Time and Work is one of the most important and predictable chapters in quantitative aptitude. Most questions follow standard formulas, and once students understand the core concepts of work rate, days required, efficiency, and proportional relationships, they can solve any problem with accuracy. The topic appears regularly in SSC, Banking, Railways, UPSC CSAT, and campus exams, making it essential to master. If you understand three ideas clearly:
✔ Work done per day
✔ Total days required
✔ Ratio of efficiency
Then solving any Time and Work question becomes direct and mechanical. This complete guide explains formulas, concepts, shortcuts, patterns, tables, and FAQs to help you master every question type easily.
Quick Overview: Time and Work Formulas
| Concept / Situation | Work Considered | Time / Efficiency Used | Formula (with Meaning of Symbols Inside Row) |
|---|---|---|---|
| Work from Days | Total work = 1 unit | Uses days (n) | 1 day’s work = 1/n (n = total number of days to finish the work) |
| Days from Work | Total work = 1 unit | Uses daily work fraction | Total days = 1 ÷ (1/n) = n (1/n = 1 day’s work of worker) |
| Efficiency Concept | Work is constant | Efficiency increases or decreases | Efficiency ∝ 1/Time (If time reduces, efficiency increases) |
| A is x times as good as B | Same total work | Efficiency ratio used | Efficiency ratio = x : 1, Time ratio = 1 : x |
| Combined Work (A + B) | Combined daily output | Use 1 day’s work | (A+B)’s 1 day’s work = A’s 1 day + B’s 1 day, Days = 1 ÷ (A+B) |
| LCM Method | Work assumed as LCM of days | Use daily unit work | Total Work = LCM, 1 day’s work = Work ÷ Days |
| More Efficiency → Less Time | Same work | Uses efficiency ratio | Time ratio = 1/Efficiency |
| Less Efficiency → More Time | Same work | Uses efficiency ratio | Time ∝ 1/Efficiency |
| Work from Efficiency Ratio | Work done in equal time | Efficiency ratio | Work ratio = Efficiency ratio |
| Time from Efficiency Ratio | Workers compared | Efficiency ratio | Time ratio = Inverse of Efficiency Ratio |
Time and Work: Formulas
Understanding how work and time depend on each other is the foundation of this chapter. Every question, whether individual efficiency, combined work, ratios, or alternate-day work, comes from these basic formulas.
Work from Days
If a person completes a work in n days, then the amount of work done in one day is only a part of the whole job. This fraction is called 1 day’s work. It helps convert “total days” into “daily efficiency.” After this, it becomes easier to compute combined work or compare different workers.
Formula:
1 day’s work = 1/n
Where:
n = total days required to complete the whole work
This formula is used at the very start of most questions.
Days from Work
If we already know how much work a person completes in one day, then finding total days becomes direct. Since a full job is considered as 1 unit (100% work), dividing it by daily work gives the time required.
Formula:
If 1 day’s work = 1/n
Then total days to finish = n
This is simply the reverse of the previous formula.
Ratio of Efficiency
Comparing workers becomes easier when using ratios. Efficiency represents how much work a person can do in a specific time. If one worker is more efficient, they finish the job faster. If one worker is less efficient, they require more time. Understanding this relationship helps solve ratio-based questions quickly.
Formula:
Efficiency ∝ 1/Time
More efficiency → Less time
Less efficiency → More time
Efficiency Ratio Example (A is Thrice as Good as B)
When the problem states that one worker is “twice,” “thrice,” or “half as good” as another, it means efficiency is directly multiplied in the same ratio. But the time taken becomes exactly the opposite ratio. This inverse relationship is the most common test concept in exams.
Given
A is thrice as good a workman as B.
Work Ratio
A : B = 3 : 1
Time Ratio
Since time is inversely proportional to efficiency:
Time ratio = 1 : 3
A finishes the work three times faster than B.
Smart Tips and Practical Tricks for Solving Time and Work Problems
Mastering Time and Work becomes simple when you understand how days, work fractions, and efficiency relate to each other. Most students struggle not because formulas are difficult, but because they apply them without understanding the situation. This section breaks down the most important concepts into clear, actionable tips so you can solve questions faster and more accurately.
1. Convert Days into 1 Day’s Work First
Many questions become confusing when you try to calculate total work directly. Converting days to “1 day’s work” makes everything simple.
If A completes work in n days:
1 day’s work = 1/n
Example:
A finishes work in 12 days → 1 day’s work = 1/12.
This single step simplifies combination, ratio, and efficiency questions.
2. Identify the Exact Work That Must Be Counted
Students often forget that work changes depending on who is working and how many days are involved.
Working alone → Work = individual efficiency
Working together → Work = sum of efficiencies
Working alternately → Work = efficiency added day by day
Work done in 'x' days → x × 1 day’s work
Visualising work as a fixed quantity makes this concept very easy to understand.
3. Use Efficiency Instead of Days for Faster Calculations
Whenever people or groups work together, efficiency is more useful than days.
If A finishes in 6 days, efficiency = 1/6
If B finishes in 8 days, efficiency = 1/8
Combined efficiency = 1/6 + 1/8
Recognizing efficiency patterns instantly reduces calculation time.
4. Use the LCM Method for Combination Problems
A very underrated but powerful trick.
- Assume Total Work = LCM of days
- Convert each worker’s daily efficiency into “units per day”
- Add or subtract units easily
This method prevents mistakes with fractions and gives clearer understanding.
5. Focus on Patterns Instead of Memorizing Many Formulas
Most questions follow repeated patterns:
• A alone
• B alone
• A + B
• A + B + C
• A works for x days, B finishes
• Efficiency ratio
• A is “x times” as good as B
• Alternate day work
• Pipes and cisterns (same logic)
All of these come from the same base rule:
Work = Time × Efficiency
If you learn to identify the pattern, solving becomes automatic.
6. Double-Check Whether Time or Efficiency Is Given
Students often mix time and efficiency. In Time & Work:
More efficiency → Less time
Less efficiency → More time
Before calculating, always check:
✔ Is the ratio about time or efficiency?
✔ Should I invert the ratio?
✔ Do I need 1/n or n?
This prevents the most common exam mistakes.
7. Practice Typical Exam Patterns
Time and Work questions appear frequently in:
• SSC (CGL, CHSL, GD)
• Banking (IBPS, SBI)
• Railway RRB
• UPSC CSAT
• CAT, MAT, Campus aptitude tests
Practicing these patterns increases familiarity and drastically reduces time per question.
FAQs About Time and Work
Q1. Why is 1 day’s work important in Time and Work?
It helps convert total days into daily efficiency, which makes combining work and comparing workers very easy.
Q2. Why is time inversely proportional to efficiency?
Because if someone works faster, they finish the work sooner. More efficiency means less time.
Q3. How do you find time if you know 1 day’s work?
If 1 day’s work = 1/n, then total time required = n days.
Q4. Why do we invert ratios for time and efficiency?
Efficiency increases work speed, so higher efficiency means lower time. This makes them inversely related.
Q5. What does “A is thrice as good as B” mean in Time and Work?
It means A’s efficiency is three times that of B. So work ratio is 3:1, and time ratio is 1:3.
Q6. Why is LCM used in Time and Work problems?
LCM simplifies total work and helps calculate work done per day without fractions.
Q7. How do we find combined work of two persons?
Add their 1 day’s work and take reciprocal to get total days.
Q8. Why does efficiency help in ratio-based questions?
Efficiency directly tells how fast work is done. It removes long calculations.
Q9. What is the quickest method to solve Time and Work?
Convert everything into 1 day’s work, add/subtract, then invert to get total days.
Q10. Why do students mix up days and work?
Because they forget that days represent time, and 1/n represents work fraction. Keeping them separate solves the confusion.