Time and Work Test: IQ and Logical Reasoning Questions, Tricks, and Practice

Time and Work Test is an important part of IQ and Logical Reasoning that tests your ability to understand work rates, efficiency, and the time required to complete tasks individually or in groups.

For Officer Cadet Entrance Exam preparation, these questions help develop numerical ability, problem-solving skills, logical thinking, and the ability to apply work-rate relationships accurately. Explore the complete Officer Cadet Exam resources and IQ for Officer Cadet preparation for additional practice and study materials.

What is Time and Work Test?

Time and Work Test 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?
Solution:
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

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

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).

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.

Types of Time and Work Questions

Time and work problems generally fall into a handful of recurring patterns:

1. Basic Time and Work (Two Workers)

These questions involve two workers working together to complete a task by combining their individual work rates.

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?
Solution:
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

2. Three Workers Together

These questions involve three workers working together, requiring you to combine their individual rates to determine the total time needed.

Example:
A can do a work in 10 days, B in 20 days, and C in 30 days. How long will they take together?
Solution:
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)

3. Finding Individual Time from Combined Time

These questions provide the time taken by workers together and one worker individually, and ask you to find the time taken by the other worker.

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?
Solution:
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

4. Work Done on Alternate Days

These questions involve workers working on different days, such as one worker working on one day and another working on the next.

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?
Soultion:
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

5. Pipes and Cisterns

These questions deal with pipes filling or emptying a tank, where inlet pipes add water and outlet pipes remove water at different rates.

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?
Solution:
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

6. Efficiency Ratio Problems

These questions compare the efficiencies of two or more workers to determine their relative work rates or the time they need to complete a task.

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?
Solution:
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

7. Leave or Absence Problems

These questions involve a worker joining or leaving a task partway through, requiring you to calculate the remaining work and completion time.

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?
Solution:
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

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.

Effective Tricks to Solve Time and Work Questions

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.

Important Tips to Solve Time and Work Questions

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 subtopic under the Numerical Reasoning Test topic in the IQ and Logical Reasoning course on the Pratima Academy LMS.

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