Introduction
Time & Work is best solved using the efficiency (work-per-day) method rather than
fraction-based equations — this single technique also directly powers the next chapter, Pipes &
Cisterns.
The Efficiency Method — Core Idea
Flowchart — Efficiency Method Setup
Assume Total Work = LCM of all given time values
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Efficiency (work/day) of each person = Total Work ÷ their individual time
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Combine efficiencies as needed, then Time = Total Work ÷ Combined Efficiency
Q. A can complete a work in 12 days and B can complete it in 15 days. In how many days will they complete it together?
Total Work = LCM(12,15) = 60 units
A's efficiency = 60/12 = 5 units/day; B's efficiency = 60/15 = 4 units/day
Combined efficiency = 9 units/day
Time together = 60/9 = 6⅔ days
Basic Relations
| Relation |
|---|
| If A does a work in "n" days, A's 1-day work = 1/n |
| If A is twice as efficient as B, A takes half the time B takes |
| More men/more efficient → less time (inverse proportion) |
"A Leaves Midway" Pattern
Q. A and B together can finish a work in 10 days. They worked together for 4 days, then A left. B finished the remaining work in 9 more days. In how many days can A alone finish the work?
Total Work = 10 units/day combined → Total = 10×10 = wait, use LCM method instead:
Let total work = 90 units (convenient LCM-style number)
Combined rate = 90/10 = 9 units/day
Work done in 4 days together = 4×9 = 36 units
Remaining = 90−36 = 54 units, done by B alone in 9 days → B's rate = 6 units/day
A's rate = 9 − 6 = 3 units/day → A alone takes 90/3 = 30 days
Wages Division in Time & Work
💡 Key Rule: When a total wage is divided among people who worked together, it is split in the ratio of their individual efficiencies (work done), not equally and not by time taken.
Q. A can do a piece of work in 6 days and B in 8 days. They work together and earn ₹280. Find A's share.
Efficiency ratio = 1/6 : 1/8 = 4:3 (multiply both by 24)
A's share = (4/7) × 280 = ₹160
Men-Days-Work Formula (M-D-W)
| Formula |
|---|
| M₁D₁/W₁ = M₂D₂/W₂ (add hours/day term H if given: M₁D₁H₁/W₁ = M₂D₂H₂/W₂) |
Q. 12 men can complete a work in 18 days. How many days will 8 men take to complete the same work?
M₁D₁ = M₂D₂ → 12×18 = 8×D₂ → D₂ = 216/8 = 27 days
✅ Practice Focus: LCM-based efficiency method (fastest approach for almost all questions) · "Leaves midway" combined-then-solo work pattern · Wage division by efficiency ratio · M-D-W formula for men-days-work variations.