AQA GCSE Mathematics Paper 2 (Foundation), June 2025: Question 21

Combining Percentages of Amounts

📋 What this question tests

This question assesses your ability to find a percentage of a percentage (or a fraction of a portion), work systematically with complementary percentages (summing to 100%), and combine parts to find an overall total percentage.

Question 21 • 3 Marks

Discs Removed from a Box

70% of the discs in a box are red and the rest are blue. 40% of the red discs are removed. 50% of the blue discs are removed. In total, what percentage of the discs are removed from the box?

✅ Correct Answer

43%

Mark Scheme Breakdown:
• M1: Method to calculate 40% of 70% (e.g. 0.4 × 70 = 28)
• M1: Method to calculate 50% of 30% (e.g. 0.5 × 30 = 15)
• A1: Correct total of 43% (28 + 15)

💡 Key Knowledge

Total parts sum to 100%: If 70% are red, then 100% − 70% = 30% are blue.
Percentage of a percentage: "40% of 70%" means multiplying their decimal or fractional equivalents:
0.40 × 70% = 28% of the whole.
Smart Assumption Strategy: When working purely with percentages, you can assume there are 100 discs in total to make calculations intuitive.

📐 Step-by-Step Calculations

Method 1: Assuming a Total of 100 Discs (Easiest & Most Reliable)

1 Find the initial count of each colour:
Suppose there are 100 discs in total.
• Red discs = 70
• Blue discs = 100 − 70 = 30

2 Calculate how many of each colour are removed:
• Red removed: 40% of 70 = 0.4 × 70 = 28 discs [M1]
• Blue removed: 50% of 30 = 0.5 × 30 = 15 discs [M1]

3 Total removed discs:
• Total removed = 28 + 15 = 43 discs
Since we started with 100 discs, 43 out of 100 is directly 43% [A1] .

Method 2: Using Decimals (Direct Percentage Multipliers)

• Proportion of box that is red removed = 0.70 × 0.40 = 0.28 (or 28%) [M1]
• Proportion of box that is blue removed = (1 − 0.70) × 0.50 = 0.30 × 0.50 = 0.15 (or 15%) [M1]
• Total removed = 0.28 + 0.15 = 0.43 = 43% [A1]

❌ Common Errors & Misconceptions

Adding percentages directly: Calculating 40% + 50% = 90%. You cannot add percentages when they apply to different sized groups!
Finding what remains instead of what is removed: Calculating 60% of 70 + 50% of 30 = 57%. This gives the discs left in the box. (Marks awarded: SC2: 57 ).
Leaving the answer as a decimal: Writing 0.43 instead of 43 when the "%" symbol is outside the answer line (though 0.43 generally implies method marks).
Writing "40% of 70%" without evaluation: Simply re-writing the words from the question using "of" does not show mathematical method; you must show the multiplication.

🧠 Exam Technique & Examiner Insight

State the number base: Writing "Assume 100 discs" at the top makes your method crystal clear and prevents slips with decimals.
Reread the final requirement: Check whether the question asks for the percentage removed or the percentage remaining.
Partial credit is generous: Even if your final addition goes wrong, writing down either 28 or 15 guarantees method marks.