Time and Work: Complete Guide with Formulas, Theory, and Examples
Time and Work is one of the most important and scoring topics in quantitative aptitude, frequently appearing in competitive exams like SSC, Banking, Railways, and others. Mastering this topic requires a strong understanding of basic concepts, formulas, and problem-solving strategies.
1. Basic Concepts
Work
Work refers to any task that requires effort to complete. The total work is usually considered as 1 unit or 100%, which can be divided among people working together.
Time
Time is the duration required to complete a work. If a person can complete a task alone in a certain number of days, their efficiency can be calculated.
Efficiency
Efficiency is the rate at which a person can complete work.
Observation
- More efficiency → Less time to complete work
- Less efficiency → More time to complete work
Relation Between Work, Time, and Efficiency
2. Fundamental Formulas
Work Formula
Where:
W = Total work
R = Rate of work or efficiency
T = Time taken
Individual Work
If A can do a work in x days and B can do the same in y days:
- Work done by A in 1 day: 1/x
- Work done by B in 1 day: 1/y
Combined Work
Work with Different Hours
If efficiencies differ or multiple people work different hours:
Work Fraction Method
Total work = 1 unit (or 100%)
Fraction of work done = Time spent / Total time required
3. Types of Problems in Time and Work
Single Person Work
Basic calculation: If a person completes work in x days, the work done in 1 day = 1/x.
Multiple Persons Working Together
Use efficiency method: Sum the 1-day work of all persons.
Persons Working Alternately
- Calculate work done in 1 cycle (A + B)
- Repeat cycles until the remaining work is left
- Solve remaining work separately
Persons Joining or Leaving Midway
- Calculate the work done by each group separately
- Total work = Sum of work done in each phase
Efficiency Ratio Problems
If efficiency ratio of A : B : C = 2 : 3 : 5, then divide total work in same ratio.
Pipe and Cistern Problems (Time and Work Applied)
Water filled or emptied = Work
Rate of filling/emptying = Efficiency
Work with Different Hours per Day
- Calculate total units of work done per day for each person
- Add them for combined daily work
- Total time = Total work ÷ Daily combined work
4. Advanced Concepts
Work and Wages Problems
Wages are proportional to the work done.
Work with Efficiency Changes
If efficiency increases or decreases after some days:
Work with Fractional or Partial Completion
If a person does a fraction of work alone, calculate remaining work and divide by combined efficiency to find time required.
5. Key Tips and Tricks
- Always assume total work = 1 unit for simplicity
- Use efficiency per day to avoid confusion in multiple-person scenarios
- Alternate work problems can often be solved by finding work per 2-day or multi-day cycles
- Pipes, cisterns, and machines follow same time and work principles
- For ratio efficiency problems, always convert ratio to actual efficiency using a common multiplier
- Break complex problems into phases, calculate work for each phase, then sum
6. Examples
Basic Problem
A can complete a work in 10 days. How much work will A do in 4 days?
Solution:
Work done per day = 1/10
Work in 4 days = 4 × (1/10) = 2/5 of total work
Multiple Persons
A can do a work in 6 days, B in 8 days. Find days required together.
Solution:
1-day work: A = 1/6, B = 1/8
Combined 1-day work = 1/6 + 1/8 = 7/24
Total time = 24/7 ≈ 3.43 days
Efficiency Ratio
A : B : C = 2 : 3 : 5, Total work = 100 units
Solution:
Efficiency per day: assume multiplier = 1
A = 2 units/day, B = 3 units/day, C = 5 units/day
Pipe Problem
Tank can be filled by Pipe A in 12 hours and emptied by Pipe B in 20 hours. Time to fill tank with both pipes open:
Solution:
Net work/day = 1/12 - 1/20 = 5/60 - 3/60 = 2/60 = 1/30
Time = 30 hours
7. Summary of Formulas
| Concept | Formula |
|---|---|
| Work Done | Work = Efficiency × Time |
| 1-day work | 1-day work = 1 / Total days |
| Combined Work | 1-day work together = Sum of individual 1-day work |
| Days Required Together | T = xy / (x + y) |
| Wages Distribution | Individual Wage = (Individual Work / Total Work) × Total Wages |
| Pipe/Cistern | Time = Total Capacity / Net Rate |
Conclusion
Time and Work is a highly logical topic in aptitude. By understanding basic concepts, memorizing key formulas, and practicing different types of problems—like multiple persons, alternate work, efficiency ratios, and pipe problems—you can solve almost all questions quickly. Efficiency methods and unit work methods are particularly powerful in competitive exams.