Time and Work
About 6 min · Quantitative Aptitude (Basic Arithmetic Skill) · English
Time worked out from the lesson's 446 words at 150 words a minute, plus a minute for each question.
The topic tests your ability to relate the amount of work done to the time taken and the efficiency of workers. Understanding this chapter is critical because the same logic extends to Pipes and Cisterns problems, which are essentially Time and Work dressed in different language.
Key ideas
- Work is constant: If no quantity is mentioned, assume total work = 1 unit. Alternatively, use the LCM of all given times as total work to avoid fractions.
- Efficiency = Work done per unit time: If A completes work in 10 days, A's one-day work = 1/10. Efficiency is inversely proportional to time taken.
- Joint work formula: If A does work in x days and B in y days, working together they complete 1/(1/x + 1/y) days, which simplifies to (xy)/(x+y) days.
- Man-Day equivalence: Total Work = Number of persons × Number of days. If 5 men finish in 6 days, then 1 man finishes in 30 days (or 30 man-days of work exist).
- Negative work in Pipes: A filling pipe adds work (positive efficiency), while an emptying/leak pipe removes work (negative efficiency). Combine them algebraically.
Watch out for
- Adding times instead of rates: Students often add 12 days + 15 days = 27 days when combining two workers. Fix: Always add rates (1/12 + 1/15), never times.
- Forgetting negative sign for emptying pipes: Treating an emptying pipe as positive work leads to absurd answers (tank fills faster with a leak!). Fix: Subtract the emptying rate explicitly.
- Confusing efficiency ratio with time ratio: If A is twice as efficient as B, students incorrectly assume A takes twice the time. Fix: Efficiency and time are inversely proportional — if A:B efficiency = 2:1, then A:B time = 1:2.
Quick reference
- A in x days, B in y days → Together in (xy)/(x+y) days
- Total Work = LCM of all given days → Avoid fractions
- Efficiency ∝ 1/Time → Double efficiency = Half time
- Man-Day constant: M₁D₁ = M₂D₂ for same work
- Pipes: Add filling rates, subtract emptying rates
Check yourself: 3 questions
1. A can complete a piece of work in 15 days and B can complete the same work in 20 days. If they work together for 6 days, what fraction of the work remains incomplete?
2. A can complete a work in 12 days and B can complete the same work in 18 days. If they work together, in how many days will they complete the work?
3. A can complete a piece of work in 12 days and B can complete the same work in 18 days. If they work together, in how many days will they complete the work?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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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