Functional Skills Level 2 — Percentages

Percentage Change

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Calculating Percentage Change

Percentage change tells us how much something has changed relative to its original value. A positive result is an increase; a negative result is a decrease.

\(\text{Percentage change} = \dfrac{\text{change}}{\text{original}} \times 100\)
where change = new value − original value
Percentage change = (Change ÷ Original) × 100 Change = New value − Original value A positive result = increase A negative result = decrease Number Line: £40 → £50 £0 £40 £50 £60 £10 Change = £10, Original = £40, % change = (10/40)×100 = 25%

Example 1: A price rises from £40 to £50. What is the percentage increase?

Step 1
Change = £50 − £40 = £10
Step 2
% change = (10 ÷ 40) × 100
Step 3
= 0.25 × 100 = 25% increase

Example 2: A population falls from 8,000 to 6,800. What is the percentage change?

Step 1
Change = 6,800 − 8,000 = −1,200
Step 2
% change = (1,200 ÷ 8,000) × 100
Step 3
= 0.15 × 100 = 15% decrease
Common mistake: Always divide by the ORIGINAL value, not the new one. Using the wrong number is the most common mistake in percentage change questions.
✓ Quick Check 1 — Calculating Percentage Change
Percentage Profit and Loss

In business and buying/selling, we often express profit or loss as a percentage of the cost price (what was paid).

\(\text{% profit} = \dfrac{\text{profit}}{\text{cost price}} \times 100\)     \(\text{% loss} = \dfrac{\text{loss}}{\text{cost price}} \times 100\)
Profit and Loss: Cost Price £60 Cost Price £60 Buy low Selling Price? Sell at £75 → Profit £15 (15/60)×100 = 25% profit Sell at £48 → Loss £12 (12/60)×100 = 20% loss Always calculate % profit/loss as % of the COST price Profit and Loss Examples Scenario Cost Price Selling Price Profit/Loss % Example A £60 £75 £15 profit 25% profit Example B £60 £48 £12 loss 20% loss Example C £200 £250 £50 profit 25% profit Note: Examples A and C both give 25% profit — same ratio, different amounts

Example 3: A trader buys goods for £60 and sells for £75. What is the percentage profit?

Step 1
Profit = £75 − £60 = £15
Step 2
% profit = (15 ÷ 60) × 100
Step 3
= 25% profit

Example 4: A car is bought for £8,000 and sold for £6,400. What is the percentage loss?

Step 1
Loss = £8,000 − £6,400 = £1,600
Step 2
% loss = (1,600 ÷ 8,000) × 100
Step 3
= 20% loss
Key rule: Always calculate profit or loss as a percentage of the COST price (what you paid), not the selling price.
✓ Quick Check 2 — Percentage Profit and Loss
Real-Life Percentage Changes and Comparisons

We often need to compare percentage changes between two items to find which changed more. A larger cash change does not always mean a larger percentage change.

Comparing Price Rises: Same % but Different Cash Amounts Supermarket A Bread: £1.20 → £1.32 Change = £0.12 (0.12 ÷ 1.20) × 100 = 10% rise Supermarket B Bread: £1.50 → £1.65 Change = £0.15 (0.15 ÷ 1.50) × 100 = 10% rise B's cash rise is larger (£0.15 vs £0.12) but both have the same 10% percentage rise Pay Rise Comparison Worker A £20,000 £21,000 5% rise Worker B £30,000 £31,200 4% rise Worker B earns more cash (£1,200 vs £1,000) but Worker A got the better % rise (5% vs 4%)

Example 5: Two shops both increase pen prices by 12p. Compare the percentage rises.

Shop A
Pen: £0.80 → £0.92. % change = (0.12 ÷ 0.80) × 100 = 15%
Shop B
Pen: £1.20 → £1.32. % change = (0.12 ÷ 1.20) × 100 = 10%
Conclusion
Even though the cash increase is the same (12p), Shop A's percentage increase is higher because the original price was lower.

Example 6: A worker earns £28,000 and gets a £1,400 pay rise. What percentage rise is this?

Step 1
Change = £1,400
Step 2
% = (1,400 ÷ 28,000) × 100
Step 3
= 5% rise
✓ Quick Check 3 — Real-Life Percentage Changes and Comparisons

Practice: Percentage Change

Enter your answer as a number (e.g. 25 for 25%). Correct within ±0.1 is accepted.

#QuestionAnswerResult
1Price: £40 → £50. % change?
2Value: £500 → £400. % decrease?
3Cost £60, sell £75. % profit?
4Salary: £24,000 → £25,200. % rise?
5Cost £200, sell £150. % loss?
6Score: 60 → 72. % increase?
7Price: £1.20 → £1.32. % change?
8Cost £400, sell £320. % loss?
9Rent: £600 → £660. % rise?
10Cost £45, sell £54. % profit?

⚠ Things to Watch Out For

  • Subtracting from the wrong value: % change = (change ÷ ORIGINAL) × 100. The original value always goes on the denominator — not the new value.
  • Not identifying increase vs decrease: If new > original it's an increase; if new < original it's a decrease. State clearly which one it is.
  • Dividing change by new value: % change = (new−old)/old × 100. Using the new value as denominator gives a different (incorrect) percentage.
  • Negative percentage change: A negative result from the formula means a decrease. The percentage change is the magnitude — state it as a "decrease of X%".
  • Not giving answer as a percentage: The formula gives a decimal — multiply by 100 to get the percentage. 0.15 → 15%.
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