TNPSC Group IV · Bite-size lessons
Time and Work
About 6 min · Aptitude and Mental Ability Test · English
Time worked out from the lesson's 418 words at 150 words a minute, plus a minute for each question.
Time and Work is a foundational quantitative aptitude topic in the TNPSC Group IV syllabus. This topic tests your ability to calculate how long workers take to complete jobs individually or together, and how pipes fill or empty tanks.
Key ideas
- Work as a unit: Assume total work = 1 unit (or LCM of given days for easier calculation). If A completes work in 10 days, A's 1 day work = 1/10.
- Combined work: When A and B work together, their combined 1 day work = 1/A + 1/B. Time to complete = 1/(combined rate).
- Inverse relationship: More workers = less time (assuming equal efficiency). If 5 men finish in 10 days, 10 men finish in 5 days.
- Efficiency concept: If A is twice as efficient as B, A does in 1 day what B does in 2 days. Efficiency and time are inversely proportional.
- Pipes filling tanks: Inlet pipe fills, outlet pipe empties. Net rate = filling rate − emptying rate.
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), not days.
- Forgetting negative sign for outlet pipes: Wrong: Adding emptying rate to filling rate. Correct: Subtract the outlet pipe's rate from inlet pipe's rate.
- Confusing efficiency with time: Wrong: "A is twice as efficient, so takes twice the time." Correct: Higher efficiency means less time (inverse relationship).
Quick reference
- A alone in 'a' days, B alone in 'b' days → Together = ab/(a+b) days
- More men, less days: M₁D₁ = M₂D₂
- Inlet fills, outlet empties → Net = 1/inlet − 1/outlet
- Efficiency doubled = Time halved
- LCM method: Total work = LCM, individual rate = LCM/days
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 A and B work together, how many days will they take to complete the work?
2. A pipe can fill a tank in 15 hours. Due to a leak at the bottom, it takes 20 hours to fill the tank. If the tank is full, how long will the leak take to empty it?
3. A and B can do a piece of work in 10 days, B and C can do it in 15 days, and A and C can do it in 20 days. How many days will A alone take to complete the work?
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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