Time and Work
Delhi Police Exam
1. What is Time & Work?
Time and Work is a very important topic in Quantitative Aptitude. It deals with how much time a person (or a group) takes to complete a certain amount of work.
Work: Task or job to be completed
Time: Duration to complete work
Efficiency: Rate of completing work
Basic Relationship: Work = Time × Efficiency
Simple Definition: If someone is more efficient, they take less time to finish the same work.
Examples:
| Person | Work Done | Time Taken | Efficiency |
|---|---|---|---|
| A | Completes 1 work | in 5 days | 1/5 work per day |
| B | Completes 1 work | in 10 days | 1/10 work per day |
2. Basic Formulas
| Formula | Description | Example |
|---|---|---|
| Work = Time × Rate | Rate = Efficiency | A does 1/5 work/day → 5 days for 1 work |
| Time = Work / Rate | To find time taken | 1 ÷ (1/5) = 5 days |
| Efficiency ∝ 1/Time | More efficiency → Less time | If A is twice efficient, time halves |
3. Concept of "1 Day's Work"
Definition
If A completes a work in N days, then A's 1 day's work = 1/N of the total work.
Example
If A finishes a job in 8 days, then in one day A completes 1/8 of the work.
4. Combined Work
When two or more people work together:
Combined 1 Day's Work = (A's 1 Day's Work) + (B's 1 Day's Work)
Example:
A can do a work in 10 days, B in 15 days.
Their 1-day work = 1/10 + 1/15 = 1/6
→ Together, they'll finish in 6 days.
5. Efficiency Ratio Method
If A : B = 2 : 3 (Efficiency Ratio) then their Time Ratio = 3 : 2
Efficiency ∝ 1/Time
Example:
A and B together can complete a job in 12 days.
If A alone can do it in 30 days,
then B's efficiency = 12 × (1/12 – 1/30) = 20 days.
6. Alternate Working Days
Find each person's 1 day's work
Add 2 days' work (A + B)
Divide total work accordingly
Example:
A can do a work in 4 days, B in 6 days.
In 2 days, they complete (1/4 + 1/6) = 5/12 work.
Work done in 4 days = 10/12 = 5/6
Left = 1/6 → done by A (in 1/4 day)
Total time = 4 + ¼ = 4.25 days
7. Work and Wages
If the amount of work done is directly proportional to wages: Wages ∝ Work Done
Example:
A and B complete a work together for ₹600.
A works 6 days, B works 4 days.
If their efficiency ratio = 3:2,
Total work ratio = (6×3):(4×2) = 18:8 = 9:4
A:B wages = ₹400 : ₹200.
8. Pipes and Cisterns (Related Concept)
Pipes problems are based on Time & Work logic.
| Type | Formula / Trick |
|---|---|
| Inlet pipe fills a tank | + Work |
| Outlet pipe empties a tank | – Work |
| Together effect | Add or subtract 1/day work accordingly |
Example:
A pipe fills tank in 10 min, outlet empties in 15 min.
Net 1 min work = (1/10 – 1/15) = 1/30 → Fills in 30 min
9. Short Tricks & Ratios
| Concept | Shortcut / Relation |
|---|---|
| If A can do work in x days, B in y days | Together = (xy)/(x+y) days |
| If efficiency ratio = a : b | Time ratio = b : a |
| Total work | LCM of time of all workers |
| Combined work | Add their 1-day works |
10. Real-Life Analogy
Think of Time & Work like two people painting a wall
Fast Worker
A paints fast (high efficiency)
finishes sooner
Slow Worker
B paints slowly
takes longer
If both paint together, they finish quicker! It's just like teamwork in real life — the more people, the faster the job (if they're efficient).
11. Common Delhi Police / SSC Exam Facts
A's 1 day's work = 1 / (days taken by A)
Work = Time × Efficiency
Together work formula = (xy)/(x + y)
Efficiency ∝ 1/Time
If A:B = 3:4 (Efficiency), then Time = 4:3
Pipes & Cisterns use same formula logic
Wages ∝ Work Done
Alternate day working questions are common
12. Quick Recap
| Concept | Summary |
|---|---|
| Work | Task to be completed |
| Time | Duration required to complete work |
| Efficiency | Ability to do work faster |
| Combined Work | Sum of individual 1-day works |
| Ratio Relation | Efficiency ∝ 1/Time |
| Pipes & Cisterns | Same logic as Time & Work |
| Wages | ∝ Work done |
You've completed Time and Work Concepts!
Courage Tip: Practice time and work problems regularly, focusing on different types like combined work, efficiency ratios, and pipes and cisterns. Remember the key formulas and relationships between efficiency and time to solve problems quickly in exams.
Master Time and Work for Competitive Exams!
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