Time and Work is one of the most important chapters of Arithmetic, with questions regularly asked in competitive examinations such as SSC, RRB, Defence, Police, Banking and other government exams. Therefore, a strong understanding of this chapter is important for complete preparation for competitive-exam Maths.
If you have already studied Direct and Inverse Proportion in our Ratio and Proportion section, you will find a familiar idea here. Many Time and Work problems use similar proportional and unitary-method reasoning to relate the amount of work, time and efficiency. However, Time and Work introduces its own concepts and formulas, which we will develop step by step in this chapter.
We have organized Time and Work into a dedicated learning hub covering formulas, solved questions, important problem types, practice questions and previous-year questions. This structure is designed to help aspirants learn the concepts first and then gradually move towards exam-level practice.
So, let us start with Time and Work.
For complete preparation of competitive-exam Maths, explore our:
- Maths Notes
- Maths Formulas
- Practice Questions
- PYQs for SSC, RRB, Defence, Banking, UPSC CSAT and Police Exams
Aspirants who want to know the syllabus can refer to our Competitive Exams Maths Syllabus. If you have a query, correction, suggestion or addition request, feel free to Contact Us.
What is Time and Work?
Suppose you want to build your home and need workers. If you deploy one worker, it takes 800 days to complete the work. But if you engage more workers, you can complete the same work in less time.
Here, you can see that when the number of workers increases, the time required to complete the same work decreases.
So, more workers → less time.
Time and Work Formula & Concepts
Our Time and Work Formula section covers the important formulas and explains how they are applied to Time and Work questions, helping aspirants understand the methods used to solve different types of problems.
For the above example, if one worker completes the work in 800 days:
- 2 workers will complete it in = 800 ÷ 2 = 400 days
- 4 workers will complete it in = 800 ÷ 4 = 200 days
- 8 workers will complete it in = 800 ÷ 8 = 100 days
- 16 workers will complete it in = 800 ÷ 16 = 50 days
- 32 workers will complete it in = 800 ÷ 32 = 25 days
This is because, when all workers have the same efficiency, more workers require less time to complete the same amount of work.
Therefore, for the same work:
Number of Workers × Time = Constant
or
Time ∝ 1 / Number of Workers
Our Time and Work Formula section covers this relationship and many other important formulas, concepts and applications in much more detail.
Time and Work Questions
This section covers different types of Time and Work questions with answers and solutions.
After learning the concepts and formulas, this section will help aspirants practice applying them to different problems and understand which formula or concept to use in a particular situation.
Example 1:
A Track Maintenance Incharge is building his house and requires 30 workers to complete the work in 90 days. However, with the rainy season approaching in two months, he wants to complete the work within 60 days. How many additional workers should he employ to complete the work on time?
Solution:
30 workers complete the work in 90 days.
Total work = 30 × 90 = 2700 worker-days
Workers required for 60 days = 2700 ÷ 60 = 45 workers
Additional workers required = 45 − 30 = 15 workers
Answer: 15 additional workers.
For more Time and Work questions with detailed answers and solutions, explore our Time and Work Questions with Answers and Solutions section.
Work and Wages Questions
This section specifically covers Work and Wages questions commonly asked in competitive examinations. These questions help aspirants understand how the concepts of work, time, workers and wages are connected.
Example 2:
A railway contractor hires 60 workers to construct an overbridge at Kathgodam Railway Station. Each worker is paid ₹600 per day. The work is scheduled to be completed in 45 days, but the contractor is asked to complete it in 30 days. How many additional workers will be required, and how much additional wage will the contractor have to pay per day?
Solution:
Total work = 60 × 45 = 2700 worker-days
Workers required for 30 days = 2700 ÷ 30 = 90 workers
Additional workers = 90 − 60 = 30 workers
Additional daily wages = 30 × ₹600 = ₹18,000
Answer: 30 additional workers and ₹18,000 additional wages per day.
For more Work and Wages questions with answers and solutions, explore our dedicated section.
Efficiency Questions
Efficiency is an important concept in Time and Work. After learning the efficiency formulas and concepts in our Time and Work Formula & Concepts section, this section will help aspirants understand how to apply them to different types of questions.
Example 3:
An IRCTC contractor has 30 workers who can complete a particular work in 90 days. He is asked to complete the same work in 75 days. If the number of workers remains unchanged, by what percentage must their overall efficiency increase to complete the work within the new deadline?
Solution:
Let original efficiency = 1.
90 days = Efficiency 1
For the same work:
75 days = Efficiency = 90/75 = 1.2
Increase in efficiency:
1.2 − 1 = 0.2 = 20%
Answer: 20% increase in efficiency.
Check our Efficiency Questions with Answers and Solutions section for more practice on efficiency questions.
Men, Women and Days Questions
Questions involving men, women and days are also commonly asked in competitive examinations. They may look complicated at first, but with sufficient practice, they become easier to understand and solve.
Example 4:
4 men or 6 women can complete a piece of work in 12 days. In how many days will 2 men and 3 women complete the same work?
Solution:
If 4 men = 6 women,
then 2 men = 3 women.
Therefore,
2 men + 3 women = 6 women = 4 men
So, 2 men and 3 women will complete the same work in 12 days.
Answer: 12 days.
For more questions and detailed solutions on Men, Women and Days, explore our dedicated Men, Women and Days Questions with Answers and Solutions section.
Time and Work Practice Questions
In this section, we will cover MCQs, True/False, Fill in the Blanks and Word Problems so that aspirants can practice sufficiently after learning the concepts and formulas of Time and Work.
Practice Question 1:
2 men can complete a work in 22 days. How many additional men should be engaged to complete the same work in 11 days?
Practice Question 2:
18 women or 12 men can complete a work in 20 days. In how many days will 6 women and 4 men complete the same work?
Answer: Practice Question 1: 2 additional men, Practice Question 2 (revised): 30 days.
Explore our dedicated Time and Work Practice Questions section to attempt the complete set of Time and Work questions.
Time and Work PYQs
In this chapter, we will solve Previous Year Questions (PYQs) from competitive examinations such as SSC, RRB, Defence, Banking, Police and other competitive exams.
To make the questions more relatable and engaging for MathsByNITian aspirants, we may modify the names, context and some non-essential text while retaining the underlying mathematical concept and question pattern.
Example 5:
A railway contractor and his supervisor together can complete a particular work in 15 days, while the supervisor alone can complete the same work in 20 days. In how many days can the railway contractor alone complete the work?
This question was asked in an SSC examination. We have modified the context and some text to make it more relatable and engaging while retaining the original mathematical concept.
Can you solve this?
Solution:
Work done by both in 1 day = 1/15
Work done by supervisor in 1 day = 1/20
Work done by contractor in 1 day:
= 1/15 − 1/20
= (4 − 3)/60
= 1/60
Therefore, the contractor alone can complete the work in 60 days.
Answer: 60 days.
For more Time and Work PYQs with answers and solutions, explore our dedicated Time and Work PYQs section.
How to Prepare Time and Work for Competitive Exams
- Learn the concepts first. Don’t skip any important chapter or concept.
- Solve the examples yourself after learning the concepts, without looking at the solutions.
- If you forget a concept or have a doubt, revisit the relevant concept and try the question again.
- Read the question carefully. Reading it twice, when necessary, can help you understand every condition and avoid missing important information. Read it word by word, especially in lengthy questions.
- Don’t skip the Practice section. Regular practice is essential for improving speed and accuracy.
- Follow the learning sequence from top to bottom. Don’t jump between sections. Learn the concepts first, solve questions, practice sufficiently, and attempt PYQs towards the end.
- Don’t solve a difficult question only once. Revisiting important or difficult questions 2–3 times can help you understand the method more deeply and remember it for longer.
- Follow the complete sequence consistently. If you follow these steps and practice regularly, Time and Work can become much easier to solve in competitive examinations.
Related Chapters to Time and Work
- Ratio & Proportion
- Percentage
- Pipes & Cisterns
- Time, Speed & Distance
- Partnership