The Time and Work Test is a fundamental topic in Numerical Reasoning that evaluates your understanding of efficiency, work rates, and the time required to complete tasks. These questions test your ability to calculate how long it takes for individuals or groups to complete a job, how much work is done in a given time, and how efficiency affects productivity. The key skill is to quickly establish the relationship between work, time, and efficiency, and apply the correct formula.
For Officer Cadet Entrance Exam preparation, mastering this topic is essential because it combines arithmetic skills with logical reasoning in a structured, formula-based format.
In this guide, we’ll explore what time and work problems involve, the key formulas you need, the common question types you’ll encounter, proven methods to solve them, and practical tricks to boost your speed and accuracy.
- What is Time and Work in Numerical Reasoning?
- What Skills Do These Questions Measure?
- Important Terms and Definitions
- Fundamental Formulas
- How to Solve Time and Work Questions
- Types of Time and Work Questions
- Basic Time and Work (Two Workers)
- Three Workers Together
- Finding Individual Time from Combined Time
- Work Done on Alternate Days
- Pipes and Cisterns
- Efficiency Ratio Problems
- Leave or Absence Problems
- Important Tricks
- Trick 1: Use the LCM Method
- Trick 2: Use the Combined Time Formula
- Trick 3: Extend to Multiple Workers
- Trick 4: Use Ratios for Efficiency Problems
- Trick 5: Match the Pipe Formula to the Situation
- Trick 6: Handle Alternate-Day Work in Cycles
- Trick 7: Use "n Times More Efficient" Directly
- Trick 8: Stick with Fractions, Not Decimals
- Common Mistakes to Avoid
- Quick Solving Checklist
- Practice Questions
- Conclusion
What is Time and Work in Numerical Reasoning?
Time and Work problems involve calculating the time required for one or more individuals or machines to complete a task, or determining how much work is completed within a given time frame. These problems rest on one core principle:
Work = Rate × Time
If a person takes T days to complete a job, then in 1 day they complete 1/T of the work. The more efficient a person is, the less time they need to finish the same task.
Example: A can do a work in 12 days and B can do the same work in 20 days. How many days will they take to complete it together? Adding their individual one-day work rates gives the combined rate, and taking the reciprocal of that combined rate gives the total time. Answer: 7.5 days
These problems reflect real-world scenarios such as workers completing a construction project, pipes filling or emptying a tank, machines producing goods in a factory, and comparing the efficiency of different workers.
What Skills Do These Questions Measure?
Time and work questions test your ability in:
- Arithmetic calculation – working accurately with fractions and rates
- Understanding of rates and proportions – seeing how work, time, and efficiency relate
- Applying formulas quickly – matching the right formula to the given scenario
- Logical reasoning in multi-step problems – chaining several calculations together correctly
- Speed and accuracy – solving under exam time pressure without careless errors
Time and Work is a high-scoring topic in the Numerical Reasoning section because questions follow predictable patterns with straightforward formulas. Common scenarios include individual work, group work, alternate-day work, pipes and cisterns, efficiency comparisons, leave-or-absence problems, and combined work between people with different productivity levels.
Important Terms and Definitions
- Work – the total effort required to complete a task, treated as a single unit (1) unless stated otherwise
- Time – the duration required to complete a given amount of work; inversely proportional to efficiency
- Efficiency – the rate at which work is done per unit of time: Efficiency = Work Done ÷ Time
- One-day work – the fraction of a task completed by a person in a single day; if a person finishes in X days, their one-day work is 1/X
- Man-days – the total work done by a certain number of people over a certain number of days: Total Work = Number of Men × Number of Days
Fundamental Formulas
Basic Time and Work Formulas
| Scenario | Formula |
|---|---|
| One-day work of A (completes work in A days) | 1 / A |
| Time taken by A alone | 1 / (A’s one-day work) |
| Work done by A in x days | x / A |
| Time taken by A and B together | AB / (A + B) |
| Time taken by A, B, and C together | ABC / (AB + BC + CA) |
Combined Work Formula
If A completes a job in X days and B completes it in Y days:
- A’s one-day work = 1/X
- B’s one-day work = 1/Y
- (A + B)’s one-day work = 1/X + 1/Y = (X + Y) / (XY)
- Time taken together = XY / (X + Y)
Efficiency Formula
Efficiency is inversely proportional to time (Efficiency ∝ 1/Time), so the ratio of two workers’ efficiencies equals (1/T₁) : (1/T₂).
Pipes and Cisterns Formulas
| Scenario | Formula |
|---|---|
| Inlet pipe fills in X hours | One-hour work = 1/X |
| Outlet pipe empties in Y hours | One-hour work = 1/Y |
| Net filling rate with both open | (1/X) − (1/Y) |
| Time to fill with both open | XY / (Y − X) |
Man-Days Formula
M₁ × D₁ × H₁ = M₂ × D₂ × H₂, where M = number of men, D = days, and H = hours — the total work stays constant across both sides of the equation.
How to Solve Time and Work Questions
Follow this step-by-step method during your exam.
Step 1: Read the Question Carefully
Identify what’s given — the time each worker takes individually, the number of workers, the time required working together, or an efficiency ratio.
Step 2: Identify the Type of Question
Determine whether it’s individual or group work, a pipes-and-cisterns problem, alternate-day work, an efficiency comparison, or a leave/absence problem.
Step 3: Calculate One-Day Work
For each person, find their one-day work: if A completes the job in X days, A’s one-day work is 1/X.
Step 4: Add or Subtract Work Rates
Add individual rates for combined work (1/X + 1/Y), subtract the outlet rate for pipes with an outlet (1/X − 1/Y), or add rates for the specific days worked in alternate-day problems.
Step 5: Find Total Time
Take the reciprocal of the combined rate to find the total time required.
Step 6: Verify Your Answer
Check that the result is logical: the combined time should be less than the time taken by the fastest individual worker, and time can never come out negative.
Types of Time and Work Questions
Time and work problems generally fall into a handful of recurring patterns:
- Basic time and work with two workers combining their effort
- Three workers together, extending the same logic to a third rate
- Finding an individual’s time when the combined time is already known
- Work done on alternate days, where different people work on different days
- Pipes and cisterns, involving inlet and outlet rates
- Efficiency ratio problems, comparing relative work rates
- Leave or absence problems, where one person joins or leaves partway through
Basic Time and Work (Two Workers)
Example: A can do a work in 12 days and B can do the same work in 20 days. How many days will they take to complete it together? A’s one-day work is 1/12 and B’s is 1/20; adding these gives a combined rate of 2/15, and the reciprocal of that rate is the total time. Answer: 7.5 days
Three Workers Together
Example: A can do a work in 10 days, B in 20 days, and C in 30 days. How long will they take together? Adding the three one-day work rates (1/10 + 1/20 + 1/30) gives a combined rate of 11/60, and the reciprocal of that rate gives the total time. Answer: 60/11 days (≈ 5.45 days)
Finding Individual Time from Combined Time
Example: A and B together can complete a work in 6 days. A alone can complete it in 10 days. In how many days can B alone complete it? Subtracting A’s one-day work (1/10) from the combined one-day work (1/6) isolates B’s individual rate, and taking its reciprocal gives B’s time alone. Answer: 15 days
Work Done on Alternate Days
Example: A can do a work in 15 days and B can do it in 20 days. If they work on alternate days starting with A, how many days will they take to complete the work? Each two-day cycle of A and B together completes 7/60 of the work, so after several full cycles you track the remaining fraction and finish counting individual days until the work is complete. Answer: 17 days (found through continued cycle-by-cycle addition)
Pipes and Cisterns
Example: Pipe A fills a tank in 6 hours and Pipe B empties it in 8 hours. If both pipes are opened together, how long will it take to fill the tank? Since B works against A, its rate is subtracted rather than added: 1/6 − 1/8 gives a net rate of 1/24 per hour, so the tank fills in the reciprocal of that rate. Answer: 24 hours
Efficiency Ratio Problems
Example: The ratio of efficiencies of A and B is 2:3. A alone can complete a work in 15 days. In how many days can B alone complete the work? Since efficiency is inversely proportional to time, the 2:3 efficiency ratio corresponds to a 3:2 ratio of times, so B’s time can be found by setting up that proportion against A’s known 15 days. Answer: 10 days
Leave or Absence Problems
Example: A can do a work in 8 days and B in 12 days. A started the work and B joined him after 2 days. In how many days was the work completed? A alone completes 1/4 of the work in the first 2 days, leaving 3/4 remaining; once B joins, their combined rate of 5/24 per day finishes that remaining share in 3.6 more days. Answer: 5.6 days
Important Tricks
Trick 1: Use the LCM Method
Instead of working with fractions, find the LCM of the given time periods and treat it as the total work. For example, if A takes 12 days and B takes 18 days, the LCM of 12 and 18 is 36, so A’s rate becomes 36/12 = 3 units/day and B’s becomes 36/18 = 2 units/day — a combined rate of 5 units/day, giving a total time of 36/5 = 7.2 days.
Trick 2: Use the Combined Time Formula
If A takes x days and B takes y days alone, the time together is xy/(x + y).
Trick 3: Extend to Multiple Workers
If A, B, and C take a, b, and c days respectively, the time together is abc / (ab + bc + ca).
Trick 4: Use Ratios for Efficiency Problems
If the efficiency ratio of A to B is m:n and A takes T days alone, B’s time is T × (m/n).
Trick 5: Match the Pipe Formula to the Situation
If the inlet fills faster than the outlet empties (Y > X), use XY / (Y − X); if the outlet is faster (X > Y), use XY / (X − Y).
Trick 6: Handle Alternate-Day Work in Cycles
Calculate the work done in one full two-day cycle (1/X + 1/Y), multiply by cycles to cover most of the work, then handle the small remainder day by day.
Trick 7: Use “n Times More Efficient” Directly
If A is n times more efficient than B, then A’s time = B’s time ÷ n — so if A takes x days, B takes nx days.
Trick 8: Stick with Fractions, Not Decimals
Working with fractions like 1/X instead of decimal approximations avoids compounding rounding errors across multi-step problems.
Common Mistakes to Avoid
- Adding times instead of rates — you can never add the number of days two workers take directly; always add their one-day work rates
- Forgetting to subtract the outlet rate — in pipe problems, an emptying pipe’s rate works against the filling rate, not with it
- Mixing up ratio direction in efficiency problems — a higher efficiency means a lower time, so double-check which ratio applies to which quantity
- Losing track of partial work already done — in leave/absence and alternate-day problems, always calculate exactly how much work remains before switching workers
- Skipping verification — a combined time should always be shorter than the fastest individual worker’s time alone
Quick Solving Checklist
Before selecting your answer, use this checklist:
- Read the question carefully
- Identified each individual’s time period
- Calculated one-day work for each person
- Added or subtracted rates appropriately for the scenario
- Used the LCM method where it speeds up calculation
- Applied the correct formula for the situation
- Verified the answer makes logical sense
- Avoided spending too much time on one question
Practice Questions
Conclusion
Mastering the Time and Work Test is essential for the Nepal Army Officer Cadet Entrance Examination. Success requires systematic application of rate and efficiency concepts — not guesswork — across scenarios involving individual work, group work, alternate days, pipes and cisterns, and efficiency comparisons.
Follow this disciplined approach:
Read → Identify → Calculate Rates → Apply Formula → Verify → Answer
Time and Work is one of the most scoring topics because it follows fixed rules and requires minimal calculation once you know the right shortcuts. With the LCM method and the other tricks above, these questions can be solved quickly and accurately.
This resource is part of the Officer Cadet Entrance Exam Preparation series, focusing on IQ and Logical Reasoning for the Nepal Army Officer Cadet Entrance Exam. For structured lessons, comprehensive practice banks, and mock tests, explore the Time and Work Test course on the Pratima Academy LMS.