Time & Work – Quantitative Aptitude Study Notes
(For LIC / GIC Insurance Program)
Time & Work deals with how long it takes to finish a job and how much of the job is done by each person or team.
In exams you’ll usually have to convert between rate (how much work is done per unit time) and time (how long it takes to do a given amount of work).
1. Simple Explanation
| Concept | Definition | Formula |
|---|---|---|
| Total Work (W) | The amount of job that has to be completed. | W (often set to 1 to simplify) |
| Rate of Work (R) | Portion of the job done in one unit of time. | R = W / T |
| Time (T) | How long it takes to complete the job. | T = W / R |
| Combined Rate | Sum of individual rates when people work together. | R_total = R₁ + R₂ + … |
| Work Done by a Person | W_i = R_i × T_i |
Key idea:
If the work is constant, time and rate are inversely proportional.
If someone works twice as long, they finish twice the work (assuming the same rate).
2. Key Points (What to Remember)
| Point | What to remember |
|---|---|
| 1. Set Total Work = 1 | This removes the need for units and makes fractions easier. |
| 2. Rate of a person | Rate = 1 / (days to finish 1 unit) |
| 3. Combined work | When two or more persons work together, add their rates. |
| 4. Partial work | If they work for d days, Work_done = Rate × d. |
| 5. Remaining work | Remaining = 1 – Work_done. |
| 6. Time for remaining work | Time_remaining = Remaining / Rate_of_remaining_person(s) |
| 7. Changing rates | If a person stops working, remove their rate from the total. |
| 8. Fractional days | Always keep fractions; convert to decimal only at the end if needed. |
| 9. Check units | Days × rate (1/day) = unitless work. |
| 10. Common traps | • Mixing “days” and “hours” without conversion. • Forgetting to subtract the work already done. |
3. Worked Example
Problem
A can finish a piece of work in 12 days.
B can finish the same work in 15 days.
They work together for 4 days.
After that, A leaves.
How many days will B alone need to finish the remaining work?
Step‑by‑step Solution
-
Set total work
W = 1(unit of work) -
Find individual rates
- A’s rate:
R_A = 1 / 12work/day - B’s rate:
R_B = 1 / 15work/day
- A’s rate:
-
Combined rate while both work
R_total = R_A + R_B = 1/12 + 1/15 = (5 + 4)/60 = 9/60 = 3/20work/day -
Work done together in 4 days
Work_done = R_total × 4 = (3/20) × 4 = 12/20 = 3/5 -
Remaining work
Remaining = 1 – 3/5 = 2/5work -
Time for B alone to finish remaining work
Time_B = Remaining / R_B = (2/5) ÷ (1/15) = (2/5) × 15 = 6days
Answer: B will need 6 days to finish the remaining work.