Numerical Ability Work Problems Explained: Civil Service Exam Guide

Numerical Ability is a core component of the Civil Service Exam, and work problems are among the most frequently tested and most confusing question types. These problems appear simple on the surface, but many examinees lose points due to poor understanding of concepts like work rate, time relationships, and efficiency.

This guide explains work problems step by step, from basic concepts to advanced variations, using clear logic rather than shortcuts that are easy to forget under exam pressure. By the end of this article, you should be able to solve work problems accurately and confidently.

Understanding Work Problems in the Civil Service Exam

Work problems generally involve people, machines, or groups completing a task over time. The goal is to determine how long the work takes, how many workers are needed, or how much work is done within a certain period.

Typical keywords include:

• complete a job

• finish the work

• working together

• per day / per hour

• faster / slower

These problems test your ability to:

• Interpret rates correctly

• Set up equations logically

• Avoid common calculation traps

The Core Concept: Work, Rate, and Time

At the heart of all work problems is a simple relationship:

Work = Rate × Time

Where:

• Work is the total task (often treated as 1 whole job)

• Rate is the amount of work completed per unit of time

• Time is how long the work takes

If one person completes a job in 10 days, their rate is:

1 job ÷ 10 days = 1/10 job per day

Understanding this idea is far more important than memorizing formulas.

Single Worker Work Problems

These are the simplest form of work problems and often serve as the foundation for more complex questions.

Example 1

A worker can complete a job in 8 days. How much work does the worker complete in 1 day?

Solution

• Total work = 1 job

• Time = 8 days

• Rate = 1 ÷ 8 = 1/8 job per day

This concept becomes critical when combining multiple workers later.

Multiple Workers Working Together

When workers work together, their rates add up, not their times.

Example 2

Worker A can finish a job in 6 days.
Worker B can finish the same job in 12 days.
How long will they take if they work together?

Step 1: Convert time into rate

• Worker A rate = 1/6 job per day

• Worker B rate = 1/12 job per day

Step 2: Add rates

• Combined rate = 1/6 + 1/12

• Find common denominator: 1/6 = 2/12

• Combined rate = 2/12 + 1/12 = 3/12 = 1/4 job per day

Step 3: Find time

• Time = 1 ÷ (1/4) = 4 days

Common Mistake: Adding Time Instead of Rates

Many examinees mistakenly do this:

6 days + 12 days = 18 days ❌

This is incorrect because time does not combine linearly. Only rates combine.

Remember:

• Work rates add

• Time never adds directly

Different Work Efficiency Levels

Not all workers are equally efficient. Some complete work faster than others.

Example 3

A can do a job in 10 days, while B is twice as efficient as A. How long will B take to complete the same job?

Solution

• If B is twice as efficient, B works twice as fast

• A’s rate = 1/10 job per day

• B’s rate = 2 × (1/10) = 1/5 job per day

Time for B

• Time = 1 ÷ (1/5) = 5 days

Efficiency comparisons are common in the Civil Service Exam.

Work Problems Involving Partial Work

Sometimes a worker starts a job, then another finishes it.

Example 4

A can complete a job in 12 days. A works for 4 days, then B completes the rest in 6 days. How long would B take to complete the whole job alone?

Step 1: Work done by A

• A’s rate = 1/12

• Work done in 4 days = 4 × (1/12) = 1/3

Step 2: Remaining work

• Remaining work = 1 − 1/3 = 2/3

Step 3: B’s rate

• B finishes 2/3 work in 6 days

• B’s rate = (2/3) ÷ 6 = 2/18 = 1/9 job per day

Step 4: Time for B alone

• Time = 1 ÷ (1/9) = 9 days

Pipes and Cisterns (Work with Loss)

These problems involve filling and emptying, which is still a work problem at its core.

Example 5

A pipe fills a tank in 8 hours, while another pipe empties it in 12 hours. If both pipes are opened together, how long will it take to fill the tank?

Step 1: Rates

• Filling rate = 1/8 tank per hour

• Emptying rate = −1/12 tank per hour

Step 2: Net rate

• Net rate = 1/8 − 1/12

• Common denominator = 24

• Net rate = 3/24 − 2/24 = 1/24

Step 3: Time

• Time = 1 ÷ (1/24) = 24 hours

Work Problems with Men, Women, and Children

Sometimes work capacity is given in ratios.

Example 6

3 men can do the same work as 5 women. If 6 men work for 4 days, how many days will 10 women take to do the same work?

Step 1: Establish equivalence

• 3 men = 5 women

• 1 man = 5/3 women

Step 2: Convert work

• 6 men = 6 × (5/3) = 10 women

Step 3: Compare time

• Same number of workers doing the same work

• Time required = 4 days

Work and Wages Problems

These questions combine work rates with proportional pay.

Example 7

A and B work together for 10 days and earn ₱4,000. A alone can complete the job in 20 days, while B alone can complete it in 30 days. How much should A receive?

Step 1: Rates

• A’s rate = 1/20

• B’s rate = 1/30

Step 2: Ratio of work

• A : B = (1/20) : (1/30)

• Multiply by 60 → 3 : 2

Step 3: Divide wages

• Total = ₱4,000

• A’s share = 3/5 × 4,000 = ₱2,400

• B’s share = 2/5 × 4,000 = ₱1,600

Shortcut Method Using LCM (When Appropriate)

For some problems, especially under time pressure, you can use the LCM method.

Example 8

A finishes a job in 4 days, B in 6 days. How long together?

Step 1: LCM of 4 and 6 = 12

• A’s work per day = 12/4 = 3 units

• B’s work per day = 12/6 = 2 units

Step 2: Combined work

• Total per day = 3 + 2 = 5 units

Step 3: Time

• Time = 12 ÷ 5 = 2.4 days

Use this method only if you are comfortable with it.

Common Traps in Civil Service Exam Work Problems

Avoid these frequent mistakes:

• Adding time instead of rates

• Forgetting to subtract emptying rates

• Misreading “twice as efficient” as twice the time

• Ignoring partial work already completed

• Rushing without setting up equations

Exam Tips for Solving Work Problems Faster

• Always convert time to rate first

• Treat total work as 1 job unless stated otherwise

• Write rates clearly before calculating

• Estimate answers to catch mistakes

• Practice regularly under timed conditions

Final Thoughts

Work problems are not about complex mathematics; they are about clear thinking and proper setup. Once you master the relationship between work, rate, and time, even the hardest-looking problems become manageable.

In the Civil Service Exam, accuracy matters more than speed. Build a strong foundation, practice systematically, and approach each problem with confidence and logic.

Problem Sets With Answer Keys

Problem Set 1: Basics of Work Rate

1. A can finish a job in 15 days. What fraction of the work does A complete in 1 day?
   Answer: 115\frac{1}{15}151​

2. A can finish a job in 18 days. How much work will A complete in 6 days?
   Answer: 6×118=136 \times \frac{1}{18} = \frac{1}{3}6×181​=31​

3. A finishes a job in 20 days. How long will A take to finish 35\frac{3}{5}53​ of the job?
   Answer: 35×20=12\frac{3}{5} \times 20 = 1253​×20=12 days

4. A does 29\frac{2}{9}92​ of a job in 4 days. How long will A take to finish the whole job?
   Answer: Rate =2/94=118=\frac{2/9}{4}=\frac{1}{18}=42/9​=181​ job/day ⇒ Time $=18$ days

5. A can complete a job in 24 days. B can complete the same job in 32 days. Who is faster and by how many days (working alone)?
   Answer: A is faster by $32-24=8$ days

Problem Set 2: Working Together

6. A can finish a job in 8 days and B can finish it in 12 days. How long will they take together?
   Answer: Rate =18+112=524=\frac{1}{8}+\frac{1}{12}=\frac{5}{24}=81​+121​=245​ ⇒ Time =245=4.8=\frac{24}{5}=4.8=524​=4.8 days

7. A can finish a job in 9 days and B can finish it in 18 days. How long together?
   Answer: Rate =19+118=16=\frac{1}{9}+\frac{1}{18}=\frac{1}{6}=91​+181​=61​ ⇒ Time $=6$ days

8. A and B together finish a job in 10 days. A alone can do it in 15 days. How long can B alone do it?
   Answer: Together rate =110=\frac{1}{10}=101​. A rate =115=\frac{1}{15}=151​.
   B rate =110−115=130=\frac{1}{10}-\frac{1}{15}=\frac{1}{30}=101​−151​=301​ ⇒ B time $=30$ days

9. A can do a job in 6 days, B in 8 days, and C in 12 days. How long if all work together?
   Answer: Rate =16+18+112=4+3+224=924=38=\frac{1}{6}+\frac{1}{8}+\frac{1}{12}=\frac{4+3+2}{24}=\frac{9}{24}=\frac{3}{8}=61​+81​+121​=244+3+2​=249​=83​
   Time =83=223=\frac{8}{3}=2\frac{2}{3}=38​=232​ days

10. A and B can do a job in 5 days. B and C can do it in 6 days. A and C can do it in 7.5 days. How long will A, B, and C take together?
    Answer:
    15+16+17.5=2(A+B+C)\frac{1}{5}+\frac{1}{6}+\frac{1}{7.5}=2(A+B+C)51​+61​+7.51​=2(A+B+C) rate.
    Compute: 15=630\frac{1}{5}=\frac{6}{30}51​=306​, 16=530\frac{1}{6}=\frac{5}{30}61​=305​, 17.5=17.5=215=430\frac{1}{7.5}=\frac{1}{7.5}=\frac{2}{15}=\frac{4}{30}7.51​=7.51​=152​=304​. Sum =1530=12=\frac{15}{30}=\frac{1}{2}=3015​=21​.
    So 2(A+B+C)=122(A+B+C)=\frac{1}{2}2(A+B+C)=21​ ⇒ A+B+C=14A+B+C=\frac{1}{4}A+B+C=41​.
    Time $=4$ days.

Problem Set 3: Partial Work / Switching Workers

11. A can finish a job in 16 days. A works for 6 days, then B finishes the remaining work in 5 days. How long would B take alone?
    Answer: A work $=6/16=3/8$. Remaining $=5/8$.
    B rate $=(5/8)/5=1/8$ ⇒ B time $=8$ days

12. A can do a job in 12 days and B can do it in 18 days. They work together for 4 days, then A leaves. How many more days will B need to finish?
    Answer: Together rate =112+118=536=\frac{1}{12}+\frac{1}{18}=\frac{5}{36}=121​+181​=365​.
    Work in 4 days =4×536=2036=59=4 \times \frac{5}{36}=\frac{20}{36}=\frac{5}{9}=4×365​=3620​=95​. Remaining =1−59=49=1-\frac{5}{9}=\frac{4}{9}=1−95​=94​.
    B rate =118=\frac{1}{18}=181​. Time $=(4/9)/(1/18)=(4/9)\times 18=8$ days

13. A completes 14\frac{1}{4}41​ of a job in 3 days. B completes 13\frac{1}{3}31​ of the same job in 4 days. How long will they take together to finish the whole job?
    Answer: A rate $=(1/4)/3=1/12$. B rate $=(1/3)/4=1/12$.
    Together rate $=1/6$. Time $=6$ days

14. A can finish a job in 10 days. B can finish it in 15 days. A works alone for 2 days, then A and B work together. Total time to finish?
    Answer: A work in 2 days $=2/10=1/5$. Remaining $=4/5$.
    Together rate $=1/10+1/15=1/6$.
    Time for remaining $=(4/5)/(1/6)=(4/5)\times 6=24/5=4.8$ days
    Total $=2+4.8=6.8$ days

15. A and B together can finish a job in 8 days. A alone can finish it in 12 days. If they work together for 3 days then stop, how much work remains?
    Answer: Together rate $=1/8$. Work done in 3 days $=3/8$.
    Remaining $=1-3/8=5/8$

Problem Set 4: Efficiency Comparisons

16. A can do a job in 14 days. B is 40% faster than A. How many days will B take?
    Answer: B rate $=1.4\times (1/14)=1/10$. Time $=10$ days

17. A can do a job in 20 days. B takes 25% more time than A. How long will B take?
    Answer: $20\times 1.25=25$ days

18. A is twice as efficient as B. If A finishes a job in 9 days, how long will B take?
    Answer: B is half as fast ⇒ time doubles ⇒ $18$ days

19. A and B together finish a job in 6 days. A is 50% more efficient than B. How long will A take alone?
    Answer: Let B rate $=x$. A rate $=1.5x$.
    Together rate $=2.5x=1/6$ ⇒ $x=1/15$.
    A rate $=1.5/15=1/10$ ⇒ A time $=10$ days

20. A can finish a job in 12 days. B is 20% less efficient than A. How long will B take?
    Answer: B rate $=0.8\times (1/12)=1/15$. Time $=15$ days

Problem Set 5: Pipes and Cisterns (Work With Loss)

21. A pipe fills a tank in 6 hours. Another fills it in 8 hours. How long to fill if both are opened together?
    Answer: Rate $=1/6+1/8=7/24$. Time $=24/7\approx 3.43$ hours

22. A pipe fills a tank in 10 hours. A leak empties it in 15 hours. How long to fill with both open?
    Answer: Net rate $=1/10-1/15=1/30$. Time $=30$ hours

23. Two pipes can fill a tank in 12 hours and 18 hours. A drain can empty it in 9 hours. If all are opened, what happens?
    Answer: Net rate $=1/12+1/18-1/9=3/36+2/36-4/36=1/36$.
    Tank will still fill in 36 hours.

24. A pipe fills a tank in 5 hours. After 2 hours, a leak opens that can empty the full tank in 10 hours. How long total to fill?
    Answer:
    First 2 hours work $=2/5$. Remaining $=3/5$.
    Net rate after leak $=1/5-1/10=1/10$.
    Time for remaining $=(3/5)/(1/10)=6$ hours
    Total $=2+6=8$ hours

25. A pipe fills in 9 hours. A drain empties in 12 hours. Both opened for 6 hours, then drain closed. How much more time to fill?
    Answer: Net rate first $=1/9-1/12=1/36$. Work done in 6 hours $=6/36=1/6$.
    Remaining $=5/6$. Filling rate alone $=1/9$.
    Time $=(5/6)/(1/9)=(5/6)\times 9=7.5$ hours

Problem Set 6: Work and Wages

26. A and B earn ₱1,800 for completing a job. A can do it in 12 days and B in 18 days. Divide the wages fairly.
    Answer: Work ratio $=(1/12):(1/18)=3:2$.
    A = $3/5\times 1800=₱1,080$, B = $2/5\times 1800=₱720$

27. A, B, and C complete a job and earn ₱3,600. Their daily work rates are in the ratio 2:3:5. How much does C receive?
    Answer: C share $=5/(2+3+5)=5/10=1/2$.
    C gets ₱1,800

28. A and B work together for 6 days and earn ₱2,700. If A is twice as efficient as B, how much does A get?
    Answer: Work ratio A:B = 2:1.
    A = $2/3\times 2700=₱1,800$, B = $₱900$

29. A alone can finish in 16 days, B alone in 24 days. They earn ₱4,000 working together. How much more does A earn than B?
    Answer: Ratio $=(1/16):(1/24)=3:2$.
    A = ₱2,400; B = ₱1,600; Difference = ₱800

30. A, B, and C earn ₱5,000. A does 40% of the work, B does 35%, C does the rest. How much does C earn?
    Answer: C work = 25% ⇒ C earns $0.25\times 5000=₱1,250$

Civil Service Exam Philippines: Complete Preparation and Passing Guide