Time and Work problems are some of the most common aptitude topics in exams like SSC, CUET, Banking, Railways, and JEE. These questions revolve around how long a task takes, how fast people work, and how their efficiencies combine. The formulas for Work, Time, and Efficiency help you quickly calculate who can finish a job, how long they take, or how work is shared among multiple workers. Understanding these formulas makes the entire chapter simple and logical.
Work Time Formula Overview
| Formula | Variables | When It Is Used |
|---|---|---|
| Work = Efficiency × Time | Work = total task | To find total work completed |
| Time = Work ÷ Efficiency | Time = duration | To calculate how long it takes |
| Efficiency = Work ÷ Time | Efficiency = rate of work | To compare or calculate speed of workers |
What is Work and Time in Maths?
1. Work
In Maths (especially aptitude problems), work means a complete task or job.
It is usually taken as 1 whole unit, like painting a wall, building a house, or completing an assignment.
Work is often expressed in fractions.
Example: If a person finishes a job in 10 days, then in one day they complete 1/10 of the work.
2. Time
Time represents how long it takes to finish the work.
If a task takes 5 days, then the time is 5 days.
Time may be given in hours, days, or minutes depending on the problem.
How Time & Work Problems Work
Time and Work questions are based on the idea that if a person completes a job in n days, then their 1-day work = 1/n of the job.
Steps to Solve Time & Work Questions:
- Find the 1-day work (daily work rate).
- Multiply daily work × time to get total work.
- Use formulas to find unknown values (time, work, or efficiency).
These formulas are extremely useful in CUET, SSC, Banking, Railways, JEE, and everyday planning like team projects or construction timelines.
Examples to Calculate Work, Time & Efficiency
Example 1: Daily Work Calculation
A can finish a work in 12 days. How much work does he do in 1 day?
Step 1: Daily work = 1 ÷ 12
Answer: A completes 1/12 of the work in one day.
Example 2: Work Done Together
A can complete a work in 10 days, B in 20 days. How long will they take together?
Step 1: A’s 1-day work = 1/10
Step 2: B’s 1-day work = 1/20
Step 3: Combined 1-day work = 1/10 + 1/20 = 3/20
Step 4: Total time = 1 ÷ (3/20) = 20/3 = 6.67 days
Final Answer: They finish the work together in 6⅔ days.
FAQs about Work Time Formula
Q1. What is the unit of work in time & work problems?
Work is considered as one whole task. It has no fixed physical unit and is expressed in fractions.
Q2. What is efficiency in time & work?
Efficiency is the rate of doing work, such as completing 1/10 of a job in a day.
Q3. How do we solve problems with multiple workers?
Calculate each worker’s 1-day work, add them, and then apply the formula Time = Work ÷ Efficiency.
Q4. Why are time & work questions important in exams?
They test calculation speed, logic, and understanding of work rate concepts in aptitude exams.
Q5. Can efficiency be compared between workers?
Yes. If A takes 10 days and B takes 20 days, then A is twice as efficient as B.
Q6. Are shortcuts available for faster solving?
Yes, the LCM method (taking LCM of days to assume total work) is the fastest method for competitive exams.