Aptitude · Lesson 5 of 9
Time & work
Work rates, combined work, efficiency and pipes & cisterns.
Think in rates: if A finishes a job in a days, A does 1/a of it per day. Rates add when people work together.
- A and B together finish in
ab / (a + b)days. - LCM method: take total work = LCM of the days, find each person's units per day — avoids fractions.
- If A is twice as efficient as B, A takes half the time.
- Pipes & cisterns: filling pipes add, emptying pipes (leaks) subtract.
Example: A can finish a project in 12 days and B in 18 days. How long together?
- Total work = LCM(12, 18) = 36 units.
- A = 3 units/day, B = 2 units/day → 5 units/day.
- 36 / 5 = 7.2 days.
Answer: 7.2 days (that is, 7⅕ days)
Example: A tank fills in 6 hours, but a leak empties a full tank in 12 hours. How long to fill with the leak open?
- Total = LCM(6, 12) = 12 units.
- Fill = +2/hr, leak = −1/hr → net 1 unit/hr.
Answer: 12 hours
Key points
- Work per day = 1 / days.
- LCM method avoids fractions.
- Leaks are negative rates.
Quick check
A does a job in 10 days and B in 15 days. Together they take…
10 × 15 / (10 + 15) = 150 / 25 = 6.
Practice task
A and B together finish a job in 10 days; A alone takes 15 days. How long will B take alone?
Show answer
Total = LCM(10, 15) = 30 units; A+B = 3/day, A = 2/day → B = 1/day → 30 days.
Interview corner
If 6 people build a wall in 8 days, how many days for 12 people?
Person-days = 48; 48 / 12 = 4 days (assuming equal efficiency).
How do you handle 'A works for 3 days and then leaves'?
Subtract the work done in those days from the total, then divide the remaining work by the remaining people's combined rate.
Original lesson written by the InfoparkDaily team · © 2026 InfoparkDaily · Free to learn — no paid course or subscription.