10 sample questions on percentages and ratio and solution

Here are 10 sample questions on percentages and ratios, along with their solutions:

### Percentage Questions

1. **Question:** A dress originally costs $80 but is on sale for 25% off. What is the sale price?
   - **Solution:**  
     Sale discount = 25% of $80 = $ 0.25 \times 80 = 20 $  
     Sale price = $ 80 - 20 = 60 $  
     **Answer:** $60

2. **Question:** If 60% of a number is 90, what is the original number?
   - **Solution:**  
     Let the original number be $ x $.  
     $ 0.6x = 90 $  
     $ x = \frac{90}{0.6} = 150 $  
     **Answer:** 150

3. **Question:** A student scores 80 out of 100 in an exam. What is the percentage score?
   - **Solution:**  
     Percentage = $ \frac{80}{100} \times 100 = 80\% $  
     **Answer:** 80%

4. **Question:** A population of 10,000 people increases by 15%. What is the new population?
   - **Solution:**  
     Increase = 15% of 10,000 = $ 0.15 \times 10,000 = 1,500 $  
     New population = $ 10,000 + 1,500 = 11,500 $  
     **Answer:** 11,500

5. **Question:** A store marks up a product's price by 40%. If the original price is $50, what is the marked-up price?
   - **Solution:**  
     Increase = 40% of $50 = $ 0.4 \times 50 = 20 $  
     Marked-up price = $ 50 + 20 = 70 $  
     **Answer:** $70

### Ratio Questions

6. **Question:** The ratio of boys to girls in a class is 3:2. If there are 30 boys, how many girls are there?
   - **Solution:**  
     Let the number of girls be $ x $.  
     $ \frac{3}{2} = \frac{30}{x} $  
     Cross-multiplying: $ 3x = 60 $  
     $ x = 20 $  
     **Answer:** 20 girls

7. **Question:** Divide $500 between two people in the ratio 4:1.
   - **Solution:**  
     Total parts = $ 4 + 1 = 5 $  
     Share of first person = $ \frac{4}{5} \times 500 = 400 $  
     Share of second person = $ \frac{1}{5} \times 500 = 100 $  
     **Answer:** $400 and $100

8. **Question:** The ratio of apples to oranges in a basket is 5:3. If there are 24 oranges, how many apples are there?
   - **Solution:**  
     Let the number of apples be $ x $.  
     $ \frac{5}{3} = \frac{x}{24} $  
     Cross-multiplying: $ 3x = 120 $  
     $ x = 40 $  
     **Answer:** 40 apples

9. **Question:** A recipe requires ingredients in the ratio 2:3:5 for sugar, flour, and butter respectively. If there is 200g of butter, how much sugar is needed?
   - **Solution:**  
     Let the amount of sugar be $ x $.  
     $ \frac{2}{5} = \frac{x}{200} $  
     Cross-multiplying: $ 5x = 400 $  
     $ x = 80 $  
     **Answer:** 80g of sugar

10. **Question:** The ratio of the length to the width of a rectangle is 7:4. If the width is 12 cm, what is the length?
   - **Solution:**  
     Let the length be $ x $.  
     $ \frac{7}{4} = \frac{x}{12} $  
     Cross-multiplying: $ 4x = 84 $  
     $ x = 21 $  
     **Answer:** 21 cm

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Would you like more detailed explanations for any of these questions, or do you have any other questions?

### Related Questions:
1. If a price is increased by 20% and then decreased by 10%, what is the net change?
2. How do you convert a ratio into a percentage?
3. If the ratio of boys to girls is 5:7 and there are 70 girls, how many boys are there?
4. What is 25% of 300?
5. A mixture contains milk and water in a 3:1 ratio. How much water is there if there are 12 liters of milk?

### Tip:
When working with percentages, converting them into decimal form (e.g., 25% = 0.25) can make calculations faster.

Explore 10 sample questions on percentages and ratios, with step-by-step solutions. Topics include calculating sale prices, population growth, and dividing amounts based on ratios. Ideal for students in Grades 6-8.

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