Multiple Choice

1. Convert $125\%$ to a simplified mixed number.

   $\frac{5}{4}$

   $1\frac{25}{100}$

   $1\frac{1}{4}$

   $1.25$

2. Convert $\frac{5}{6}$ to a percentage, rounded to two decimal places.

   $83.33\%$

   $83.34\%$

   $0.83\%$

   $83.3\%$

3. Convert $0.0075$ to a percentage.

   $0.75\%$

   $0.0075\%$

   $75\%$

   $7.5\%$

4. Convert $16\frac{1}{2}\%$ to a decimal.

   $1.65$

   $0.16$

   $16.5$

   $0.165$

5. Convert $0.8\overline{3}$ to a simplified fraction.

   $\frac{83}{100}$

   $\frac{5}{60}$

   $\frac{5}{6}$

   $\frac{3}{4}$

6. Which of the following decimals is equivalent to $\frac{7}{16}$?

   $0.437$

   $0.44$

   $0.4375$

   $0.43$

7. Which of the following represents the largest value?

   $\frac{5}{8}$

   $0.65$

   $64\%$

   $0.655$

8. A store offers a $37.5\%$ discount on all items. What fraction of the original price does a customer pay?

   $0.625$

   $\frac{1}{2}$

   $\frac{5}{8}$

   $\frac{3}{8}$

9. A recipe calls for $\frac{3}{8}$ cup of sugar. What percentage of a cup is this?

   $3.75\%$

   $38\%$

   $37.5\%$

   $0.375\%$

10. A quantity increased by $150\%$. If the original quantity was $X$, which of the following expressions represents the new quantity?

    $X + 1.5$

    $250X$

    $1.5X$

    $2.5X$

11. Express $175\%$ as an improper fraction in simplest form.

    $\frac{175}{100}$

    $\frac{1}{75}$

    $\frac{7}{4}$

    $\frac{7}{5}$

12. The decimal $0.006$ is equivalent to what percentage?

    $0.06\%$

    $6\%$

    $0.6\%$

    $0.00006\%$

13. Convert the fraction $\frac{5}{12}$ to a decimal, rounded to the nearest thousandth.

    $0.42$

    $0.417$

    $0.41$

    $0.416$

14. What is $12.5\%$ expressed as a fraction in its simplest form?

    $\frac{1}{4}$

    $\frac{1}{8}$

    $\frac{12}{100}$

    $\frac{25}{200}$

15. The percentage $33\frac{1}{3}\%$ is equivalent to which fraction?

    $\frac{1}{3}$

    $\frac{1}{6}$

    $\frac{33}{100}$

    $\frac{2}{3}$

16. A bicycle originally priced at $\$240$ is on sale for $25\%$ off. If a store member gets an additional $10\%$ discount on the sale price, what is the final price the store member pays?

    $168$

    $162$

    $156$

    $165.60$

17. After a $15\%$ increase, the rent for an apartment is $\$920$ per month. What was the original rent before the increase?

    $850$

    $1058$

    $800$

    $782$

18. A car's value depreciated from $\$18,000$ to $\$13,500$ in one year. What was the percentage decrease in its value?

    $33.33\%$

    $75\%$

    $25\%$

    $20\%$

19. A jacket is priced at $\$80$. It's on sale for $20\%$ off. If a $5\%$ sales tax is applied to the discounted price, what is the final cost of the jacket?

    $67.60$

    $68$

    $60.80$

    $67.20$

20. A store offers two deals for a $\$120$ item: Deal A is a $30\%$ discount. Deal B is a $20\%$ discount, then an additional $10\%$ off the discounted price. Which deal is better for the customer, and what is the final price?

    Deal B, $\$86.70$

    Both deals result in the same price of $\$84$

    Deal A, $\$87$

    Deal A, $\$84$

21. The population of a town was $15,000$. In the first year, it increased by $10\%$. In the second year, it decreased by $5\%$ from the new population. What was the population at the end of the second year?

    $15750$

    $15675$

    $16500$

    $14250$

22. In a school, $40\%$ of the students play a musical instrument. Of those who play a musical instrument, $25\%$ play the piano. What percentage of the total students in the school play the piano?

    $10\%$

    $12.5\%$

    $15\%$

    $65\%$

23. A farmer has $300$ acres of land. $60\%$ of the land is used for growing corn. Of the land used for corn, $15\%$ is reserved for organic farming. How many acres are reserved for organic corn?

    $45$ acres

    $30$ acres

    $27$ acres

    $18$ acres

24. A store increased the price of a backpack by $20\%$ and then later decreased the new price by $25\%$. If the final price of the backpack is $\$72$, what was the original price?

    $64.80$

    $80$

    $60$

    $75$

25. The side length of a square is increased by $20\%$. By what percentage does the area of the square increase?

    $40\%$

    $44\%$

    $20\%$

    $24\%$

26. A shirt is on sale for $\$27$, which is a $25\%$ discount from its original price. What was the original price of the shirt?

    $\$33.75$

    $\$30$

    $\$35$

    $\$36$

27. A store increased the price of a laptop by $10\%$ in January. In February, due to low sales, they decreased the new price by $10\%$. If the original price of the laptop was $\$800$, what was its final price after both changes?

    $\$780$

    $\$792$

    $\$810$

    $\$800$

28. A farmer harvested $30\%$ of his apple crop on Monday. On Tuesday, he harvested $40\%$ of the remaining crop. If he still has $630$ kg of apples left to harvest, what was the total weight of his initial apple crop?

    $1500 \text{ kg}$

    $1800 \text{ kg}$

    $1200 \text{ kg}$

    $1400 \text{ kg}$

29. A school's enrollment increased from $400$ students to $460$ students last year. This year, the enrollment decreased by the same percentage as last year's increase. What is the current enrollment?

    $395$ students

    $380$ students

    $391$ students

    $400$ students

30. In a class, $60\%$ of the students are girls. If $25\%$ of the girls wear glasses and $40\%$ of the boys wear glasses, and there are $18$ girls who wear glasses, what is the total number of students in the class?

    $100$

    $90$

    $150$

    $120$

31. After a $20\%$ increase in value, a painting is now worth $\$720$. What was its original value?

    $\$600$

    $\$864$

    $\$576$

    $\$680$

32. A car's value depreciated by $10\%$ in the first year and then by an additional $15\%$ of its reduced value in the second year. If its initial value was $\$20,000$, what is its value after two years?

    $\$15,300$

    $\$16,200$

    $\$15,000$

    $\$17,000$

33. A shirt's price was increased by $25\%$. To return to its original price, by what percentage must the new price be reduced?

    $20\%$

    $25\%$

    $15\%$

    $33.33\%$

34. A vendor sells an item for $\$150$ and makes a profit of $20\%$ on the selling price. What was the cost price of the item?

    $\$120$

    $\$135$

    $\$140$

    $\$125$

35. Mark's salary was $\$4000$ per month. He received a $10\%$ raise. Emily's salary was $\$3800$ per month. She received a $15\%$ raise. Who now earns more, and by how much?

    Mark by $\$20$

    Mark by $\$30$

    Emily by $\$20$

    Emily by $\$30$

36. A shop increases the price of an item by $20\%$ and then offers a $15\%$ discount on the new price. If the final selling price is $\$204$, what was the original price of the item?

    $\$210$

    $\$208$

    $\$200$

    $\$190$

37. The population of a town increased by $10\%$ in one year and then decreased by $5\%$ the following year. If the population at the end of the second year was $20,900$, what was the population at the beginning of the first year?

    $20,000$

    $21,000$

    $22,000$

    $19,000$

38. A student calculated the area of a rectangle as $120 \text{ cm}^2$. If the actual area was $150 \text{ cm}^2$, what is the percentage error in the student's calculation, relative to the actual area?

    $18\%$

    $20\%$

    $15\%$

    $25\%$

39. A shop owner buys a bicycle for $\$200$. They mark up the price by $60\%$. During a sale, they offer a $25\%$ discount on the marked price. What is the shop owner's profit as a percentage of the original cost?

    $30\%$

    $25\%$

    $20\%$

    $15\%$

40. In a school, $60\%$ of the students are girls. $30\%$ of the girls wear glasses, and $40\%$ of the boys wear glasses. What percentage of the total student population wears glasses?

    $34\%$

    $38\%$

    $35\%$

    $32\%$

41. After a $30\%$ discount, a shirt was sold for $\$24.50$. What was its original price?

    $\$35.00$

    $\$30.00$

    $\$31.85$

    $\$32.50$

42. A stock's value increased by $20\%$ on Monday and then decreased by $15\%$ on Tuesday. If its original value was $\$1000$, what was its final value after these changes?

    $\$1000$

    $\$1020$

    $\$980$

    $\$1050$

43. A retailer sold a watch for $\$180$, which represented a $20\%$ profit on the cost price. What was the cost price of the watch?

    $\$170$

    $\$160$

    $\$144$

    $\$150$

44. After a $15\%$ increase, a town's population reached $23,000$. What was the town's population before this increase?

    $20000$

    $19550$

    $22000$

    $21000$

45. The price of an item was first increased by $10\%$, and then the new price was decreased by $10\%$. If the final price was $\$99$, what was the original price?

    $\$105$

    $\$101$

    $\$100$

    $\$99$

Fill-in-the-Blank

46. A town's population first increased by 15% and then decreased by 10%. If the initial population was 20,000, its final population is [blank].

47. If a quantity is decreased by 20%, it must then be increased by [blank]% to return to its original value.

48. A company increases its product's price by 20%, and then due to competition, it lowers the new price by 10%. The final price represents an overall increase of [blank]% from the original.