Use these percentages and ratios sample questions to review percent equations, percent increase and decrease, sales tax, discounts, area changes, and part-to-whole ratios. Answer each question before opening the explanation.
Topics Covered
- Finding a percent of a number
- Finding the original amount
- Converting decimals to percentages
- Sales tax and total cost
- Discounts and regular prices
- Percent increase and decrease
- Successive percentage changes
- Ratios and part-to-whole relationships
Sample Questions
- A. 27
- B. 30
- C. 60
- D. 75
- E. 90
Show Answer
Let x represent the unknown number. Convert 60% to the decimal 0.60 and write the equation:
0.60x = 45
Divide both sides by 0.60:
x = 45 ÷ 0.60 = 75
- A. 65%
- B. 80%
- C. 85%
- D. 90%
- E. 125%
Show Answer
Let x represent the decimal form of the percent. Write the equation:
48x = 60
Divide both sides by 48:
x = 60 ÷ 48 = 1.25
Convert 1.25 to a percent by multiplying by 100:
1.25 × 100% = 125%
- A. $23,320
- B. $23,540
- C. $24,200
- D. $31,200
- E. $35,200
Show Answer
First calculate the sales tax:
0.06 × $22,000 = $1,320
Add the tax to the original price:
$22,000 + $1,320 = $23,320
- A. 20%
- B. 25%
- C. 45%
- D. 70%
- E. 80%
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Find the amount of the increase:
$40 − $32 = $8
Divide the increase by the original price:
$8 ÷ $32 = 0.25
Convert the decimal to a percent:
0.25 × 100% = 25%
- A. 32
- B. 35
- C. 36
- D. 39
- E. 41
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Convert 78% to the decimal 0.78 and multiply:
0.78 × 50 = 39
- A. 30%
- B. 69%
- C. 90%
- D. 105%
- E. 900%
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Use an original side length of 10 units. Increasing it by 30% gives a new side length of 13 units.
The original area is:
102 = 100
The new area is:
132 = 169
The area increased by 69 square units. Relative to the original area of 100 square units, that is a 69% increase.
- A. $23.50
- B. $23.94
- C. $24.00
- D. $24.23
- E. $26.46
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Let x represent the price before tax. A 5% tax makes the final price 105% of the original price:
1.05x = $25.20
Divide both sides by 1.05:
x = $25.20 ÷ 1.05 = $24.00
- A. $86.68
- B. $94.56
- C. $96.00
- D. $98.50
- E. $105.67
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A 20% discount means the sale price is 80% of the regular price. Let x represent the regular price:
0.80x = $78.80
Divide both sides by 0.80:
x = $78.80 ÷ 0.80 = $98.50
- 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%.
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Use an original value of 100. Increasing it by 20% gives:
100 × 1.20 = 120
Then decrease 120 by 30%:
120 × 0.70 = 84
The final value is 16 less than the original value of 100, so the overall change is a 16% decrease.
- A. 212
- B. 224
- C. 256
- D. 322
- E. 420
Show Answer
The ratio contains 8 + 7 = 15 total parts. Girls account for 7 of those 15 parts.
Multiply the total number of students by the fraction representing girls:
480 × 7 ÷ 15 = 224
How to Use These Questions
Work each problem before opening the answer. When reviewing a missed question, identify whether the error came from choosing the wrong base amount, converting a percent incorrectly, or applying the percentage change to the wrong value.
For successive increases and decreases, apply each percentage to the current value rather than combining the percentages directly.