LCM Method: Take LCM of days as Total Work units. Each person's efficiency = Total/Their days. Add efficiencies for combined work. Time = Total/Combined efficiency.
Time & Work LCM Shortcut
SBI POIBPS POSSC CGLRRB
Items to Memorize
- LCM Method: Total work = LCM of individual days
- Efficiency = Total Work / Days
- Combined efficiency = Sum of individual efficiencies
- If A does in x days, B in y days: Together = xy/(x+y) days
- Pipes: Filling pipe = positive efficiency, Draining = negative
- If work increases, time increases proportionally
- Half work = half time (at same efficiency)
- A is twice as efficient as B → A takes half the time
- Alternate day work: find 2-day cycle output
- Wages: distributed in ratio of work done (efficiency × days)
Mnemonic Tricks
How It Maps
| Cue | Maps To |
|---|---|
| Step 1 | Total Work = LCM(days of A, days of B, ...) |
| Step 2 | Efficiency of A = Total/A's days |
| Step 3 | Combined = Eff(A) + Eff(B) |
| Step 4 | Together days = Total/Combined |
Why It's Faster
The LCM method converts fractions into whole numbers, making mental math dramatically faster. You never need to add fractions like 1/12 + 1/15.
Pipes shortcut: Treat filling pipes as +ve workers and draining pipes as −ve workers. Same LCM method applies.
Why It's Faster
Students often treat pipes as a separate topic, but it's identical to time & work with sign conventions. One method covers both.
Frequently Asked Questions
What is the LCM method for time and work?
Take LCM of all workers' individual completion times as Total Work. Each worker's efficiency = Total Work ÷ Their days. Add efficiencies to find combined rate. Time together = Total Work ÷ Combined efficiency.
How to solve pipe and cistern problems?
Use the same LCM method as time & work. Filling pipes have positive efficiency, draining pipes have negative efficiency. Net efficiency = sum of all (with signs).
What is the shortcut for alternate day work?
Calculate how much work is done in one complete cycle (e.g., 2 days if A and B alternate). Then find how many complete cycles fit, and handle the remainder separately.