CAT 2026 Time and Work: Formulas, Efficiency Method, Pipes & Cisterns, PYQs PDF

CAT 2026 Time and Work: Important Concepts

Time and Work questions are based on the relationship between the amount of work completed, the time taken and the efficiency of the worker.

The fundamental relationship is:

$Work = Efficiency \times Time$

If A completes a task in 10 days, A's one-day work is: 110

If B completes the same task in 15 days, B's one-day work is: 115

When they work together: 110+115=16

Therefore, A and B together complete the task in 6 days.

For CAT 2026, the major Time and Work question types include:

• Individual and combined work

• Efficiency-based questions

• Workers joining or leaving

• Work and wages

• Men and days

• Alternate-day work

• Pipes and Cisterns

• Partial completion of work

• Changes in efficiency

*CAT 2025 had 2 questions from time and work across 3 slots.

CAT Time and Work Formula and Efficiency Method

The efficiency method is one of the fastest ways to solve CAT Time and Work questions. Instead of repeatedly working with fractions, the total work can be assumed to be the LCM of the individual completion times.

Suppose A completes a task in 12 days and B completes it in 18 days.

Take total work as: $LCM(12,18)=36$ units.

Therefore:

• A's efficiency = 36/12=3 units/day

• B's efficiency = 36/18=2 units/day

• Combined efficiency = 3+2=5 units/day

Hence, the time taken together is: 365=7.2 days

This approach is especially useful when a question involves three or more workers.

Important Time and Work Shortcuts

If A completes a task in $x$ days and B completes it in $y$ days, their combined completion time is: xyx+y

For example, if A takes 12 days and B takes 18 days:

121812+18=7.2 days

Efficiency and time are inversely proportional. Therefore, if A takes 10 days and B takes 20 days:

Efficiency A: Efficiency B=20:10=2:1$

So, A is twice as efficient as B.

For work and wages: $Wages \propto Efficiency \times Time$

Thus, wages depend on both how efficiently and how long a person works.

Pipes and Cisterns for CAT 2026

Pipes and Cisterns follow exactly the same work-rate principle as Time and Work. The difference is that a filling pipe adds water, while an outlet removes it.

A pipe that fills a tank in $x$ hours has a rate of: 1x

A pipe that empties a tank in $y$ hours has a rate of: -1y

Therefore, when both operate together: $Net\ Rate=\frac{1}{x}-\frac{1}{y}$

For example, a pipe fills a tank in 8 hours and an outlet empties it in 12 hours.

The net rate is: 18-112=124

Hence, the tank will take 24 hours to fill.

Pipes and Cisterns Shortcut

The quickest way to handle these questions is to assign positive rates to inlet pipes and negative rates to outlets.

If a tank has three pipes with rates: 110,115,-130

the net rate becomes: 110+115-130=215

Therefore, the tank takes: 152=7.5 hours.

The key is to focus on the rate rather than the amount of water mentioned in the question.

Get a slot-wise CAT 2025 weightage analysis to understand how questions were distributed across sections and topics. Use the data to identify important CAT topics and make a more targeted CAT 2026 preparation strategy.

Download CAT 2025 Slot-by-Slot Master Weightage Matrix

CAT Time and Work PYQs: Important Question Patterns

CAT Time and Work questions can appear straightforward but often combine two concepts. A worker may start alone, another may join later, or the efficiency of a worker may change midway.

The most important patterns to practise are shown below.

These patterns should form the core of CAT 2026 Time and Work practice.

CAT Time and Work: 10 CAT-Level Practice Questions

The following 15 questions provide a focused practice set covering workers, efficiency, Pipes and Cisterns, wages, alternate-day work and changing work conditions.

Question 1: A and B together can complete a piece of work in 12 days, while B and C together can complete it in 15 days. A works alone for 6 days, after which B joins A. After another 4 days, C replaces A. If the entire work is completed in 18 days, in how many days can C alone complete the work?

1. 24 days

2. 30 days

3. 36 days

4. 45 days

Question 2: A, B and C can independently complete a task in 24, 36 and 48 days respectively. They start working together, but after every 4 days, the efficiency of A increases by 25%, while the efficiencies of B and C remain unchanged.

If the task is completed exactly at the end of the 12th day, what fraction of the total work was completed by A during the last 4 days?

1. 18

2. 524

3. 14

4. 724

Question 3: A and B work on alternate days, starting with A. A can complete the work alone in 20 days, while B can complete it alone in 30 days. However, after every second day of work, A's efficiency increases by 20% compared with its efficiency during the previous working day, while B's efficiency remains unchanged.

If the work is completed during A's $n$th working day, find the smallest possible value of $n$.

1. 5

2. 6

3. 7

4. 8

Question 4: Pipe A can fill a tank in 12 hours, Pipe B can fill it in 18 hours, and Pipe C can empty it in 24 hours. A and B are opened together for 3 hours. C is then opened while B is closed. After another 4 hours, B is reopened and C is closed.

How many more hours are required to fill the remaining tank?

1. 115

2. 135

3. 3

4. 165

Question 5: A group of men can complete a project in 24 days. If 8 additional men join the group, the project is completed 6 days earlier. However, if the efficiency of every original worker decreases by 20%, the original group requires 30 days to complete the project.

How many men were originally in the group?

1. 24

2. 28

3. 32

4. 36

Question 6: A takes 40% more time than B to complete a task. B and C together can complete the task in 12 days, while A and C together can complete it in 15 days.

If A works alone for 6 days and then B and C work together until the task is completed, how many days in total are required?

1. 14 days

2. 15 days

3. 16 days

4. 18 days

Question 7: A, B and C undertake a project. A works for 12 days, B for 15 days and C for 20 days. Their daily efficiencies are in the ratio 5:4:3, respectively.

However, A receives 20% more wage per unit of work than B, while C receives 10% less wage per unit of work than B.

If the total amount paid for the project is ₹1,20,000, what is the amount received by B?

1. ₹36,000

2. ₹40,000

3. ₹42,000

4. ₹45,000

Question 8: 8 men and 12 women can complete a piece of work in 15 days. The efficiency of a man is twice that of a woman.

After 5 days, 4 men and 6 women leave the project. The remaining work is completed by the workers left behind in another 15 days.

If the same work had instead been completed by only women, how many women would have been required to finish it in 20 days?

1. 24

2. 27

3. 30

4. 32

Question 9: Pipe A fills a tank in 16 hours and Pipe B fills it in 24 hours. When both are opened simultaneously, a leak causes the tank to fill 4 hours later than it would have without the leak.

If the tank is initially empty and A, B and the leak are opened together, how long will it take to fill the tank?

1. 16 hours

2. 18 hours

3. 20 hours

4. 22 hours

Question 10: A, B and C can complete a task individually in 18, 24 and 36 days respectively.

A and B start the work together. After 3 days, A leaves and C joins B. After another 4 days, B leaves and A rejoins C. The work is completed 5 days later.

If A's efficiency is increased by 50% from the day A rejoins C, what was the original ratio of the work completed by A during the first 3 days to the work completed by C during the final 5 days?

1. 3:5

2. 4:7

3. 5:8

4. 7:10

CAT Time and Work: Top 30 Practice Questions PDF Download

Strengthen your CAT Time and Work preparation with 30 carefully selected CAT-level practice questions covering workers, efficiency, pipes and drains, and changing work rates. The ebook includes step-by-step solutions to improve calculation speed, accuracy and problem-solving skills.

Download CAT Time and Work Top 30 Practice Questions PDF

CAT Time and Work PYQs PDF Download

Practice with CAT Time and Work PYQs to strengthen your understanding of one of the important Arithmetic topics in CAT Quantitative Aptitude. The resource provides previous-year questions to help you identify recurring question patterns, improve calculation speed, and develop an exam-oriented approach to solving Time and Work problems.

Download CAT Time and Work PYQs PDF

CAT Time and Work: Common Mistakes

Time and Work questions often become difficult because of incorrect interpretation rather than difficult mathematics.

Adding Time Instead of Work Rates

If A takes 10 days and B takes 20 days, their combined time is not 30 days. Their rates must be added.

Confusing Efficiency and Time

If one worker takes half the time taken by another, the first worker is twice as efficient.

Forgetting Negative Rates in Pipes

A filling pipe contributes positively, while an outlet contributes negatively.

Ignoring Work Completed Earlier

If a worker leaves midway, first calculate how much work has already been completed.

Using Percentages Directly

If A is 50% more efficient than B, the efficiency ratio is: A: B=150:100=3:2$

Converting percentages into ratios often makes CAT calculations faster.

CAT 2026 Time and Work Preparation Strategy

Time and Work should be prepared as part of the broader Arithmetic block rather than as an isolated chapter. The concepts overlap strongly with Ratio and Proportion, Percentages and Pipes and Cisterns.

A focused preparation sequence is:

1. Learn work-rate and efficiency basics.

2. Practise LCM-based Time and Work questions.

3. Move to workers joining and leaving.

4. Practise efficiency and work-wage questions.

5. Add alternate-day problems.

6. Learn Pipes and Cisterns using positive and negative rates.

7. Solve CAT PYQs under a time limit.

8. Maintain an error log for conceptual and calculation mistakes.

9. Reattempt incorrect questions without checking the solution first.

The objective should be to identify the correct rate relationship within a few seconds and then perform only the necessary calculation.

CAT 2026 Free Mock Test

Test your preparation with a CAT 2026 Free Mock Test and experience a structured CAT practice environment. Use your mock performance to evaluate speed, accuracy, time management and section-wise preparation before the CAT exam.

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CAT 2026 Time and Work Formula Sheet

A quick CAT formula revision sheet can help consolidate the formulas before a mock test or CAT Quant revision session.

CAT Quant PYQs: Complete 5-Year Question Bank (2021-2025)

Practise CAT Quantitative Aptitude PYQs from 2021 to 2025 with this comprehensive question bank designed to help aspirants understand recurring question patterns and strengthen CAT Quant preparation.

Download CAT Quant PYQs: 2021-2025

CAT 2026 Quant Sample Paper

Practise with the CAT 2026 Sample Paper for quant to familiarise yourself with CAT-level Quantitative Aptitude questions and assess your preparation. It can help improve question selection, calculation speed, accuracy and exam readiness.

Download CAT 2026 Quant Sample Paper

CAT 2026 Time and Work: Final Takeaway

Time and Work becomes much easier when every question is converted into an efficiency or work-rate problem. For CAT 2026, candidates should prioritise combined work, changing efficiency, workers joining or leaving, Pipes and Cisterns, alternate-day work and PYQs. Regular timed practice can turn lengthy-looking Arithmetic questions into short calculations based on a few core relationships.