Percentage change in workplace data: guide and free practice

The original value is the base

Percentage change equals the difference divided by the original value, multiplied by 100. Going from 80 to 100 is a 25% increase, but returning from 100 to 80 is a 20% decrease. The difference in units is the same; the reference quantity is different.

Reverse a percentage with division

After a 20% discount, the new price is 80% of the original. Divide the discounted price by 0.80 to recover the original. Adding 20% to the discounted price uses the wrong base and does not undo the discount.

Combine successive changes

Multiply the factors: an increase of 10% followed by a decrease of 5% gives 1.10 times 0.95 = 1.045, or a net 4.5% increase. Add percentages only when they explicitly refer to the same base and the operation justifies addition.

Percentage points are different

A rate moving from 12% to 15% rises by three percentage points. Its relative increase is 3 divided by 12 = 25%. Read whether the question requests a change in the rate itself or a relative change.

Estimate and check

If a value rises by roughly one tenth, the answer should be near 10%. Check the sign, original period and requested rounding before comparing options. These workplace exercises mix direct changes, missing originals and changes in rates.

Before this lesson

Be comfortable converting a percentage to a decimal and multiplying or dividing by it. The numerical reasoning introduction explains matching quantities and units. For pooled results, also study weighted averages.

Worked example: reverse two price rises

A fictional annual service fee rises by 10%, then by 20%, to £231. Let the original fee be P. The final fee is P × 1.10 × 1.20 = P × 1.32, so P = 231 ÷ 1.32 = £175. Check forwards: £175 becomes £192.50, then £231. Adding the increases would give a factor of 1.30 and the wrong original fee.

Worked example: combine departments

One department has 200 requests and grows by 5%; another has 600 and grows by 15%. The new counts are 210 and 690. Total requests rise from 800 to 900, an increase of 100 ÷ 800 = 12.5%. The answer lies nearer 15% because the faster-growing department has more of the original requests. A simple average of 5% and 15% gives 10%, which wrongly weights both departments equally.

Worked example: a lower rate can hide a higher count

A team makes errors in 5% of 1,600 records, or 80 records. Later it makes errors in 4% of 2,500 records, or 100. The error rate falls by one percentage point, but the number of erroneous records rises by 20 ÷ 80 = 25%. Decide whether the question asks for the rate, the count or a percentage-point change.

Common mistakes to check

• Wrong denominator: label the earlier quantity before dividing a change by it.
• Adding sequential rates: multiply their factors when the second change uses the new value.
• Averaging unequal groups: reconstruct the total quantities or use the original weights.
• Rounding too soon: retain intermediate precision and round only the final result to the requested places.
• Zero starting value: a relative percentage increase from zero is undefined because the formula divides by zero. Describe the absolute increase instead; do not call it 100% growth.

Choose a next step

Foundation practice introduces the calculations; intermediate practice combines changing bases and reverse operations; advanced practice adds pooled totals and per-unit comparisons. These are teaching labels, not measured ability levels. After the sets, practise table interpretation to select the right figures or profit margins to distinguish margin from markup.

Your first practice session

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

Try 10 questions with explanations

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.

• Foundation: 10 questions — direct changes, missing originals and percentage points.
• Intermediate: 10 questions — Connect reverse percentages, changing bases and successive changes in ten original workplace problems.
• Advanced: 10 questions — Reason through weighted growth, changing rates, per-unit measures and compound changes in ten original problems.

Continue learning

• Numerical reasoning
• Budget variance reasoning
• Profit margin, markup and contribution

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.