Time and Work
About 6 min · Quantitative Aptitude · English
Time worked out from the lesson's 439 words at 150 words a minute, plus a minute for each question.
The core principle is simple: time is inversely proportional to efficiency when the amount of work is fixed. Mastering this topic means understanding how to combine individual work rates, handle multiple workers, and solve pipe-and-cistern variations where filling and emptying happen simultaneously.
Key ideas
- Work is constant: If A completes work in n days, A's one-day work = 1/n. Total work can be assumed as 1 unit or calculated as LCM of given times for easier arithmetic.
- Inverse relationship: If efficiency doubles, time halves. If time is reduced by 1/3, efficiency must increase by 1/2 (not 1/3). This trips many students.
- Combined work rate: When A and B work together, (A+B)'s one-day work = A's one-day work + B's one-day work. Time taken together = Total work ÷ Combined rate.
- Work from days: If a group completes work in t days, their one-day work = 1/t. If they complete fraction f of work in t days, their one-day work = f/t.
- Negative work (pipes and cisterns): Filling pipes add positive work; emptying pipes add negative work. Net work rate = Σ(inlet rates) − Σ(outlet rates).
Watch out for
- Adding times instead of rates → Wrong: "A takes 10 days, B takes 15 days, together = 25 days." Correct: Add rates (1/10 + 1/15), then invert for time.
- Confusing efficiency ratio with time ratio → If A is twice as efficient as B, A takes half the time, not twice. Efficiency and time are inversely proportional.
- Ignoring negative work → When a pipe empties or a worker undoes work, subtract that rate. Students often add all rates as positive, getting absurdly fast completion.
Quick reference
- Time together formula: (t₁ × t₂)/(t₁ + t₂) when two workers combine.
- LCM trick: Total work = LCM(all times) makes all rates integers—faster arithmetic.
- Efficiency ∝ 1/Time: Double efficiency = half time; triple efficiency = one-third time.
- Pipes net rate: Inlet rate − Outlet rate. If net is negative, tank never fills.
- Man-days equivalence: 12 men in 10 days = 8 men in 15 days (both = 120 man-days for same work).
Check yourself: 3 questions
1. A can do a piece of work in 12 days, B in 15 days. Working together, they finish it in:
2. Pipe A fills a tank in 6 hours; pipe B can empty it in 8 hours. If both are opened together when the tank is empty, time to fill is:
3. A and B together can do a work in 8 days. A alone can do it in 12 days. B alone can do it in:
This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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