Time & Work – Quick & Easy Study Notes
(For SSC JE – Quantitative Aptitude)
1. What is “Work”?
- Think of a job as a cake you want to finish.
- Work = how much of that cake will be finished.
- We usually call the whole cake 1 unit of work (or 100 %).
2. Three Key Ideas
| Idea | What it means | Shortcut |
|---|---|---|
| Rate | How fast a person can finish the cake. | “X does 1/10 of the cake in 1 hour” → rate = 1/10 cake per hour |
| Time | How long it takes to finish the cake. | “It takes 5 hours” |
| Work | Amount of cake finished. | “1 whole cake” |
Formula
Work = Rate × Time
or, rearranged
Time = Work / Rate
Rate = Work / Time
3. Everyday Analogy
- Rate = speed of a car (how many kilometers per hour).
- Time = how long you drive.
- Work = distance travelled.
If a car travels 60 km in 2 hrs, its rate is 30 km/hr (60 ÷ 2).
If the car’s rate is 30 km/hr, how long to travel 90 km?
Time = 90 ÷ 30 = 3 hrs.
4. Working Together
When two or more people work on the same cake:
- Add their rates.
- Then find the time using
Time = Work / Total Rate.
Tiny Example
| Person | Time alone | Rate (cake/hr) |
|---|---|---|
| Alice | 10 hrs | 1/10 |
| Bob | 15 hrs | 1/15 |
Step 1: Add rates
1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 cake per hour.
Step 2: Time together
Time = 1 / (1/6) = 6 hrs.
So Alice + Bob finish the cake in 6 hrs.
5. Common Problem Types
| Type | What to Do | Tiny Example |
|---|---|---|
| Both start together | Add rates → find time. | Alice (10 hrs) + Bob (15 hrs) → 6 hrs |
| One stops early | Work done by first person = rate × time. Subtract from total. Then finish with remaining people. | Alice works 3 hrs, then stops. She does 3 × 1/10 = 3/10 cake. Remaining 7/10 cake done by Bob alone → 7/10 ÷ (1/15) = 10.5 hrs |
| One starts later | Treat the later start as “work left” after the earlier person finishes some time. | Bob starts 2 hrs after Alice. Alice works 2 hrs → 2 × 1/10 = 1/5 cake done. Remaining 4/5 cake shared by Alice & Bob. |
| Work left after a break | Compute work done before break, then treat the rest as a new problem with the remaining workers. | 3 workers finish 30 % of cake, 2 workers join → compute new rate for 5 workers, finish remaining 70 %. |
6. Quick Tips
- Use fractions – they keep numbers exact.
- Common denominator – makes adding rates easier.
- Check units – everything should be “cake” in the same units.
- Cross‑check – add the times you calculated for each part; it should equal the total time given (if any).
7. Frequently Asked Questions
| Question | Simple Answer |
|---|---|
| What if the “rate” is given as “X workers can finish the job in Y hrs”? | Treat the job as 1 unit. Rate of each worker = 1/(Y × X). |
| Can I use minutes instead of hours? | Yes – just keep the same unit for all. |
| What if the work is “paint the wall”? | Same logic: paint per hour × hours = wall painted. |
8. One‑Last Tiny Example
Problem
- Worker P can finish a job in 8 hrs.
- Worker Q can finish the same job in 12 hrs.
- They work together for 2 hrs, then P stops.
- How many more hours does Q need to finish the job?
Solution
- Rates:
- P: 1/8 cake/hr
- Q: 1/12 cake/hr
- Together rate: `1/8 + 1