Time & Work — Formula Sheet
1. One-Day Work
If A completes a work in x days: A’s 1-day work = 1/x
Ex: A completes a work in 10 days.
1- day work = 1/10
2. One - Day Work of B
If B completes a work in y days: B’s 1-day work = 1/y
3. A and B Working Together
1- day work = 1/x + 1/y
Taking LCM: = x + y/xy
4. Time Taken by A and B Together
If A takes x days and B takes y days:
Together Time = xy/x+y
Ex: A = 10 days, B = 15 days
10×15/10+15 = 150/25 = 6 days
5. A, B and C Working Together
If A, B and C take x, y and z days respectively:
Together Time = xyz / xy+yz+zx
6. Basic Work Formula
Work = Work Rate × Time
Therefore: Work Rate = Work/Time, Time = Work / Work Rate
7. Efficiency
Efficiency is directly proportional to the amount of work done in a given time.
Efficiency ∝ Work Rate
Higher efficiency → More work in less time.
8. Efficiency and Time
For the same amount of work: Time ∝ 1/Efficiency
So:
Efficiency ↑ → Time ↓
Efficiency ↓ → Time ↑
9. Efficiency Ratio → Time Ratio
If
A : B efficiency = a : b
then
A : B time = b : a
Trick:
Efficiency ratio and Time ratio are opposite.
Ex:
A : B efficiency = 3 : 4
Then:
A : B time = 4 : 3
10. Wages
- Wages are proportional to the work done : Wages ∝ Work Done
- If working time is the same: Wages ∝ Efficiency
- If efficiency and time both differ: Wages ∝ Efficiency × Time
Rules
- Work and Time are inversely proportional.
- Add the one-day works first.
- Efficiency is the key.
- Higher efficiency = Less time.
- Lower efficiency = More time.
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