UP Police Constable · Bite-size lessons
Time and Work
About 7 min · Numerical & Mental Ability · English
Time worked out from the lesson's 453 words at 150 words a minute, plus a minute for each question.
This chapter tests your ability to convert real-world productivity scenarios into mathematical equations and solve them efficiently.
Key ideas
- Work is constant: Total work is typically assumed as 1 unit or taken as LCM of all given days for easier calculation. This allows you to focus on rates rather than absolute quantities.
- Rate (Efficiency) = 1/Time: If A completes work in 10 days, A's one-day work = 1/10. If B does it in 15 days, B's rate = 1/15. Combined rate when working together = 1/10 + 1/15.
- Time taken together = Total Work / Combined Rate: When multiple workers collaborate, add their individual rates to get the combined efficiency, then divide total work by this sum.
- Negative work for emptying: In pipes and cisterns problems, outlet pipes (emptying) have negative rates. If inlet fills in 6 hours and outlet empties in 8 hours, net rate = 1/6 - 1/8.
- Work done = Efficiency × Time: If A works for 5 days at rate 1/10 per day, work done = 5 × (1/10) = 1/2. Remaining work = 1 - 1/2 = 1/2.
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), then invert to get time (6 days).
- Forgetting negative rate for outlet pipes → In cistern problems, always subtract the emptying rate. An outlet reduces net filling speed.
- Assuming equal efficiency when distributing wages → Wages depend on (efficiency × time), not just time. Two workers for the same duration but different efficiencies get different pay.
Quick reference
- If A does work in a days and B in b days, together = ab/(a+b) days.
- Total work = LCM of individual days. Efficiency = LCM/Days. Sum efficiencies for combined rate.
- Pipes: Inlet rate (+), Outlet rate (−). Net rate = sum of all rates.
- Man-days: M₁D₁ = M₂D₂. More men → fewer days (inverse proportion).
- Wages split = ratio of (efficiency × days worked) for each person.
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, in how many days will they 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, in how many hours will the leak empty it?
3. 15 men can complete a work in 20 days. After 10 days, 5 more men joined them. In how many more days will the work be completed?
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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