NPAT Time and Work Questions: Formulas, Shortcuts, Solved Examples & Practice

NPAT Time and Work Questions are an important part of quantitative aptitude preparation for students appearing for the NPAT exam. These questions test how well you understand the relationship between time, work, efficiency, and the number of people involved in completing a task.

At first, Time and Work problems can look complicated because a question may involve two or more people, different efficiencies, or workers joining and leaving a task. However, the basic idea behind these questions is quite simple.

If you understand how much work a person completes in one day, you can solve most NPAT Time and Work Problems step by step.

This guide covers the important NPAT Time and Work formulas, shortcuts, solved questions, common mistakes, and practice questions. It helps students build a strong foundation in NPAT quantitative aptitude.

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What Are NPAT Time and Work Questions?

Time and Work questions deal with the amount of work one or more people complete within a specific period.

For example, if A can complete a job in 10 days, then A completes 1/10 of the work in one day.

Therefore, in 5 days, A will complete: 5 × 1/10 = 1/2

So, A completes half of the job in five days.

This basic concept is used repeatedly in NPAT Time and Work Questions.

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NPAT Time and Work Practice Questions for 2027

Now test your understanding with these practice questions.

Question 1: A can complete a job in 16 days. What fraction of the job will A complete in 4 days?

A 1/2

B 1/4

C 3/4

D 1/8

Question 2: A can complete a job in 10 days and B can complete it in 15 days. How long will they take together?

A 5 days

B 6 days

C 7 days

D 8 days

Question 3: A and B can complete a job in 12 and 24 days respectively. What fraction of the work can they complete together in one day?

A 1/8

B 1/6

C 1/4

D 1/3

Question 4 : A is twice as efficient as B. If B takes 24 days to complete a job, how long will A take?

A  6 days

B  8 days

C 12 days

D 48 days

Question 5: 10 workers can complete a job in 18 days. Assuming equal efficiency, how many days will 15 workers take?

 A 10 days

B 12 days

C 15 days

D 20 days

Question 6 :A can complete a job in 20 days and B can complete it in 30 days. What fraction of the work will they complete together in 5 days?

A 1/3

B 5/12

C 1/2

D 7/12

Answers to NPAT Time and Work Practice Questions

Question	Correct Answer	Explanation
1	B — 1/4	4/16 = 1/4
2	B — 6 days	1/10 + 1/15 = 1/6
3	A — 1/8	1/12 + 1/24 = 1/8
4	C — 12 days	Twice the efficiency means half the time
5	B — 12 days	10 × 18 = 15 × D
6	B — 5/12	Combined daily work = 1/20 + 1/30 = 1/12

Also Read: Most important NPAT topics to Prepare Now

Common Types of NPAT Time and Work Problems

Here are the most common question types that are asked in exams covering the NPAT time and work topic:

Type of Question	What You Usually Need to Find
One person working	Time or amount of work
Two people working together	Combined time
Three or more people	Combined work rate
Efficiency questions	Efficiency or time
Men and days	Number of workers or days
Work and wages	Individual wage share
Someone joins the work	Remaining time
Someone leaves the work	Remaining work/time
Partial work	Work completed or remaining

Understanding these categories makes it easier to identify the right approach when solving NPAT Time and Work Questions. 

Also attempt a free NPAT mock test to get an idea of the topics that are frequently asked in the exam.

Important NPAT Time and Work Formulas

You do not need to memorise dozens of formulas. The following concepts are enough for most basic and intermediate NPAT Time and Work Questions.

Concept	Formula
One-day work	1 / Number of days
Work completed	Daily work × Number of days
Time required	Total work / Daily work
Work	Efficiency × Time
Combined work	Sum of individual work rates
Efficiency	Work / Time
Men and days	Men × Days = Constant
Efficiency relationship	Efficiency ∝ 1 / Time

Example

Suppose A completes a job in 20 days.

Particular	Calculation
Total work	1
Time	20 days
Work in one day	1/20
Work in 5 days	5/20
Simplified work	1/4

Therefore, A completes 1/4 of the work in 5 days.

How to Solve NPAT Time and Work Questions?

A simple four-step approach works for many NPAT time-and-work problems.

Step 1: Find One-Day Work

If a person completes a job in D days:

One-day work = 1/D

Step 2: Find Combined Work

If two people work together, add their individual daily work rates.

Step 3: Calculate Completed or Remaining Work

If the workers have already worked for a certain number of days, calculate how much work has been completed.

Step 4: Find the Required Time

Use: Time = Remaining Work ÷ Daily Work

Quick Method

Given Information	What to Do
A completes work in 10 days	A’s daily work = 1/10
B completes work in 15 days	B’s daily work = 1/15
A + B work together	Add 1/10 + 1/15
Work already completed	Multiply daily work by days
Remaining work	Total work − completed work

This approach is particularly useful when solving NPAT Time and Work Questions under time pressure. To prepare faster and more effectively, follow the NPAT study plan.

NPAT Time and Work Questions on Efficiency

Efficiency is one of the most important concepts in Time and Work.

If a person is more efficient, they can complete the same amount of work in less time.

The relationship is: Efficiency ∝ 1/Time

This means efficiency and time are inversely proportional.

Efficiency and Time Table

Efficiency	Time
1×	Original time
2×	Half the original time
3×	One-third of original time
4×	One-fourth of original time
1/2×	Double the original time

Example

A is twice as efficient as B. B takes 20 days to complete a job.

Therefore:

A’s time = 20 ÷ 2 = 10 days

Answer: 10 days

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Efficiency Ratio and Time Ratio Questions

This is another common pattern in NPAT Time and Work Questions.

If: A’s efficiency: B’s efficiency = 2 : 3

then: A’s time : B’s time = 3 : 2

The ratio is reversed because efficiency and time are inversely proportional.

Efficiency Ratio	Time Ratio
1 : 2	2 : 1
2 : 3	3 : 2
3 : 4	4 : 3
4 : 5	5 : 4
5 : 7	7 : 5

Example

A is 50% more efficient than B.

Therefore:

A’s efficiency = 150%

B’s efficiency = 100%

Efficiency ratio: 3 : 2

Time ratio: 2 : 3

If B takes 18 days:

A’s time = 18 × 2/3 = 12 days

Answer: 12 days

Two People Working Together Questions

One of the most common NPAT Time and Work Questions involves two people working on the same task.

Suppose:

• A completes the work in 12 days.
• B completes the work in 18 days.

Their daily work is:

Person	Time Taken	Work Per Day
A	12 days	1/12
B	18 days	1/18
A + B	—	5/36

Therefore:

Combined work = 5/36 per day

Time required: 36/5 = 7.2 days

Shortcut Formula

If A completes work in x days and B completes it in y days:

Combined time = xy/(x + y)

For 12 and 18 days:

12 × 18 / (12 + 18)

= 216/30

= 7.2 days

Important Point

When two people work together, their combined time should normally be less than the time taken by either person individually.

Solved NPAT Time and Work Question 1

Question

A can complete a job in 15 days. What fraction of the work will A complete in 5 days?

Solution

Step	Calculation
One-day work	1/15
Work in 5 days	5 × 1/15
Simplified answer	1/3

Answer

A completes 1/3 of the work.

NPAT Time and Work Questions to Practice Now

Question1: A can complete a job in 12 days, and B can complete it in 18 days. How long will they take if they work together?

Solution

Person	One-Day Work
A	1/12
B	1/18
Combined	1/12 + 1/18
Combined work	5/36

Therefore: Time = 36/5 = 7.2 days

Answer 7.2 days

Question 2 : A can complete a job in 20 days. A works alone for 5 days. What fraction of the work remains?

Solution

Step	Result
One-day work	1/20
Work completed in 5 days	5/20 = 1/4
Total work	1
Remaining work	1 − 1/4
Final answer	3/4

Answer

3/4 of the work remains.

Question 3. A can complete a job in 10 days and B can complete the same job in 15 days. How long will they take together?

Solution

A’s daily work:1/10

B’s daily work: 1/15

Combined work: 1/10 + 1/15

Taking LCM 30: 3/30 + 2/30 = 5/30 = 1/6

Therefore:

Time = 6 days

Answer 6 days

Question 4: A and B can complete a job in 10 and 15 days respectively. They work together for 3 days, after which A leaves. How many more days will B need to finish the job?

Step 1: Combined Daily Work

Person	Daily Work
A	1/10
B	1/15
Together	1/6

Step 2: Work Completed in 3 Days

3 × 1/6 = 1/2

So, half the work is completed.

Step 3: Remaining Work

1 − 1/2 = 1/2

Step 4: B Works Alone

B’s daily work = 1/15

Time required:

1/2 ÷ 1/15 = 15/2

= 7.5 days

Answer

B needs 7.5 more days.

Some NPAT Time and Work Questions involve three or more workers.

Example

A can complete a job in 12 days, B in 18 days, and C in 36 days. How long will all three take together?

Person	Time	Daily Work
A	12 days	1/12
B	18 days	1/18
C	36 days	1/36
Total	—	1/6

Therefore:

Time = 6 days

Answer: 6 days

LCM Method for NPAT Time and Work Questions

The LCM method can make calculations easier, especially when the question contains several fractions.

Suppose A takes 12 days and B takes 18 days.

Instead of assuming total work as 1, take:

Total work = LCM(12, 18) = 36 units

Now calculate:

Person	Total Work	Days	Daily Work
A	36 units	12	3 units
B	36 units	18	2 units
Together	36 units	—	5 units

Combined time:

36 ÷ 5 = 7.2 days

Why Is the LCM Method Useful?

Fraction Method	LCM Method
Uses fractions	Uses whole numbers
Can involve more steps	Often quicker
May be difficult mentally	Easier for many students
Good for understanding	Useful for exam calculations

The LCM approach is especially useful when solving multiple NPAT Time and Work Questions during a timed practice session.

Men and Days Questions for NPAT 2027

Men-and-days questions are based on the idea that, when all workers have equal efficiency:

Men × Days = Constant

Example

8 workers can complete a job in 15 days. How many days will 12 workers take?

Workers	Days
Workers	Days
8	15
12	D

Therefore:

8 × 15 = 12 × D

D = 10 days

Answer: 10 days

Quick Relationship

Number of Workers	Time Required
Number of Workers	Time Required
Increases	Decreases
Decreases	Increases
Doubles	Time becomes half
Halves	Time becomes double

This shortcut works when the workers have equal efficiency and the other working conditions remain unchanged.

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Work and Wages Questions for NPAT 2027

Work and wages questions are closely related to Time and Work.

The basic idea is: Wages are proportional to the work completed.

Suppose A and B have an efficiency ratio of 3:2 and work for the same amount of time.

Their work ratio will also be: 3:2

Therefore, their wage ratio will be: 3:2

Worker	Efficiency	Work Share	Wage Share
A	3	3 parts	3 parts
B	2	2 parts	2 parts
Total	5	5 parts	5 parts

If workers spend different amounts of time on the job, consider both efficiency and working time. Solve the above mentioned types of questions to get more familiar with the NPAT exam pattern.

NPAT Time and Work Questions Shortcuts

Here are some useful shortcuts to remember while practising NPAT Time and Work Questions.

Situation	Shortcut
A completes work in D days	Daily work = 1/D
Two people work together	Add their daily work
Three people work together	Add all daily work rates
A person leaves	Subtract their daily work
Efficiency doubles	Time becomes half
Efficiency triples	Time becomes one-third
Workers double	Days become half, if efficiency is equal
Workers halve	Days double, if efficiency is equal
Several fractions appear	Use LCM method
Same work, different efficiencies	Use inverse efficiency-time ratio

Common Mistakes in NPAT Time and Work Questions

Even when the concept is simple, students can lose marks because of calculation or interpretation errors.

Common Mistake	What you should do
Adding the number of days	Add daily work rates
Forgetting inverse proportion	Higher efficiency means less time
Ignoring work already completed	Calculate remaining work
Applying Men × Days blindly	Check the efficiency assumption
Making unnecessary fraction calculations	Try the LCM method
Not checking the final answer	Compare it with the individual times
Spending too much time on one problem	Move on and return later when appropriate

How to Prepare NPAT Time and Work Questions for 2027?

A good preparation strategy should move from easy questions to more complicated ones.

Stage	Preparation Focus
1	Understand basic work and time
2	Practise one-person questions
3	Practise two-person questions
4	Learn efficiency and time ratios
5	Practise three-person questions
6	Solve men-and-days questions
7	Practise joining and leaving problems
8	Attempt work-and-wages questions
9	Solve mixed NPAT questions
10	Practise under a time limit

Do not simply count how many questions you solve.

After each practice session, make a note of the questions you got wrong and identify the reason.

Eroor Type	Example
Conceptual	Used efficiency incorrectly
Calculation	Arithmetic mistake
Interpretation	Misread the question
Time management	Spent too long on one question
Formula	Used an inappropriate shortcut

This approach can make your NPAT quantitative aptitude preparation much more effective.

Conclusion

The easiest way to get comfortable with NPAT Time and Work Questions is to understand the concept instead of memorising every possible shortcut.

Keep these points in mind: Start with basic NPAT Time and Work Problems, then gradually move to efficiency, combined-work, men-and-days, and joining/leaving questions.

The more familiar you become with these patterns, the less time you will spend figuring out which method to use. Regular practice, careful error analysis, and timed revision can help you approach NPAT Time and Work Questions with much greater confidence.

For NPAT preparation, the goal should not simply be to solve more questions. The goal is to understand the method, avoid repeated mistakes, and solve familiar question patterns efficiently.

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