
- Line 2: Cross-multiply and solve [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct proportion setup
Marks
1
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?
Marks
3
Topic
Proportion - Rate and Time
Difficulty
medium
Template Id
T7
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.
Question Type
short_answer
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
Marks
1
Criteria
Correct speed calculation
Marks
1
Criteria
Correct use of distance formula
Marks
1
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.
Marks
3
Topic
Ratio - Finding Unknown Terms
Difficulty
medium
Template Id
T8
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
Question Type
short_answer
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
Marks
1
Criteria
Correct setup with common factor x
Marks
1
Criteria
Correct calculation of x = 7
Marks
1
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.
Marks
5
Topic
Percentage - Profit and Loss
Difficulty
hard
Template Id
T9
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
Question Type
long_answer
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
Marks
1
Criteria
Correct marked price calculation
Marks
1.5
Criteria
Correct selling price after discount
Marks
1.5
Criteria
Correct profit equation setup
Marks
1
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?
Marks
5
Topic
Ratio - Mixture Problems
Difficulty
hard
Template Id
T10
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.
Question Type
long_answer
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
Marks
2
Criteria
Correct calculation of initial milk and water quantities
Marks
1
Criteria
Understanding that for 1:1 ratio, milk = water
Marks
1
Criteria
Correct calculation of additional water
Marks
1
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.
Marks
1
Topic
Percentage - Basic Conversion
Difficulty
easy
Template Id
T11
Examiner Tip
To convert decimal to percentage, multiply by 100 and add % sign
Model Answer
0.375 × 100% = 37.5%
Question Type
very_short_answer
Answer Structure
- Multiply decimal by 100 and add % sign [1 mark]
Scoring Breakdown
Marks
1
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.
Marks
2
Topic
Percentage - Finding Base
Difficulty
easy
Template Id
T12
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.
Question Type
short_answer
Answer Structure
- Line 1: Set up equation with unknown [1 mark]
- Line 2: Solve for the unknown [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct equation setup: 0.24x = 96
Marks
1
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.
Marks
3
Topic
Percentage - Increase/Decrease
Difficulty
medium
Template Id
T13
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%.
Question Type
short_answer
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
Marks
1
Criteria
Correct calculation of increase = 15,000
Marks
1
Criteria
Correct formula for percentage increase
Marks
1
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.
Marks
3
Topic
Ratio - Three Terms
Difficulty
medium
Template Id
T14
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.
Question Type
short_answer
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
Marks
1
Criteria
Correct setup with 2x, 3x, 5x
Marks
1
Criteria
Correct calculation of x = 20
Marks
1
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?
Marks
2
Topic
Percentage - Applications
Difficulty
easy
Template Id
T15
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.
Question Type
short_answer
Answer Structure
- Line 1: Calculate marks scored using percentage [1 mark]
- Line 2: Find marks lost by subtraction [1 mark]
Scoring Breakdown
Marks
1
Criteria
Correct calculation of marks scored = 102
Marks
1
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
Dos
- Show the key calculation step
- Include proper units/symbols
- Write answer clearly
Donts
- Over-explain simple concepts
- Skip the calculation step
- Forget units or % signs
Marks
1
Strategy
Direct application of formula or simple calculation. No need for detailed explanation.
Expected Length
1 line with calculation
Time Allocation
30-45 seconds
Dos
- State the formula used
- Show substitution of values
- Calculate step-by-step
Donts
- Jump to final answer
- Use wrong formula
- Make arithmetic errors
Marks
2
Strategy
Show formula/method and calculation. Brief explanation may earn partial marks.
Expected Length
2-3 lines
Time Allocation
1-2 minutes
Dos
- Identify given information
- Show all calculation steps
- State final answer clearly
- Use proper mathematical language
Donts
- Skip intermediate steps
- Use unclear notation
- Forget to conclude properly
Marks
3
Strategy
Include problem interpretation, method selection, detailed calculation, and clear conclusion.
Expected Length
4-5 lines
Time Allocation
2-3 minutes
Dos
- Define variables clearly
- Show complete working
- Explain each major step
- Verify answer makes sense
- Present solution logically
Donts
- Rush through steps
- Use shortcuts without explanation
- Make computational errors
- Present disorganized working
Marks
5
Strategy
Comprehensive solution with clear problem understanding, systematic approach, detailed working, and verification if possible.
Expected Length
6-8 lines
Time Allocation
4-6 minutes
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
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