Rates and productivity: guide and free practice

Solve productivity problems by converting work into a rate per person, machine or hour, then scale only the quantities the question says are constant.

Separate output, time and resources

When equal machines operate at a constant rate, output equals the number of machines times operating hours times output per machine-hour. Doubling machine count doubles capacity only if the question assumes no other bottleneck.

Combine rates, not completion times

A machine completing a job in six hours works at one sixth of a job per hour. A second completing it in three hours works at one third. Together they work at one half of a job per hour and finish in two hours, provided their work combines without interference.

Account for usable time

A shift length is not necessarily the operating time. Deduct stated breaks, setup and maintenance before multiplying a production rate. If a problem supplies utilisation, apply it to the available capacity rather than adding it to a headcount.

Find the limiting stage

In a sequence of processing steps, the lowest sustained capacity limits overall throughput when sufficient input is available. Increasing a faster stage may not increase the final output. Keep separate the number processed and the backlog waiting.

Check assumptions

These problems deliberately state constant rates and identical resources where needed. Real productivity may vary with fatigue, learning and equipment. Use the simplified model given, keep units visible and round whole-resource requirements up when a fractional person or machine cannot meet a deadline.

Your first practice session

Use the constant-rate and identical-resource assumptions explicitly stated. Deduct stated downtime. Round required whole resources up, not to the nearest integer.

Try 10 questions with explanations

Worked examples

  1. 1. Four identical machines produce 960 units in six hours. How many units does one machine produce per hour?
    1. 60
    2. 160
    3. 30
    4. 40

    Reference: q-12746fac-106 · Report this question

    Show answer and solution

    Answer: D. 40

    Divide 960 by four machines and six hours: 960/24 = 40 units per machine-hour.
  2. 2. Three identical packing lines each produce 45 boxes per hour. How many boxes do they produce in four hours?
    1. 540
    2. 600
    3. 180
    4. 405

    Reference: q-9a1c62b8-108 · Report this question

    Show answer and solution

    Answer: A. 540

    Output is 3 times 45 times 4 = 540 boxes.
  3. 3. An operator processes 24 records per hour. How long does 180 records take at that rate?
    1. 7 hours
    2. 7.5 hours
    3. 8 hours
    4. 6 hours

    Reference: q-8a55d3fe-88 · Report this question

    Show answer and solution

    Answer: B. 7.5 hours

    Time equals work divided by rate: 180/24 = 7.5 hours.

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About this practice

These are independently written teaching questions. A practice score helps you review your answers; it is not a validated hiring prediction or an official employer score.