Rule of Three Exercises with Solutions: 20 Practice Problems
Practice makes perfect! Here are 20 Rule of Three exercises with complete solution paths — from easy to challenging. Perfect for students and anyone wanting to refresh their skills.
Simple Proportional Problems
Problem 1: 4 notebooks cost $6.00. How much do 10 cost?
Solution: 1 notebook = $6.00 / 4 = $1.50 → 10 notebooks = $1.50 × 10 = $15.00
Problem 2: 200 g of cheese costs $3.60. How much do 350 g cost?
Solution: 1 g = $3.60 / 200 = $0.018 → 350 g = $0.018 × 350 = $6.30
Problem 3: A car uses 7 liters per 100 km. How much does it use for 280 km?
Solution: 1 km = 7 / 100 = 0.07 L → 280 km = 0.07 × 280 = 19.6 liters
Problem 4: 15 m of fabric costs $67.50. How much do 23 m cost?
Solution: 1 m = $67.50 / 15 = $4.50 → 23 m = $4.50 × 23 = $103.50
Problem 5: 8 bread rolls cost $2.80. How much do 20 cost?
Solution: 1 roll = $2.80 / 8 = $0.35 → 20 rolls = $0.35 × 20 = $7.00
Medium Difficulty Proportional Problems
Problem 6: A recipe for 4 people needs 250 g of butter. How much for 7 people?
Solution: 1 person = 250 / 4 = 62.5 g → 7 people = 62.5 × 7 = 437.5 g
Problem 7: 12 workers build a wall in 5 days. How long for 3 walls with 12 workers?
Solution: 1 wall = 5 days → 3 walls = 5 × 3 = 15 days (proportional: more walls = more time)
Problem 8: 3.5 kg of flour costs $2.45. How much do 12 kg cost?
Solution: 1 kg = $2.45 / 3.5 = $0.70 → 12 kg = $0.70 × 12 = $8.40
Inverse Problems
Problem 9: 6 workers need 10 days. How long do 15 workers need?
Solution: Total effort = 6 × 10 = 60 → 15 workers = 60 / 15 = 4 days
Problem 10: One pump empties a pool in 8 hours. How long do 4 pumps take?
Solution: Total effort = 1 × 8 = 8 → 4 pumps = 8 / 4 = 2 hours
Problem 11: 5 machines produce a batch in 12 hours. How long do 20 machines take?
Solution: Total effort = 5 × 12 = 60 → 20 machines = 60 / 20 = 3 hours
Problem 12: Supplies last 8 people for 15 days. How long for 12 people?
Solution: Total supply = 8 × 15 = 120 → 12 people = 120 / 12 = 10 days
Challenging Problems
Problem 13: 250 ml of paint covers 4 m². How much for 25 m²?
Solution: 1 m² = 250 / 4 = 62.5 ml → 25 m² = 62.5 × 25 = 1,562.5 ml (approximately 1.6 liters)
Problem 14: At 60 km/h a journey takes 45 minutes. How long at 90 km/h?
Solution: Total distance = 60 × 45 = 2,700 → 90 km/h = 2,700 / 90 = 30 minutes (inverse)
Problem 15: 100 g of chocolate has 540 kcal. How many kcal in 35 g?
Solution: 1 g = 540 / 100 = 5.4 kcal → 35 g = 5.4 × 35 = 189 kcal
Compound Problems
Problem 16: 4 workers produce 120 parts in 6 hours. How many parts do 6 workers make in 8 hours?
Solution: Step 1 (workers, proportional): 120 × 6/4 = 180. Step 2 (hours, proportional): 180 × 8/6 = 240 parts
Problem 17: 3 machines need 10 hours for 500 pieces. How many do 5 machines make in 8 hours?
Solution: Step 1 (machines, proportional): 500 × 5/3 = 833. Step 2 (hours, proportional): 833 × 8/10 = 667 pieces
Problem 18: 8 lamps run 5 hours on 10 batteries. How many batteries for 12 lamps for 3 hours?
Solution: Step 1 (lamps, proportional): 10 × 12/8 = 15. Step 2 (hours, proportional): 15 × 3/5 = 9 batteries
Problem 19: 6 printers print 2,400 pages in 4 hours. How many pages do 9 printers print in 3 hours?
Solution: Step 1: 2,400 × 9/6 = 3,600. Step 2: 3,600 × 3/4 = 2,700 pages
Problem 20: 5 chefs cook for 120 guests in 3 hours. How many chefs for 200 guests in 2 hours?
Solution: Step 1 (guests, proportional): 5 × 200/120 = 8.33. Step 2 (hours, inverse): 8.33 × 3/2 = 12.5 → 13 chefs
Tips for Practice
- Read each problem twice and identify: What is given? What is sought?
- Decide first: proportional or inverse?
- Always write out all three steps — even if you could do it mentally.
- Verify your answer — it builds confidence.
- Use our Rule of Three calculator to check your work!