The old 1/x + 1/y approach to time and work is slow and error-prone. The modern LCM method turns every problem into simple integer arithmetic. This definitive guide covers the time and work LCM method shortcut formulas, including leaving-early and alternate-days variations.
Table of Contents
The Standard Time & Work Table
| Person | Days to Complete | Total Work (LCM) | Efficiency (Units/Day) |
|---|---|---|---|
| A | a days | LCM of all days | LCM ÷ a |
| B | b days | Same LCM | LCM ÷ b |
| C | c days | Same LCM | LCM ÷ c |
Basic Example
Question: A can complete a work in 12 days and B in 18 days. How many days will they take together?
| Person | Days | Total Work (LCM of 12,18 = 36) | Efficiency |
|---|---|---|---|
| A | 12 | 36 | 3 units/day |
| B | 18 | 36 | 2 units/day |
| A + B | ? | 36 | 5 units/day |
Time = 36 ÷ 5 = 7.2 days (or 71⁄5 days).
Variation 1: Leaving Early
Question: A and B start together, but A leaves 4 days before completion. Total work is still 36 units. Combined efficiency is 5. If A works for (d − 4) days and B works for d days:
3(d − 4) + 2d = 36
3d − 12 + 2d = 36
5d = 48 → d = 9.6 days.
Variation 2: Alternate Days
Question: A (3 units/day) and B (2 units/day) work on alternate days, starting with A.
In every 2-day cycle, work done = 3 + 2 = 5 units.
For 36 units: 7 full cycles = 35 units in 14 days.
On day 15, A works and finishes the remaining 1 unit.
Total time = 15 days.
Pipes and Cisterns
Apply the same table. An inlet pipe has positive efficiency; a leak has negative efficiency.
Question: Pipe A fills a tank in 6 hours, Pipe B fills it in 9 hours, and leak C empties it in 18 hours. Time to fill?
| Pipe | Hours | Capacity (LCM of 6,9,18 = 18) | Efficiency |
|---|---|---|---|
| A | 6 | 18 | +3 |
| B | 9 | 18 | +2 |
| C (leak) | 18 | 18 | −1 |
| Net | ? | 18 | +4 |
Time = 18 ÷ 4 = 4.5 hours.
Master Time & Work in 3 Days
Shortcut Maths offers dedicated arithmetic workshops for Bank, SSC and Railway aspirants in Kolkata.
Join Workshop Call 9804490328FAQs
Q1. Why is LCM method better than 1/x + 1/y?
It avoids fractions entirely, reduces calculation errors and is 30-40% faster in exam conditions.
Q2. What if days are not whole numbers?
Convert to hours or use decimal LCM. Most exam questions use integers for this reason.
Q3. Can this method be used for wages distribution?
Yes. Wages are distributed in the ratio of efficiencies (or work done) of each person.
Last updated: June 27, 2026. For coaching in Kolkata, call +91-9804490328.