Time and Work LCM Method Shortcut Formulas

Last updated: June 27, 2026. For coaching and doubts, contactShortcut Maths, Jadavpur, Kolkata 700032. Call+91-9804490328.

The Standard Time & Work Table

Formula: Time = Total Work ÷ Combined Efficiency. No fractions until the final step.

Basic Example

Question: A can complete a work in 12 days and B in 18 days. How many days will they take together?

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?

Time = 18 ÷ 4 = 4.5 hours.

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FAQs

It avoids fractions entirely, reduces calculation errors and is 30-40% faster in exam conditions.

Convert to hours or use decimal LCM. Most exam questions use integers for this reason.

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.

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