Work & Time
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Important Formulas & Concepts
Study MaterialWork & Time
Work and Time is one of the most important and high-scoring chapters in Quantitative Aptitude. Questions from this topic are frequently asked in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, placement tests, and other competitive examinations.
This chapter deals with:
- Work efficiency of persons
- Time required to complete work
- Combined work calculations
- Pipes and cisterns concepts
- Men-days-hours problems
- Work distribution and productivity
Most Work and Time problems are based on the relationship between:
Work, Time, and Efficiency
Why Work & Time is Important?
- Frequently asked in competitive exams.
- Easy and scoring arithmetic topic.
- Useful in Time and Work applications.
- Improves logical and analytical thinking.
- Directly connected with Chain Rule and Pipes & Cisterns.
Basic Concept of Work & Time
If a person can complete a work in a certain number of days, then the amount of work done by that person in one day is called:
Efficiency or One Day's Work
Work and Time problems mainly depend on:
- Efficiency of workers
- Number of workers
- Working hours
- Total time required
Important Relations
| Quantities | Relationship |
|---|---|
| Work and Person | Directly Proportional |
| Time and Person | Inversely Proportional |
| Work and Time | Directly Proportional |
| Efficiency and Time | Inversely Proportional |
Important Formulae of Work & Time
1. One Day's Work Formula
If a person completes a work in n days:
One Day's Work = 1/n
Example:
If A completes a work in 10 days:
A's one day's work:
= 1/10
2. Days Required Formula
If a person's one day's work is 1/n:
Total Days = n
3. Efficiency Formula
Efficiency is inversely proportional to time.
Efficiency ∝ 1 / Time
More efficiency means less time.
4. Work Formula
Work = Efficiency × Time
5. Combined Work Formula
If:
- A completes work in x days
- B completes work in y days
Then together:
Combined Work = (1/x + 1/y)
Total days together:
Days = xy / (x + y)
6. Three Persons Working Together
If:
- A completes work in x days
- B completes work in y days
- C completes work in z days
Then together:
Days = xyz / (xy + yz + zx)
Man-Days-Hours Concept
For men-days-hours problems:
M × D × H / W = Constant
Where:
- M = Number of men
- D = Number of days
- H = Number of working hours
- W = Amount of work
Basic Rules of Work & Time
Rule 1: Work from Days
If a person completes work in n days:
One Day's Work = 1/n
Rule 2: Days from Work
If one day's work is 1/n:
Total Days = n
Rule 3: Efficiency Ratio
If A is n times more efficient than B:
Work Ratio = n : 1
Time Ratio = 1 : n
Rule 4: Men-Time Relation
If ratio of men is:
m : n
Then ratio of time is:
n : m
Important Concepts of Work & Time
1. Total Work is Always Assumed as 1
✔ In most aptitude problems, total work is assumed to be 1 unit.
2. More Men → Less Time
Men and time are inversely proportional.
More Men = Less Time
3. More Efficiency → Less Time
Efficiency and time are inversely proportional.
More Efficiency = Less Time
Analogy with Speed, Distance & Time
| Speed-Time Concept | Work-Time Concept |
|---|---|
| Speed | Efficiency |
| Distance | Work |
| Time | Time |
Combined Work Concept
If two or more persons work together:
- Add their efficiencies.
- Find combined one day's work.
- Take reciprocal to find total time.
Total Time = 1 / Combined Efficiency
Pipes and Cisterns Concept
Pipes and cisterns problems follow the same Work and Time concept.
- Filling pipe → Positive work
- Emptying pipe → Negative work
Alternate Work Concept
Sometimes workers work alternately.
In such cases:
- Find work done in one cycle.
- Calculate remaining work.
- Find exact final time.
Efficiency Comparison Formula
If:
- A takes x days
- B takes y days
Then:
Efficiency Ratio = y : x
Important Formula Summary
| Concept | Formula |
|---|---|
| One Day's Work | 1/n |
| Total Days | 1 / Efficiency |
| Work Formula | Efficiency × Time |
| Combined Work | (1/x + 1/y) |
| Two Persons Together | xy / (x + y) |
| Three Persons Together | xyz / (xy + yz + zx) |
| Man-Days-Hours | MDH / W = Constant |
Common Mistakes in Work & Time
- Incorrect addition of efficiencies.
- Confusion between work and time.
- Ignoring inverse proportionality.
- Calculation mistakes in fractions.
- Incorrect handling of alternate work problems.
Important Exam Tips
- Always calculate one day's work first.
- Use LCM method for faster calculations.
- Memorize combined work formulas.
- Practice efficiency-based questions regularly.
- Simplify fractions carefully.
- Use MDH formula for men-days-hours problems.
- Verify final answers carefully.
Quick Revision Table
| Condition | Relationship |
|---|---|
| More Men → Less Time | Inverse |
| More Efficiency → Less Time | Inverse |
| More Work → More Time | Direct |
| Combined Efficiency | Add Efficiencies |
Work and Time is one of the easiest and most scoring arithmetic chapters in Quantitative Aptitude. Strong understanding of efficiency, work relations, and combined work formulas helps candidates solve problems quickly and accurately in competitive examinations.