Percentage change in workplace data: Practice 3 (Advanced)

Reason through weighted growth, changing rates, per-unit measures and compound changes in ten original problems.

Instructions for this set

Use the original value as the base for relative change. Distinguish percentage points from percentages. All figures are hypothetical.

A calculator is allowed. Keep each comparison on a consistent base. For pooled growth, total the starting and ending quantities. For a rate or unit cost, calculate both ratios before finding the relative change. Reverse a chain by undoing its last operation first.

Answer keys and reasoning checked 19 October 2026. These checks do not establish psychometric validity.

Feedback mode has no time limit or negative marking. The optional timed challenge allows 20 minutes and uses the scoring shown on its rules screen. Those settings are not official assessment rules.

Practise with feedback Optional timed challenge

  1. 1. A US company has annual revenue of US$600,000 from services and US$400,000 from products. Service revenue rises by 10% while product revenue falls by 5%. What is the percentage change in total revenue?
    1. 2.5% increase
    2. 5% increase
    3. 4% increase
    4. 4% decrease

    Reference: q-6283cd96-202 · Report this question

    Show answer and solution

    Answer: C. 4% increase

    New revenue is 600,000 × 1.10 + 400,000 × 0.95 = 660,000 + 380,000 = US$1,040,000. Compared with US$1,000,000, the increase is 4%. A simple average of the two rates ignores the starting weights.
  2. 2. An Australian supplier increases its unit selling price by 20% and sells 10% fewer units. Assuming every unit sells at the stated price, what is the percentage change in sales revenue?
    1. 10% increase
    2. 2% decrease
    3. 12% increase
    4. 8% increase

    Reference: q-319a1aa4-185 · Report this question

    Show answer and solution

    Answer: D. 8% increase

    Revenue equals price × quantity. The combined factor is 1.20 × 0.90 = 1.08, so revenue increases by 8%. Subtracting 10 from 20 overlooks the interaction between price and quantity.
  3. 3. A UK team processes 12,000 records with an error rate of 3%. Next month it processes 18,000 records with an error rate of 2%. What is the percentage change in the number of erroneous records?
    1. 0%
    2. 1% decrease
    3. 33.33% decrease
    4. 50% increase

    Reference: q-df913b8-192 · Report this question

    Show answer and solution

    Answer: A. 0%

    Initially 12,000 × 0.03 = 360 records contain errors. Next month 18,000 × 0.02 = 360 do. The count is unchanged, so its percentage change is 0%; the error rate and the record count are different measures.
  4. 4. A fictional project reserve increases by 20% during a period. After this increase, £5,000 is withdrawn and £55,000 remains. What was the reserve before the increase?
    1. £45,833.33
    2. £50,000
    3. £48,000
    4. £60,000

    Reference: q-ea1cac30-166 · Report this question

    Show answer and solution

    Answer: B. £50,000

    Undo the final withdrawal first: the reserve after growth was 55,000 + 5,000 = £60,000. Then divide by 1.20 to recover the original £50,000. Applying the withdrawal before growth would reverse the stated order.
  5. 5. An Indian company initially allocates 20% of a total budget of INR 150,000 to training. The training allocation increases by 40%, while the total budget increases by 12%. By how many percentage points does training’s share of the total budget change?
    1. 2 percentage points
    2. 20 percentage points
    3. 5 percentage points
    4. 25 percentage points

    Reference: q-14ab5f7e-251 · Report this question

    Show answer and solution

    Answer: C. 5 percentage points

    Training starts at INR 30,000 and rises to 30,000 × 1.40 = INR 42,000. The new total is 150,000 × 1.12 = INR 168,000. The new share is 42,000 ÷ 168,000 = 25%, five percentage points above 20%.
  6. 6. An Australian plant spends A$120,000 making 1,000 units. In the next period, spending rises to A$138,000 and output rises to 1,200 units. What is the percentage change in cost per unit, rounded to two decimal places?
    1. 15.00% increase
    2. 5.00% decrease
    3. 4.35% decrease
    4. 4.17% decrease

    Reference: q-6a710fa8-217 · Report this question

    Show answer and solution

    Answer: D. 4.17% decrease

    Original unit cost = 120,000 ÷ 1,000 = A$120. New unit cost = 138,000 ÷ 1,200 = A$115. The reduction is 5 ÷ 120 × 100 = 4.166…%, or 4.17%. Rising total spending does not imply rising cost per unit.
  7. 7. A US data team reduces the time needed for an upload by 30%. A later change increases the reduced time by 20%. Relative to the original upload time, what is the net percentage change?
    1. 16% decrease
    2. 10% decrease
    3. 14% decrease
    4. 20% decrease

    Reference: q-5a79eb25-184 · Report this question

    Show answer and solution

    Answer: A. 16% decrease

    The new time is 0.70 × 1.20 = 0.84 of the original time. Therefore time is reduced by 16%. Adding −30% and +20% would miss the changing base.
  8. 8. A fictional UK membership count increases by 8% in year one and by 8% again in year two, each time relative to the previous year. What is the total percentage increase across the two years?
    1. 16.00%
    2. 16.64%
    3. 17.28%
    4. 8.64%

    Reference: q-4cf2e09a-190 · Report this question

    Show answer and solution

    Answer: B. 16.64%

    The two-year multiplier is 1.08 × 1.08 = 1.1664. Subtract one and multiply by 100 to get 16.64%. The second increase also applies to the members gained in year one.
  9. 9. An Indian supplier reduces a quoted price by 10%. What percentage increase in the reduced price would exactly restore the original price? Round to two decimal places.
    1. 10.00%
    2. 9.09%
    3. 11.11%
    4. 12.50%

    Reference: q-3690912d-167 · Report this question

    Show answer and solution

    Answer: C. 11.11%

    After the reduction the multiplier is 0.90. The restoring multiplier is 1 ÷ 0.90 = 1.11111…. Subtract one to get an 11.11% increase, rounded to two decimal places. A 10% increase would restore only 99% of the original.
  10. 10. An Australian retailer has two branches. North sells 400 units in April and 600 in May; South sells 600 in April and 540 in May. What is the percentage change in the combined units sold from April to May?
    1. 20% increase
    2. 40% increase
    3. 24% increase
    4. 14% increase

    Reference: q-72c28381-205 · Report this question

    Show answer and solution

    Answer: D. 14% increase

    April sales total 400 + 600 = 1,000 units. May sales total 600 + 540 = 1,140. The combined increase is 140 ÷ 1,000 × 100 = 14%. Averaging North’s 50% increase and South’s 10% decrease gives an incorrect result because the April totals differ.

Review your method

Return to the percentage change in workplace data lesson and identify the reasoning step behind each mistake before repeating the set.

Choose your practice difficulty

Difficulty labels describe the steps needed in these teaching sets; they are not validated ability bands. Start with foundation practice and move on after you can explain your method.

Continue learning