Ratio and Proportion (Copy)

IGCSE Mathematics Core Practice Exam

Topic: Ratio and Proportion
Total Marks: 40
Time: 40 minutes
(With Detailed Solutions)

Section A: Ratios and Simplification (No Calculator)

Total Marks: 18

1. Simplify the following ratios: (6 marks)
a) 20 : 30 : 50
b) 45 : 60
c) 150 : 35

2. Divide the given quantity in the specified ratio: (6 marks)
a) Divide 90 in the ratio 2 : 3
b) Divide 160 in the ratio 5 : 3
c) Divide 72 in the ratio 4 : 2 : 2

3. A sum of $180 is shared between Ali and Bilal in the ratio 7 : 5. How much does each person get? (3 marks)

4. Write the ratio 400 metres : 2 kilometres in its simplest form. Give your answer in the form 1 : n. (3 marks)

Section B: Proportion and Applications (Calculator Allowed)

Total Marks: 22

5. A recipe for 4 people uses 250g of rice. How much rice is needed for 10 people? (3 marks)

6. A map has a scale of 1 : 25,000. A distance measures 6 cm on the map. What is the actual distance in kilometers? (3 marks)

7. 5 pens cost $6. How much will 8 pens cost? (3 marks)

8. It takes 3 workers 8 hours to complete a task. How long will it take 6 workers to complete the same task (assuming they work at the same rate)? (3 marks)

9. A supermarket offers two packs of washing powder: (4 marks)

• Pack A: 2 kg for $7.80
• Pack B: 5 kg for $18.50

Which pack offers better value for money? Show your working.

10. A machine produces 240 units in 6 hours. How many units will it produce in 10 hours at the same rate? (3 marks)

Marking Scheme with Detailed Explanations

Section A

1.
a) 20 : 30 : 50 → divide by 10 → 2 : 3 : 5 (2 marks)
b) 45 : 60 → divide by 15 → 3 : 4 (2 marks)
c) 150 : 35 → divide by 5 → 30 : 7 (2 marks)

2.
a) 2 + 3 = 5 → 90 ÷ 5 = 18 → 36 : 54 (2 marks)
b) 5 + 3 = 8 → 160 ÷ 8 = 20 → 100 : 60 (2 marks)
c) 4 + 2 + 2 = 8 → 72 ÷ 8 = 9 → 36 : 18 : 18 (2 marks)

3.
7 + 5 = 12 → 180 ÷ 12 = 15
Ali = 15 × 7 = $105
Bilal = 15 × 5 = $75 (3 marks)

4.
2 km = 2000 m
400 : 2000 = 400 ÷ 400 : 2000 ÷ 400 = 1 : 5 (3 marks)

Section B

5.
4 people → 250g
10 people → 250 × (10 ÷ 4) = 625g (3 marks)

6.
6 cm × 25,000 = 150,000 cm = 1.5 km (3 marks)

7.
Cost per pen = 6 ÷ 5 = 1.20
8 pens = 8 × 1.20 = $9.60 (3 marks)

8.
More workers = less time (inverse proportion)
3 workers × 8 hours = 6 workers × x
24 = 6x → x = 4 hours (3 marks)

9.
Pack A: 7.80 ÷ 2 = $3.90 per kg
Pack B: 18.50 ÷ 5 = $3.70 per kg
Pack B is better value (4 marks)

10.
240 ÷ 6 = 40 units/hour
40 × 10 = 400 units (3 marks)