Time & Work – Quick & Easy Study Notes
For the Puducherry Police Sub‑Inspector (SI) Quantitative Aptitude Test
Goal: Learn how to calculate “time”, “work” and “rate” without heavy math or jargon.
Tip: Think of work as an amount of job that can be divided among people or machines.
1. What is “Time & Work”?
| Concept | Everyday Analogy | Simple Definition |
|---|---|---|
| Work | Painting a wall | The total amount of job that has to be finished (e.g., 1 wall). |
| Rate | How fast a painter can paint | The part of the job that a person can finish in a unit of time (e.g., 1/4 wall per hour). |
| Time | How long it takes to finish the job | The period needed to complete the whole work. |
Remember:
Work = Rate × Time
(If you paint faster or take more time, the product stays the same.)
2. How to Work With Rates
2.1 Rate of One Person
If Person A finishes the whole job in 8 hours, his rate is
Rate_A = 1 job / 8 hours = 1/8 of the job per hour
2.2 Combined Rate
When two people work together, their rates add up.
Rate_A + Rate_B = combined rate
Example:
Person A: 1/8 job per hour
Person B: 1/12 job per hour
Combined rate = 1/8 + 1/12 = 5/24 job per hour.
3. Calculating Time
If you know the combined rate and the job size (always 1 job for a single task):
Time = 1 job / Combined rate
Using the example above:
Time = 1 / (5/24) = 24/5 ≈ 4.8 hours (4 hours 48 minutes).
4. Common Question Types
| Type | What you need to find | Key idea |
|---|---|---|
| 1. Two people start together and finish the job | Time | Add rates, divide 1 by the sum. |
| 2. One person starts, another joins later | Time | Split the job: part done by first person, remaining by both. |
| 3. One person is X% faster or slower | Rate | Convert percentage into a fraction of the other rate. |
| 4. Find how many people are needed | People | Work = Rate × Time → solve for number of people. |
5. Step‑by‑Step Approach
- Read the problem carefully – identify who does the work, when, and how much.
- Translate into rates – write each person’s rate as a fraction of the whole job per hour.
- Add or subtract rates – depending on who works together or separately.
- Use
Time = 1 / Rate– that gives you the required time. - Check the answer – ensure units (hours, minutes) are correct.
6. Tiny Example (All Steps)
Problem
- Worker A can finish a road in 6 days.
- Worker B can finish the same road in 9 days.
- They start together. How many days will it take them to finish the road?
Solution
| Step | Calculation | Comment |
|---|---|---|
| 1 | Rate_A = 1/6 job per day | A finishes 1/6 of the road each day |
| 2 | Rate_B = 1/9 job per day | B finishes 1/9 of the road each day |
| 3 | Combined rate = 1/6 + 1/9 = 5/18 job per day | Add the two rates |
| 4 | Time = 1 / (5/18) = 18/5 = 3.6 days | 3 days 14.4 minutes (≈3 days 14 min) |
Answer: They finish the road in about 3.6 days.
7. Quick Practice Problems
| # | Problem | Answer |
|---|---|---|
| 1 | A can paint a wall in 5 hours. B can paint the same wall in 8 hours. Together, how long? | 1 / (1/5 + 1/8) = 1 / (13/40) = 40/13 ≈ 3.08 hrs |
| 2 | A starts a task and works alone for 3 hours. B joins and together they finish the work in 5 more hours. If B alone would take 20 hours, how long did A work alone? | 3 hours (given) |
| 3 | Three people A, B, C finish a job in 12 hours. If A alone would take 18 hours, find B and C together’s time. | Combined rate of B+C = 1/12 – 1/18 = 1/36 → 36 hours for B+C |
| 4 | A can do a job in 10 days. B is 30% slower. How many days will B take? | B’s rate = (1 – 0.30) × (1/10) = 0.7/10 → Time = 1 / (0.07) = 14.29 days |
Try solving them before looking at the answers.