Worked Examples: Ratio and Proportion Problems

This final lesson presents complete UCAT-style data sets focusing on ratios, percentages, and proportions. Each set includes 4 questions with full worked solutions, timing guidance, and strategy notes. These examples bring together all the skills covered in this course.

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Data Set 1: Business Partnership

Data: Three business partners — Ahmed, Beth, and Carlos — invest in a company in the ratio 3:5:2. The total investment is £150,000.

In the first year, the company makes a profit of £42,000, which is distributed in the same ratio as the investment.

Question 1: How much did Beth invest?

• Total ratio parts: 3 + 5 + 2 = 10
• One part: £150,000 ÷ 10 = £15,000
• Beth (5 parts): 5 × £15,000 = £75,000

Time: ~5 seconds.

Question 2: How much profit does Ahmed receive?

• Ahmed's share of profit: 3/10 × £42,000
• 42,000 ÷ 10 = 4,200
• 3 × 4,200 = £12,600

Time: ~5 seconds.

Question 3: What is Ahmed's profit as a percentage of his investment?