# Percentages and Ratios Practice Questions

**1. 60% of what number is 45?**

A. 27

B. 30

C. 60

D. 75

E. 90

**2. What percent of 48 is 60?**

A. 65%

B. 80%

C. 85%

D. 90%

E. 125%

**3. Nancy pays 6% sales tax on a car that costs $22,000. What is the cost of the car including sales tax?**

A. $23,320

B. $23,540

C. $24,200

D. $31,200

E. $35,200

**4. The price of a company’s stock increases from $32 per share to $40 per share in a three-day period. By what percent did the stock’s price increase?**

A. 20%

B. 25%

C. 45%

D. 70%

E. 80%

**5. What is 78% of 50?**

A. 32

B. 35

C. 36

D. 39

E. 41

**6. The width of a square increases by 30%. By what percent does its area increase?**

A. 30%

B. 69%

C. 90%

D. 105%

E. 900%

**7. After sales tax, a book costs $25.20. If sales tax is 5%, how much does the book cost before taxes?**

A. $23.50

B. $23.94

C. $24.00

D. $24.23

E. $26.46

**8. A coffee table is on sale for $78.80, which is 20% off the regular price. What is the regular price of the coffee table?**

A. $86.68

B. $94.56

C. $96.00

D. $98.50

E. $105.67

**9. A number increased by 20%, and the resulting number then decreased by 30%. By what overall percentage the original value increase or decrease?**

A. It decreased by 21%

B. It decreased by 16%

C. It decreased by 10%.

D. It decreased by 8%.

E. It increased by 10%.

**10. In a school with a total of 480 students, the ratio of boys to girls is 8:7. How many girls attend the school?**

A. 212

B. 224

C. 256

D. 322

E. 420

## Answer Key

**1. D.** Percent means parts per hundred, so . Notice that a percent can easily be converted to a decimal by moving the decimal point two places to the left. Translate the given problem into an equation using x for the unknown. Recall that the word “of” means multiplication.

0.6x = 45

Solve the equation by dividing both sides by 0.6.

x = 75

**2. E.** Translate the given problem into an equation using x for the unknown. Recall that the word “of” means multiplication.

x . 48 = 60

Solve the equation by dividing both sides by 48.

x = 1.25

The result is a decimal. Convert it to a percent by multiplying by 100%.

1.25 x 100% = 125%

**3. A.** First, calculate the dollar value of the sales tax. To find this value, multiply 0.06 by $22,000.

0.06 × $22,000 = $1,320

Look at the question again. It asks for the total cost of the car with sales tax. To find this, add the sales tax to the original price of the car.

$22,000 + $1,320 = $23,320

**4. B.** To find the percent increase or percent decrease of a value, first find the difference between the values; then, divide the difference by the original value and convert the result to a percentage. Subtract the prices given in the problem to find their difference.

$40 – $32 = $8

Divide the result by the original price of the stock, which was $32.

$8 $32 = 0.25

Finally, convert the result to a percent by multiplying it by 100%.

0.25 x 100% = 25%

Therefore, the price of the stock increased by 25%.

**5. D.** Percent means parts per hundred, so . Notice that a percent can easily be converted to a decimal by moving the decimal point two places to the left. Translate the given problem into an equation using x for the unknown. Recall that the word “of” means multiplication.

x = 0.78 . 50

Calculate the value x.

x = 39

**6. B.** Although it is not necessary, this problem will be easier to solve if you choose a value for the original width of the square. Say, for example, the original width of the square was 10. Since 30% of 10 is 3 (the product of 0.3 and 10), the width of the square increases to 13.

Now find the original area of the square and the area of the square after its width increases. The formula for the area of a square is A = s2, where s is the length of any side of the square.

A = (10)^{2} = 100

A = (13)^{2} = 169

Therefore, the area of the square with a width of 10 is 100 and increases to 169 as its width increases by 30%. To find the percent increase in area, first find the difference in the square’s area before and after its increase in width.

169 – 100 = 69

Then, divide the result by the original area, 100.

69 100 = 69

Finally, convert the result to a percent by multiplying it by 100%.

0.69 x100% = 69%

Therefore, the area of the square increases by 69%.

**7. C.** Let x represent the price of the book before taxes. The problem states that after a 5% sales tax (represented by 0.05x) is added, the result is $25.20. Write this statement as an equation and solve for x.

Therefore, the price of the book before taxes was $24.00.

**8. D.** Let x represent the regular price of the coffee table. The problem states that after a 20% discount (represented by 0.2x) is subtracted from the regular price, the result is $78.80. Write this statement as an equation and solve for x.

Therefore, the regular price of the coffee table is $98.50.

**9. B.** Although it is not necessary, this problem will be easier to solve if you choose a value for the original number. Say, for example, the original number was 100. Since 20% of 100 is 20 (0.2 x 100 = 20), the number first increased to 120 (100 + 20 = 120). After that, the number decreased by 30%. Since 30% of 120 is 36 (0.3 x 120 = 36), the number decreased to 84 (120 – 36 = 84).

The question asks for the percentage by which the original number increased or decreased. Obviously, the number decreased. To find the percent of the decrease, first subtract the final value from the original value of the number.

100 – 84 = 16

Then, divide the result by the original value, 100.

16 100 = 0.16

Finally, convert the result to a percent by multiplying it by 100%.

0.16 x 100% = 16%

Therefore, the number decreased by 16%.

**10. B.** The easiest way to solve the problem is to realize that if the ratio of boys to girls is 8:7, then the ratio of girls to all students in the school is 7:15 (8 + 7 = 15). To find the number of girls at this school, write this ratio as a fraction and multiply it by the total number of students in the school.

Therefore, there are 224 girls in the school.