RRB Group D · Bite-size lessons

Time and Work

About 6 min · Mathematics · English

Time worked out from the lesson's 447 words at 150 words a minute, plus a minute for each question.

The core principle is simple: work is the product of rate (efficiency) and time. Questions test your ability to relate individual work rates, combine efficiencies for joint work, and handle inverse proportions between workers and time.

Key ideas

• Work as a quantity: Total work can be assigned any convenient value—commonly 1 unit or 100%. If A finishes a job in 10 days, A's one-day work = 1/10 of the job.
• Rate (efficiency) = Work / Time: If efficiency is constant, work done is directly proportional to time spent. Doubling workers (assuming same efficiency) halves the time.
• Man-Days or Work-Units: Total work = Number of persons × Days × Hours per day. Adjust this product when comparing different groups: 6 men in 8 days = 48 man-days of work.
• Inverse proportion for time: If work is constant, Time ∝ 1/Number of workers. If 5 workers take 12 days, 10 workers take 6 days (assuming equal efficiency).
• Combined work rate: When A and B work together, their one-day combined work = (A's rate) + (B's rate). If A does 1/x per day and B does 1/y per day, together they do (1/x + 1/y) = (x+y)/(xy) per day.

Watch out for

• Confusing rate and time: Students add times instead of rates. Wrong: If A takes 4 days and B takes 6 days, together ≠ 10 days. Correct: Add rates (1/4 + 1/6) then invert.
• Forgetting to subtract for leaks/outlets: In pipe problems, always assign negative rate to outlets. Omitting the minus sign gives an inflated net rate and wrong answer.
• Not accounting for remaining work: After partial work, students apply the original time formula to the whole job. Correct: Calculate fraction completed, subtract from 1, then find time for the remainder.

Quick reference

• 1-day work = 1 / (Total days for that person)
• Together time = (Product of individual times) / (Sum of individual times) for two workers.
• Pipes: Inlet (+), Outlet/Leak (−); Net rate = sum of signed rates.
• **Efficiency ratio m:*n* ⇒ Time ratio n:*m* (inverse).**
• **Man-days: M₁D₁ = M₂D₂ for equal work and efficiency.**

Check yourself: 3 questions

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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