This study notes covers Common Mistakes within Ratio Sharing for GCSE Mathematics. Revise Ratio Sharing in Ratio & Proportion for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This topic shows up very often in GCSE exams, so students should be able to explain it clearly, not just recognise the term. It is section 6 of 6 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 6 of 6
Practice
14 questions
Recall
12 flashcards
Common Mistakes
✗ Share £50 in 2:3 → £25 and £25
✓ That's 1:1, not 2:3! Answer is £20 and £30
✗ Forgetting to add up total parts first
✓ Always add the ratio numbers FIRST
✗ Not checking the shares add up
✓ ALWAYS check: shares should = original total
Practice Questions
Q1 Share £70 in the ratio 2:3 [2 marks]
[1] 5 parts = £70, 1 part = £14
[1] 2×14=£28, 3×14=£42
Q2 Share 90 marbles in the ratio 2:5:8 [3 marks]
[1] Total parts = 2+5+8 = 15
[1] 1 part = 90 ÷ 15 = 6 marbles
[1] 12, 30, 48 marbles
Q3 Tom and Sara share money in ratio 4:5. Sara gets £20 more. Find the total. [3 marks] H
[1] Difference = 5-4 = 1 part = £20
[1] Total parts = 9
[1] Total = 9 × £20 = £180
Q4 £120 is shared in ratio 3:7. Find the larger share. [2 marks]
[1] 10 parts = £120, 1 part = £12
[1] Larger share = 7 × £12 = £84
Q5 Share £40 in the ratio 1:3 [2 marks]
[1] 4 parts = £40, 1 part = £10
[1] Shares: £10 and £30
Q6 Share 100 sweets between Alice and Ben in the ratio 3:2 [3 marks]
[1] Total parts = 5
[1] 1 part = 100 ÷ 5 = 20 sweets
[1] Alice: 60, Ben: 40
Q7 £150 is divided in the ratio 2:3. Find both shares. [3 marks]
[1] 5 parts = £150, 1 part = £30
[1] First share: 2 × £30 = £60
[1] Second share: £60 and £90
Q8 Share 60 marbles between Tom, Dick and Harry in the ratio 1:2:3 [3 marks]
[1] Total parts = 6, 1 part = 10
[1] Tom: 10, Dick: 20, Harry: 30
[1] 10, 20, 30
Q9 £80 is shared 5:3. Find the smaller share. [2 marks]
[1] 8 parts = £80, 1 part = £10
[1] Smaller: 3 × £10 = £30
Q10 Three friends win £240. They share it in the ratio 2:3:7. How much does each person get? [4 marks]
[1] Total parts = 12
[1] 1 part = £240 ÷ 12 = £20
[1] 2×20 = £40, 3×20 = £60, 7×20 = £140
[1] £40, £60, £140
Q11 A and B share money in ratio 3:5. B gets £40 more than A. How much does B get? [4 marks]
[1] Difference = 5 - 3 = 2 parts
[1] 2 parts = £40, so 1 part = £20
[1] B gets 5 parts = 5 × £20
[1] B gets £100
Q12 Tom invests £3000, Sarah invests £5000. They share £400 profit in the same ratio as their investments. How much profit does each get? [5 marks]
[1] Investment ratio: 3000:5000 = 3:5
[1] Total parts = 8
[1] 1 part = £400 ÷ 8 = £50
[1] Tom: 3 × £50 = £150
[1] Sarah: Tom: £150, Sarah: £250
Q13 400g of sweets are shared in the ratio 1:2:3:4. Find the largest share. [4 marks]
[1] Total parts = 1+2+3+4 = 10
[1] 1 part = 400 ÷ 10 = 40g
[1] Largest = 4 parts = 4 × 40
[1] = 160g
Q14 An amount is shared 2:5:8. The smallest share is £60. Find the total amount. [5 marks]
[1] Smallest share = 2 parts = £60
[1] 1 part = £60 ÷ 2 = £30
[1] Total parts = 2 + 5 + 8 = 15
[1] Total = 15 × £30
[1] = £450
Q15 £50,000 is shared between 3 children in the ratio of their ages: 5:6:9. Find each share. [5 marks]
[1] Total parts = 5 + 6 + 9 = 20
[1] 1 part = £50,000 ÷ 20 = £2,500
[1] 5 parts = £12,500
[1] 6 parts = £15,000, 9 parts = £22,500
[1] £12,500, £15,000, £22,500
Examiner says: Always check your shares add up to the original total - here £12,500 + £15,000 + £22,500 = £50,000 ✓
Q16 Concrete is made from cement, sand and gravel in the ratio 1:2:4. How much sand is in 35 kg of concrete? [4 marks]
[1] Total parts = 1 + 2 + 4 = 7
[1] 1 part = 35 ÷ 7 = 5 kg
[1] Sand = 2 parts = 2 × 5
[1] = 10 kg
Q17 Money is shared 3:7:10. The difference between the largest and smallest share is £140. Find the total. [5 marks] Challenge
[1] Difference = 10 - 3 = 7 parts
[1] 7 parts = £140, so 1 part = £20
[1] Total parts = 3 + 7 + 10 = 20
[1] Total = 20 × £20
[1] = £400
Q18 Three partners invested £20,000, £30,000 and £50,000. Profit of £15,000 is shared in the ratio of their investments. How much profit does the middle partner get? [6 marks] Challenge
[1] Simplify investment ratio: 20:30:50
[1] Divide by 10: 2:3:5
[1] Total parts = 2 + 3 + 5 = 10
[1] 1 part = £15,000 ÷ 10 = £1,500
[1] Middle partner = 3 parts = 3 × £1,500
[1] = £4,500
Q19 £300 is shared in ratio 2:5:8. Find the middle share. [5 marks] Challenge
[1] Total parts = 2 + 5 + 8 = 15
[1] 1 part = £300 ÷ 15 = £20
[1] Middle share = 5 parts
[1] = 5 × £20
[1] = £100
Q20 Money is shared 3:7. What percentage of the total does the person with the smaller share receive? [5 marks] Challenge
[1] Total parts = 3 + 7 = 10
[1] Smaller share = 3 parts out of 10
[1] Fraction: 3/10
[1] As percentage: (3/10) × 100
[1] = 30%
Q21 180g of flour, water and eggs are mixed in ratio 5:3:4. How much of each ingredient? [4 marks]
[1] Total parts = 12, 1 part = 15g
[1] Flour: 5 × 15 = 75g
[1] Water: 3 × 15 = 45g
[1] Eggs: 75g, 45g, 60g
Q22 A football team scored 63 goals. Three strikers scored in ratio 2:4:3. How many goals did the top scorer get? [4 marks]
[1] Total parts = 9, 1 part = 7 goals
[1] Top scorer = 4 parts (largest)
[1] = 4 × 7
[1] = 28 goals
Q23
£500 is shared between Amy, Ben and Cal in ratio 3:4:6.
(a) How much does Amy get? [3 marks]
(b) How much more does Cal get than Ben? [3 marks]
[6 marks] Challenge
(a) Amy's share:
[1] Total parts = 13, 1 part = £500 ÷ 13 ≈ £38.46
[1] Amy = 3 parts = 3 × £38.46
[1] = £115.38
(b) Difference:
[1] Cal = 6 parts, Ben = 4 parts
[1] Difference = 6 - 4 = 2 parts
[1] 2 × £38.46 = £76.92
Examiner says: For part (b), you can find the difference directly from parts (6-4=2) without calculating individual shares first. This saves time!
Q24 Three angles of a triangle are in ratio 2:3:4. Find the largest angle. [5 marks] Challenge
[1] Total parts = 9
[1] Angles in triangle = 180°
[1] 1 part = 180° ÷ 9 = 20°
[1] Largest = 4 parts = 4 × 20°
[1] = 80°
Q25 Three workers share £720 wages in ratio 5:8:11. The worker with the middle wage gets how much? [5 marks]
[1] Total parts = 24
[1] 1 part = £720 ÷ 24 = £30
[1] Middle wage = 8 parts
[1] = 8 × £30
[1] = £240
Q26 A 3000 m² plot is divided into gardens in ratio 2:3:5. The largest garden is how much bigger than the smallest? [6 marks] Challenge
[1] Total parts = 10
[1] 1 part = 3000 ÷ 10 = 300 m²
[1] Smallest = 2 parts = 600 m²
[1] Largest = 5 parts = 1500 m²
[1] Difference = 1500 - 600
[1] = 900 m²
Q27 A 5-litre paint mix uses red, blue and white in ratio 1:3:6. What percentage is blue? [6 marks] Challenge
[1] Total parts = 1 + 3 + 6 = 10
[1] Blue = 3 parts out of 10
[1] Fraction blue: 3/10
[1] Percentage: (3/10) × 100
[2] = 30%
Examiner says: Notice the actual volume (5 litres) wasn't needed - ratio to percentage questions only need the ratio parts!
Q28 A 3-hour exam has questions worth marks in ratio 2:3:7. How many minutes for the section worth 3 parts? [5 marks]
[1] Total parts = 12
[1] 3 hours = 180 minutes
[1] 1 part = 180 ÷ 12 = 15 minutes
[1] 3 parts = 3 × 15
[1] = 45 minutes
Q29 An amount is shared 3:7:10. The middle share is £210. Find the total. [5 marks] Challenge
[1] Middle share = 7 parts = £210
[1] 1 part = £210 ÷ 7 = £30
[1] Total parts = 3 + 7 + 10 = 20
[1] Total = 20 × £30
[1] = £600
Q30 A charity receives £12,000. It splits funds between research, education and aid in ratio 5:3:12. If education receives an extra £600 donation, what is the new ratio? [7 marks] Challenge
[1] Total parts = 20, 1 part = £600
[1] Original: Research £3000, Education £1800, Aid £7200
[1] After donation: Education = £1800 + £600 = £2400
[1] New amounts: 3000:2400:7200
[1] Divide by 600: 5:4:12
[2] New ratio: 5:4:12
Examiner says: Multi-step ratio problems require careful tracking. Find the actual amounts first, apply changes, then convert back to a simplified ratio.