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

    Time, Work, Pipes and Productivity short notes for CAT: 26 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

    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.

    Man-Hours: When Hours per Day Change

    Days alone are not enough

    If a worker finishes a job in days working hours per day:
    If that worker later works hours per day for days:

    Efficiency and Time Are Opposite

    More efficient means less time

    Time ratio
    Efficiency ratio

    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

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

    Time, Work, Pipes and Productivity short notes for CAT: 26 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.

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