MH Police Bharti · Bite-size lessons
Time & Work
About 6 min · Mathematics · English
Time worked out from the lesson's 388 words at 150 words a minute, plus a minute for each question.
Time & Work is a topic in Maharashtra Police Bharti Mathematics. Questions test your ability to calculate how long workers take to complete jobs, how wages should be distributed, and how pipes fill or empty tanks.
Key ideas
- Work Rate: If A completes work in n days, A's one day work = 1/n. This is the fundamental building block.
- Combined Work: When A and B work together, their combined one day work = 1/a + 1/b, where a and b are their individual completion times.
- LCM Method: Assume total work = LCM of individual times. This converts fractions to whole numbers, making calculations faster.
- Inverse Relationship: More workers means less time (if efficiency is same). Time is inversely proportional to number of workers.
- Work = Rate × Time: Just like Distance = Speed × Time. This formula governs all variations.
Watch out for
- Adding times instead of rates: Wrong: "A takes 10 days, B takes 15 days, together = 25 days." Fix: Add work rates (1/10 + 1/15), not times.
- Forgetting negative sign for leaks: Wrong: Adding leak rate as positive. Fix: Emptying pipes always subtract from filling rate.
- Confusing work done vs work remaining: Wrong: Calculating time for total work after partial completion. Fix: Always find remaining work first, then apply rates.
Quick reference
- A alone in n days → One day work = 1/n
- A + B together → Time = (A × B)/(A + B)
- LCM method: Total work = LCM, then work per day = LCM ÷ individual time
- Wages ratio = Work done ratio (not time ratio)
- Pipes: Fill rate positive, Leak rate negative, Net rate = sum
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, in how many days will they complete the work?
2. 15 workers can complete a construction work in 20 days. After 10 days of work, 5 more workers joined. In how many more days will the work be completed?
3. A pipe can fill a tank in 6 hours. Another pipe can empty the full tank in 9 hours. If both pipes are opened together in the empty tank, in how many hours will the tank be filled?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 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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