Math Ratios, Proportions, and Percentages

Question 1

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?

Accepted Answer

12% increase

Answer

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

Question 2

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)?

Accepted Answer

4 days

Answer

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

Question 3

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?

Accepted Answer

87.5 miles

Answer

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

Question 4

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

Accepted Answer

25%

Answer

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

Question 5

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

Accepted Answer

39 students

Answer

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.

Math Practice Test

Math Practice Test

Math Ratios, Proportions, and Percentages