TNPSC Group II · Bite-size lessons
Time and Work
About 6 min · Aptitude and Mental Ability · English
Time worked out from the lesson's 438 words at 150 words a minute, plus a minute for each question.
Time and Work is a fundamental quantitative aptitude topic in the TNPSC Group II/IIA prelims syllabus. Questions typically involve calculating how long workers take to complete tasks individually or together, or how pipes fill/empty tanks. The underlying principle is simple: work done equals rate multiplied by time.
Key ideas
- Work as a unit: The total work is often assumed as 1 unit (or taken as LCM of given days for easier calculation). Individual contribution is a fraction of this whole.
- Rate of work = 1/Time: If A completes a job in 10 days, A's one-day work = 1/10 of the total job. This rate remains constant unless specified otherwise.
- Combined work: When A and B work together, their combined rate = (1/A) + (1/B). Time to complete = 1/(combined rate).
- LCM method: Taking total work as LCM of individual times converts fractions to whole numbers, making calculations faster and error-free.
- Negative work: In pipes and cisterns, outlet pipes or leaks do negative work (emptying), while inlet pipes do positive work (filling). Net rate = filling rate - emptying rate.
Watch out for
- Adding times instead of rates: Students often add 12 + 18 = 30 days when A takes 12 days and B takes 18 days. Correct approach: Add the rates (1/12 + 1/18), not the times.
- Forgetting to subtract outlet pipe rate: In cistern problems with leaks, students add all rates. Correct approach: Outlet/leak rate must be subtracted from inlet rate.
- Ignoring remaining work: When someone leaves midway, students sometimes calculate total time afresh. Correct approach: First find work done, then calculate time for remaining work only.
Quick reference
- Work rate = 1/Time; Combined rate = Sum of individual rates
- Time together = (A × B)/(A + B) for two workers
- LCM method: Total work = LCM of days; Rate = Total work/Individual time
- Pipes filling: positive rate; Pipes emptying: negative rate
- Efficiency ∝ 1/Time — more efficient means less time
Check yourself: 3 questions
1. A can complete a work in 12 days and B can complete the same work in 18 days. If both work together, how many days will they take to complete the work?
2. 15 workers can complete a construction project in 20 days. After 10 days of work, 5 workers left. How many more days will the remaining workers take to complete the project?
3. A pipe can fill a tank in 6 hours. A drain pipe can empty the same tank in 8 hours. If both pipes are opened together, how long will it take to fill the empty tank?
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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