MPESB Group · Bite-size lessons
Time and Work
About 6 min · Mathematics · English
Time worked out from the lesson's 380 words at 150 words a minute, plus a minute for each question.
The core idea is simple: work done equals the product of efficiency and time. Mastering this topic requires understanding how to handle combined work, alternating work patterns, and the pipes-cisterns variation.
Key ideas
- Efficiency is inversely proportional to time: If A is twice as fast as B, A takes half the time B takes for the same work.
- Efficiency = Total Work ÷ Time: When A completes work in 10 days, A's efficiency is W/10 per day.
- LCM Method: Assume total work = LCM of all given times. This gives integer efficiencies, avoiding fractions entirely.
- Combined efficiency: When A and B work together, add their individual efficiencies. Time = Total Work ÷ (Efficiency of A + Efficiency of B).
- Negative efficiency for pipes: An outlet pipe or leak has negative efficiency—it subtracts from the filling rate.
Watch out for
- Adding times instead of efficiencies: Students write "12 + 18 = 30 days together." Wrong! You must add rates (1/12 + 1/18), not times. Fix: Always convert to efficiency first.
- Forgetting negative sign for outlets: Treating an emptying pipe as positive fills nothing correctly. Fix: Outlets and leaks always subtract from net rate.
- Misapplying man-days to efficiency problems: Man-days works only when all workers have equal efficiency. Fix: Use LCM method when workers have different rates.
Quick reference
- Total Work = LCM of all given times → gives integer efficiencies
- Combined time = (a × b)/(a + b) for two workers with times a and b
- Outlet/leak → negative efficiency; always subtract
- M₁D₁ = M₂D₂ → only when all workers have equal efficiency
- Remaining work = Total work − Work already done
Check yourself: 3 questions
1. 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?
2. 15 men can complete a piece of work in 20 days. How many days will 25 men take to complete the same work?
3. A pipe can fill a tank in 6 hours. Due to a leak at the bottom, it takes 9 hours to fill the tank. If the tank is full, in how many hours will the leak empty it?
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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