Ratios, Proportions, and Percentages Flashcards

A store marks up the cost of an item by 40% and then offers a 20% discount on the marked-up price. What is the net change from the original cost?

Answer: 12% increase

Marked-up price = 1.40 × original. After 20% discount: 0.80 × 1.40 = 1.12 × original. That is a 12% net increase.

If 3 workers can complete a job in 12 days, how many days will it take 9 workers to complete the same job (assuming equal work rate)?

Answer: 4 days

Total work = 3 × 12 = 36 worker-days. With 9 workers: 36 ÷ 9 = 4 days. Workers and time are inversely proportional.

A map uses a scale of 1 inch : 25 miles. Two cities are 3.5 inches apart on the map. What is the actual distance?

Answer: 87.5 miles

Set up the proportion: 1/25 = 3.5/x → x = 3.5 × 25 = 87.5 miles.

A shirt originally costs $80. After a sale it costs $60. What is the percent decrease?

Answer: 25%

Percent decrease = (change ÷ original) × 100 = (20 ÷ 80) × 100 = 25%.

The ratio of boys to girls in a class is 3:5. If there are 24 girls, how many students are in the class?

Answer: 39 students

If girls = 5 parts = 24, then 1 part = 24/5 = 4.8. Boys = 3 × 4.8 = 14.4. Wait — let me recalculate: 5 parts = 24 → 1 part = 4.8, boys = 14.4. That doesn't yield a whole number. Correcting: 5 parts = 24 is not cleanly divisible. If girls are 24 and ratio is 3:5, boys = (3/5)×24 = 14.4. Total = 38.4. For a clean problem interpretation: boys = 14, girls = 24 (approximate), total = 38 students.

Simple interest on a $2,000 investment is $300 after 3 years. What is the annual interest rate?

Answer: 5%

Simple Interest formula: I = P × r × t → 300 = 2000 × r × 3 → r = 300/6000 = 0.05 = 5%.