Time, Work, Pipes and Productivity Notes for CAT: Concepts, Formulas, Worked Examples & Practice

    Time, Work, Pipes and Productivity notes for CAT: 65 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

    Chapter Roadmap: Time, Work, Pipes and Productivity

    ⚙️
    Chapter Journey

    Time, Work, Pipes and Productivity

    Step 1 • 11 CAT PYQs • Importance 0.75

    👷 Work Rates and Efficiency

    Master work units, rates, efficiency ratios, groups, partial work, and replacement logic.

    Step 2 • 3 CAT PYQs • Importance 0.35

    🔁 Alternating Work and Rosters

    Handle day-wise cycles, alternate-day work, rotating pairs, and leftover work.

    Step 3 • 3 CAT PYQs • Importance 0.35

    💰 Payments, Wages and Cost Optimization

    Split wages by work done and choose efficient worker combinations under cost constraints.

    Step 4 • 3 CAT PYQs • Importance 0.35

    🚰 Pipes, Tanks and Drains

    Convert filling and emptying into positive and negative work rates.

    By the end of this chapter: you should be able to convert every worker, pipe, or team into a rate and add their contributions cleanly.

    Work Rates and Efficiency

    Arithmetic → Time, Work, Pipes and Productivity → Topic 1

    Work Rates and Efficiency

    The whole topic is one idea: work completed equals rate multiplied by time.

    R×T
    Work rate
    Efficiency ratios
    Man-hours
    Team productivity

    The One Formula: Work = Rate × Time

    Work grows by rate and time

    Total work

    Usually take it as job.

    Rate

    Fraction of job done per unit time.

    Time

    Days or hours worked.

    LCM Work Units: Make Fractions Disappear

    Use units when many workers appear

    If A finishes in days and B finishes in days, take total work as:
    A's daily work
    B's daily work
    Exam use: choose units when there are ratios, teams, or many partial days.

    Time, Work, Pipes and Productivity: Solved Questions with Step-by-Step Explanations (2 Problems)

    Question 1 · Quantitative Ability MCQ

    In a time and work problem, if the number of workers changes midway through the job and their daily working hours also change, which standard quantity should you equate or compare to solve the problem?

    1. A.

      Total wages

    2. B.

      Total person-hours

    3. C.

      Efficiency ratio

    4. D.

      Harmonic mean of times

    Correct Answer:

    B

    Step-by-Step Solution

    Key idea: This is a checklist trigger question for work problems with changing group sizes and hours.

    Step 1: When both the number of people and the hours per day change, the individual daily rates are no longer constant.

    Step 2: The most reliable invariant to track is the total effort expended, measured in person-hours (or man-hours).

    Step 3: You equate the person-hours used in each phase to the fraction of work completed in that phase.

    Trap: Students sometimes try to track "mandays" but forget that the hours per day have changed, making "mandays" invalid unless hours are constant.

    Answer: B

    Question 2 · Quantitative Ability MCQ

    Assertion: If a job is partly completed, the remaining work is total work minus completed work.

    Reason: The total job is split into the completed part and the uncompleted part.

    1. A.

      Both the assertion and the reason are true, and the reason explains the assertion

    2. B.

      Both the assertion and the reason are true, but the reason does not explain the assertion

    3. C.

      The assertion is true but the reason is false

    4. D.

      The assertion is false but the reason is true

    Correct Answer:

    A

    Step-by-Step Solution

    Key idea: This is a remaining-work checklist question, recognisable because it links completed work and remaining work.

    Step 1: Total work is the whole job.

    Step 2: If some part is already completed, the uncompleted part is what remains.

    Step 3: Therefore:

    Step 4: The reason states exactly why this subtraction is valid: the total job is split into completed and uncompleted parts.

    Answer: A

    More notes in this unit

    chapter
    Time, Work, Pipes and Productivity Notes for CAT: Concepts, Formulas, Worked Examples & Practice

    Time, Work, Pipes and Productivity notes for CAT: 65 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

    A question from this chapter

    Question 1

    In a time and work problem, if the number of workers changes midway through the job and their daily working hours also change, which standard quantity should you equate or compare to solve the problem?

    Question 2

    Assertion: If a job is partly completed, the remaining work is total work minus completed work.

    Reason: The total job is split into the completed part and the uncompleted part.

    Free preview ends here

    Login to view the complete notes

    Creating an account is free. You get the rest of this chapter, step-by-step solutions, and a study plan built around the topics you are actually weak at.

    Login to continueSee plans
    Why MastersUp

    Personalised first. High quality throughout.

    Most platforms hand everyone the same content. Here the content moves with your performance, topic by topic.

    Built around you, not around a syllabus PDF

    Every answer you give moves your topic-level intelligence rate. The next question, the next revision card and tomorrow's plan all change with it.

    Revision that hits your weak spots

    We only revise topics you have actually attempted and are still below the safe bar on — never the same chapter on repeat.

    Questions calibrated to the real exam

    Each question carries a measured toughness. You are served a rung above your current level, so practice keeps stretching you.

    Notes written for recall, not for volume

    Full lesson cards for first study, curated short-note cards for the last mile — with derivations, traps and exam patterns marked.

    One place for everything

    Notes, chapter practice, previous-year questions, test series and full-length papers — all feeding one picture of your preparation.

    Honest progress

    No vanity streaks. Progress here means chapters mastered and accuracy that held up on harder questions.

    Unlock the whole course

    Full notes and short notes, the complete question bank with worked solutions, mock tests, full-length papers, and an adaptive plan that rebuilds itself as you improve.

    View all plansStart free