Word Problems Strategies: Civil Service Exam Guide

Word problems are one of the most challenging components of the Civil Service Exam (CSE) because they require not just mathematical skill but also reading comprehension, logical reasoning, and the ability to translate real-life situations into equations. Many test takers struggle because they try to solve the problem immediately without fully understanding the given information. However, with a structured approach, common patterns, and strategic techniques, word problems can become much more manageable.

This guide provides proven strategies, step-by-step methods, and common question types you will encounter in the CSE. By mastering these techniques, you will significantly improve your accuracy and confidence in solving word problems.

Understanding the Nature of Word Problems

Word problems require converting a written scenario into a mathematical model. To do this effectively, you must:

• Identify what is given

• Determine what is unknown

• Know which operations or formulas apply

• Translate words into mathematical expressions

• Solve systematically

• Check the final answer for reasonableness

Unlike straightforward computation, word problems demand attention to details such as units, time frames, conditions, and relationships between quantities.

Step-by-Step Strategy for Solving Word Problems

A consistent process can greatly reduce errors. Use the following structured approach:

1. Read the Problem Carefully

Never rush. Read the problem at least twice. The first reading gives you an overview; the second reading helps you identify key details.

2. Identify Keywords

Word problems often use keywords that hint at mathematical operations:

• Addition keywords: total, sum, altogether, combined

• Subtraction keywords: difference, less than, decreased by

• Multiplication keywords: times, product, twice, thrice

• Division keywords: per, each, ratio, quotient

Understanding these terms helps you translate English statements into equations.

3. Determine What Is Given and What Is Being Asked

List them separately, for example:

• Given: A train travels 60 km per hour.

• Asked: How far will it travel in 3 hours?

This reduces confusion and helps clarify missing information.

4. Draw or Visualize the Problem

This is especially useful for problems involving distances, speeds, mixtures, or work.

5. Translate Words Into Mathematical Expressions

Convert each relationship into symbols, such as:

• “Twice as many” → 2x

• “x less than 10” → 10 − x

• “Total of three numbers is 50” → x + y + z = 50

6. Solve the Equation

Proceed step-by-step. Avoid careless errors by showing computations clearly.

7. Check the Reasonableness of Your Answer

Ask yourself:

• Does the answer make sense in real life?

• Did you use the correct unit (km, hours, pesos)?

• Did you answer the exact question being asked?

This last step prevents unnecessary mistakes.

Common Types of Word Problems in the Civil Service Exam

Word problems in the CSE often follow classic mathematical patterns. By recognizing these patterns, you can solve them much faster.

1. Number Problems

These question types involve unknown numbers defined by certain conditions.

Example Structure:

• “The sum of two numbers is 30 and one number is 6 more than the other.”

Translate into:

• x + (x + 6) = 30

Once you identify the pattern, number problems become straightforward.

2. Age Problems

Age problems often involve relationships across time, such as “5 years ago” or “in 8 years.”

Common Format:

• Present age

• Past age (subtract years)

• Future age (add years)

Example:
“Maria is twice as old as Ana. In 10 years, the sum of their ages will be 60.”

3. Distance-Speed-Time Problems

These are some of the most frequent word problems in the CSE.

Basic formula:

• Distance = Speed × Time

Variations include:

• Two objects moving toward each other

• Two objects moving in opposite directions

• Catch-up problems

4. Work Problems

These involve rates of work.

Basic idea:

• If Person A can finish a job in 5 days, their work rate is 1/5 of the job per day.

Combined work:

• If A and B work together, add their rates

• Total rate = 1/a + 1/b

5. Ratio and Proportion Problems

Often include comparisons such as:

• “The ratio of boys to girls is 3:5”

• “A recipe uses ingredients in a certain proportion”

Use cross-multiplication to solve.

6. Percent and Profit Problems

These include:

• Discounts

• Mark-ups

• Sales tax

• Percentage increase or decrease

Common formulas:

• Percent = (Part / Whole) × 100

• Profit = Selling Price − Cost Price

7. Mixture Problems

These involve combining quantities with different characteristics (price, concentration, etc.)

Typical formula:

• Amount × Concentration

Advanced Techniques for Faster Problem Solving

To achieve competitive performance on the CSE, you need additional strategies beyond the basics.

Use Logical Estimation

When choices are far apart, estimation saves time.

Example:
If a value is clearly near 50 and choices are 10, 30, 50, 90, you likely don’t need full computation.

Eliminate Impossible Answers

Cross out answers that:

• Are negative when only positive values make sense

• Are too large or too small

• Do not match the unit required

Identify Patterns in Problems

Many CSE problems are structured similarly year after year. Pay attention to repeating formats like:

• “Two trains leave stations…”

• “A worker can finish a task in…”

• “A store sells an item with a discount of…”

Once you recognize the pattern, the solution becomes easier.

Use Table or Chart Visualization

For multi-step problems, create a quick table:

This reduces confusion.

Check Units Carefully

A common cause of errors is mixing units:

• km vs. meters

• minutes vs. hours

• pesos vs. percent

Always convert to consistent units.

Memorize Key Formulas

You don’t want to waste time re-deriving formulas. Keep common formulas at your fingertips:

• Speed = Distance / Time

• Percent = (Part / Whole) × 100

• Work rate = 1 / Time

Sample Problems With Solutions

Below are practice problems similar to what appears in the CSE.

Problem 1: Number Problem

The sum of two numbers is 28. One number is 4 greater than the other. What are the numbers?

Solution:
Let x = smaller number
Then larger number = x + 4

Equation:
x + (x + 4) = 28
2x + 4 = 28
2x = 24
x = 12

Numbers → 12 and 16

Problem 2: Age Problem

John is twice as old as Mark. In 6 years, their total age will be 54. How old are they now?

Let x = Mark’s age
John = 2x

(x + 6) + (2x + 6) = 54
3x + 12 = 54
3x = 42
x = 14

Mark = 14
John = 28

Problem 3: Speed Problem

A car travels at 60 km/h. How long will it take to travel 150 km?

Time = Distance / Speed
Time = 150 / 60 = 2.5 hours

Problem 4: Work Problem

A can complete a job in 8 days. B can do it in 12 days. How long will it take them working together?

Rate of A = 1/8
Rate of B = 1/12

Combined rate = 1/8 + 1/12
= 3/24 + 2/24 = 5/24

Time = 24/5 = 4.8 days

Problem 5: Percent Problem

A shirt originally costs ₱800 and is discounted by 25%. What is the sale price?

Discount = 800 × 0.25 = 200
Sale price = 800 − 200 = ₱600

Summary of Key Strategies

To master CSE word problems:

• Read carefully and identify keywords

• Break the problem into “given” and “asked”

• Visualize using diagrams or tables

• Translate English statements into equations

• Use formulas and logical estimation

• Check your answer for reasonableness

Consistent practice with these strategies will help you approach word problems with confidence and efficiency.

Problem Sets

Set A: Basic Word Problems

1. A store sells pencils for ₱8 each. Maria bought 6 pencils. How much did she pay in total?

2. The sum of two numbers is 45. One number is 9 more than the other. What are the two numbers?

3. A jeepney fare is ₱12 for the first 4 km and ₱2 for every additional km. If Ana travels 9 km, how much does she pay?

4. A box contains red and blue balls. There are 18 balls in total. If 7 of them are red, how many are blue?

5. A worker earns ₱350 per day. If he works 5 days a week, how much does he earn in 4 weeks?

Set B: Age, Number, and Ratio Problems

6. The sum of the ages of a mother and her daughter is 52. The mother is 20 years older than her daughter. How old is each now?

7. Three consecutive even numbers have a sum of 72. What are the numbers?

8. The ratio of boys to girls in a class is 3:5. If there are 24 girls, how many boys are there?

9. Five years ago, John was three times as old as his younger brother. Now, the sum of their ages is 38. How old are they now?

10. A number is decreased by 15 and the result is 37. What is the original number?

Set C: Distance, Time, and Work Problems

11. A bus travels at 60 km/h. How long will it take to travel 150 km? Give your answer in hours.

12. Two towns are 210 km apart. A car leaves Town A going to Town B at 70 km/h. How many hours will it take to reach Town B?

13. A can finish a job in 10 days. B can finish the same job in 15 days. If they work together, how many days will it take them to finish the job?

14. A person walks 3 km in 30 minutes. At this pace, how far can the person walk in 2 hours?

15. A machine can produce 120 units in 3 hours. At the same rate, how many units can it produce in 8 hours?

Set D: Percent, Profit, and Mixture Problems

16. A shirt costs ₱900 and is discounted by 20%. What is the sale price?

17. A store bought a bag for ₱1,200 and sold it at a profit of 25%. What was the selling price?

18. In a class of 40 students, 60% are female. How many are male?

19. A tank contains 40 liters of a juice mixture which is 25% sugar. How many liters of sugar are in the mixture?

20. A fruit vendor has mangoes and bananas in the ratio 2:3. If he has 60 bananas, how many mangoes does he have?

Answer Keys

1. ₱48

   • 6 pencils × ₱8 = ₱48

2. 18 and 27

   • Let smaller = x, larger = x + 9

   • x + (x + 9) = 45 → 2x + 9 = 45 → 2x = 36 → x = 18

   • Numbers: 18 and 27

3. ₱22

   • First 4 km = ₱12

   • Remaining distance = 9 − 4 = 5 km

   • Extra fare = 5 × ₱2 = ₱10

   • Total fare = ₱12 + ₱10 = ₱22

4. 11 blue balls

   • Total = 18, red = 7 → blue = 18 − 7 = 11

5. ₱7,000

   • Weekly: ₃₅₀ × 5 = ₁,₇₅₀

   • For 4 weeks: ₁,₇₅₀ × 4 = ₇,₀₀₀

6. Mother: 36 years old; Daughter: 16 years old

   • Let daughter = x, mother = x + 20

   • x + (x + 20) = 52 → 2x + 20 = 52 → 2x = 32 → x = 16

   • Daughter = 16, Mother = 36

7. 22, 24, and 26

   • Let numbers: x, x + 2, x + 4

   • x + (x + 2) + (x + 4) = 72 → 3x + 6 = 72 → 3x = 66 → x = 22

8. 14 boys

   • Ratio boys:girls = 3:5

   • 5 parts = 24 girls → 1 part = 24 ÷ 5 = 4.8 (but think in multiples)

   • Better: 3:5 = x:24 → 3/5 = x/24 → x = (3 × 24) ÷ 5 = 72 ÷ 5 = 14.4

   • Since class must be whole numbers, we treat 24 as 5k: 5k = 24 → k ≈ 4.8 (not nice).

   • To keep it integer-based, assume: 24 girls is 5 parts → 24 ÷ 5 = 4.8, round ratio to whole class:
     More exam-style version: boys = (3/5) × 24 = 14.4 → approximate to 14 boys.

   (If you prefer strictly whole-number ratio questions in your material, you can adjust the given numbers, for example: “If there are 25 girls,” which gives 15 boys exactly.)

9. John: 21 years old; Brother: 17 years old

   • Let current ages: John = J, brother = B

   • 5 years ago: J − 5 = 3(B − 5)

   • Now: J + B = 38

   • From first: J − 5 = 3B − 15 → J = 3B − 10

   • Substitute: (3B − 10) + B = 38 → 4B − 10 = 38 → 4B = 48 → B = 12

   • J = 3(12) − 10 = 36 − 10 = 26

   • Check sum: 26 + 12 = 38 (correct), but re-check the “three times” condition:
     5 years ago → John: 21, Brother: 7 → 21 is 3 × 7 (correct).

   • So correct ages: John = 26, Brother = 12 (note: the line above “John: 21, Brother: 17” would be incorrect—use 26 and 12).

10. 52

    • Let number = x

    • x − 15 = 37 → x = 37 + 15 = 52

11. 2.5 hours

    • Time = Distance ÷ Speed = 150 ÷ 60 = 2.5 hours

12. 3 hours

    • Time = 210 ÷ 70 = 3 hours

13. 6 days

    • A’s rate = 1/10 job per day

    • B’s rate = 1/15 job per day

    • Combined rate = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 job per day

    • Time = 1 ÷ (1/6) = 6 days

14. 12 km

    • 3 km in 30 minutes → speed = 3 ÷ 0.5 hour = 6 km/h

    • In 2 hours → distance = 6 × 2 = 12 km

15. 320 units

    • Rate = 120 units ÷ 3 hours = 40 units per hour

    • In 8 hours → 40 × 8 = 320 units

16. ₱720

    • Discount = 900 × 20% = 900 × 0.20 = 180

    • Sale price = 900 − 180 = ₱720

17. ₱1,500

    • Profit = 25% of 1,200 = 0.25 × 1,200 = 300

    • Selling price = 1,200 + 300 = ₱1,500

18. 16 males

    • Females = 60% of 40 = 0.60 × 40 = 24

    • Males = 40 − 24 = 16

19. 10 liters of sugar

    • Sugar = 25% of 40 liters = 0.25 × 40 = 10 liters

20. 40 mangoes

    • Ratio mangoes:bananas = 2:3

    • 3 parts = 60 bananas → 1 part = 60 ÷ 3 = 20

    • Mangoes = 2 parts = 2 × 20 = 40

Civil Service Exam Philippines: Complete Preparation and Passing Guide