Time & Work – Study Notes
Himachal Pradesh Police Sub‑Inspector (SI) – Quantitative Aptitude
Time & Work problems deal with the amount of work done by one or more workers (persons, machines, etc.) in a given time.
The core idea is rate of work – how much work a worker can finish in a unit of time.
1. Simple Explanation
| Symbol | Meaning | Formula |
|---|---|---|
W |
Total work (in arbitrary units, e.g., “job”, “task”, “piece”) | – |
R |
Rate of work of one worker (units of work per day/hour) | R = W / T |
T |
Time taken by one worker to finish W |
– |
n |
Number of workers | – |
Key Idea
If a worker can finish a job in T days, his rate is 1/T jobs per day.
If several workers work together, their rates add up.
2. Key Points & Formulas
| Scenario | Formula | Explanation |
|---|---|---|
| Single worker | Rate = 1 / T |
If a job takes T days, the worker completes 1/T of the job each day. |
| Two workers together | 1 / T_total = 1 / T_A + 1 / T_B |
Their combined rate is the sum of individual rates. |
| n workers together | 1 / T_total = Σ (1 / T_i) |
Sum of all individual rates. |
| Work done in a given time | Work_done = Rate × Time |
Work_done can be expressed as a fraction of the total job. |