Percentages practice questions

Percentages questions

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1. 1PercentagesFoundation

   A class has 20 students and 5 are absent. What percent of the class is present?A class has 20 students and 5 are absent. What percent of the class is present?

   • A80%80%
   • B50%50%
   • C25%25%
   • D75%75%
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   Answer: 75%75%

   The question asks for present, not absent: 20 - 5 = 15 present, and 1520 = 0.75, or 75%. Reading which group is being asked for is the whole question; 25% is waiting.The question asks for present, not absent: 20 - 5 = 15 present, and 15/20 = 0.75, or 75%. Reading which group is being asked for is the whole question; 25% is waiting.

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2. 2PercentagesFoundation

   Of 250 survey responses, 60 selected the first of four listed choices. What percent selected it?Of 250 survey responses, 60 selected the first of four listed choices. What percent selected it?

   • A24%24%
   • B40%40%
   • C20%20%
   • D30%30%
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   Answer: 24%24%

   Divide the part by the whole, then convert: 60250 = 0.24, which is 24 percent. The number of listed choices is not used — it is there to invite dividing by 4.Divide the part by the whole, then convert: 60/250 = 0.24, which is 24 percent. The number of listed choices is not used — it is there to invite dividing by 4.

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3. 3PercentagesFoundation

   A jacket priced at 80 pounds is reduced by 35 percent. What is the sale price?A jacket priced at 80 pounds is reduced by 35 percent. What is the sale price?

   • A52 pounds52 pounds
   • B45 pounds45 pounds
   • C28 pounds28 pounds
   • D58 pounds58 pounds
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   Answer: 52 pounds52 pounds

   A 35 percent reduction leaves 65 percent, and 0.65 × 80 = 52 pounds. The choice 28 is the size of the discount rather than the price left after it.A 35 percent reduction leaves 65 percent, and 0.65 × 80 = 52 pounds. The choice 28 is the size of the discount rather than the price left after it.

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4. 4PercentagesFoundation

   What is 15 percent of 240?What is 15 percent of 240?

   • A3636
   • B1616
   • C2424
   • D360360
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   Answer: 3636

   15 percent is 0.15, and 0.15 × 240 = 36. A useful check: 10 percent is 24 and 5 percent is 12, and 24 + 12 = 36.15 percent is 0.15, and 0.15 × 240 = 36. A useful check: 10 percent is 24 and 5 percent is 12, and 24 + 12 = 36.

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5. 5PercentagesFoundation

   What is 18 percent of 350?What is 18 percent of 350?

   • A5353
   • B7070
   • C1818
   • D6363
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   Answer: 6363

   0.18 × 350 = 63. As a check, 10 percent is 35 and 8 percent is 28, and 35 + 28 = 63.0.18 × 350 = 63. As a check, 10 percent is 35 and 8 percent is 28, and 35 + 28 = 63.

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6. 6PercentagesFoundation

   What is 24 percent of 425?What is 24 percent of 425?

   • A9898
   • B106106
   • C120120
   • D102102
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   Answer: 102102

   0.24 × 425 = 102. As a check, 25 percent of 425 is 106.25, so the answer must be slightly below that.0.24 × 425 = 102. As a check, 25 percent of 425 is 106.25, so the answer must be slightly below that.

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7. 7PercentagesStandard

   In one group, 12 of 30 students joined a club. In another, 18 of 45 joined. Which statement is true?In one group, 12 of 30 students joined a club. In another, 18 of 45 joined. Which statement is true?

   • AThere is not enough information.There is not enough information.
   • BBoth groups have the same percentage.Both groups have the same percentage.
   • CThe second group has the greater percentage.The second group has the greater percentage.
   • DThe first group has the greater percentage.The first group has the greater percentage.
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   Answer: Both groups have the same percentage.Both groups have the same percentage.

   1230 = 0.4 and 1845 = 0.4, so both groups have 40% participation.12/30 = 0.4 and 18/45 = 0.4, so both groups have 40% participation.

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8. 8PercentagesStandard

   A shop's takings rose from $2,400 to $2,760. What was the percent increase?A shop's takings rose from $2,400 to $2,760. What was the percent increase?

   • A13%13%
   • B36%36%
   • C15%15%
   • D8.7%8.7%
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   Answer: 15%15%

   The increase is 360. Divide by the original amount, not the new one: 3602400 = 0.15, which is 15 percent.The increase is 360. Divide by the original amount, not the new one: 360/2400 = 0.15, which is 15 percent.

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9. 9PercentagesStandard

   After a 15 percent discount, a coat costs $102. What was the price before the discount?After a 15 percent discount, a coat costs $102. What was the price before the discount?

   • A$117$117
   • B$120$120
   • C$125$125
   • D$115$115
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   Answer: $120$120

   The discounted price is 85 percent of the original, so the original is 1020.85 = $120. Adding 15 percent to $102 gives $117.30, which answers a different question.The discounted price is 85 percent of the original, so the original is 102/0.85 = $120. Adding 15 percent to $102 gives $117.30, which answers a different question.

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10. 10PercentagesStandard

    A test has 45 questions. A student answers 36 correctly. What percentage did they answer correctly?A test has 45 questions. A student answers 36 correctly. What percentage did they answer correctly?

    • A75%75%
    • B85%85%
    • C90%90%
    • D80%80%
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    Answer: 80%80%

    Divide the part by the whole, then convert: 3645 = 0.80, which is 80 percent. The number correct goes on top; putting the total on top gives 1.25 and no percentage above 100 is possible here.Divide the part by the whole, then convert: 36/45 = 0.80, which is 80 percent. The number correct goes on top; putting the total on top gives 1.25 and no percentage above 100 is possible here.

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11. 11PercentagesStandard

    A jacket costs $84 after a 30 percent discount. What was the original price?A jacket costs $84 after a 30 percent discount. What was the original price?

    • A$120$120
    • B$114$114
    • C$112$112
    • D$109.20$109.20
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    Answer: $120$120

    The sale price is 70 percent of the original, so the original is 840.70 = $120. Adding 30 percent to $84 gives $109.20, which answers a different question.The sale price is 70 percent of the original, so the original is 84/0.70 = $120. Adding 30 percent to $84 gives $109.20, which answers a different question.

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12. 12PercentagesStandard

    A jacket costs 64 pounds after a 20 percent discount. Enter its original price in pounds.A jacket costs 64 pounds after a 20 percent discount. Enter its original price in pounds.

    Student-produced response: write your own answer rather than choosing one.

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    Answer: 8080

    The sale price is 80 percent of the original, so the original is 640.8 = 80 pounds. Adding 20 percent to 64 gives 76.80, which is a different quantity: 20 percent of the smaller number.The sale price is 80 percent of the original, so the original is 64/0.8 = 80 pounds. Adding 20 percent to 64 gives 76.80, which is a different quantity: 20 percent of the smaller number.

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13. 13PercentagesChallenge

    A price rises by 20 percent and then falls by 20 percent. Compared with the original price, the final price isA price rises by 20 percent and then falls by 20 percent. Compared with the original price, the final price is

    • Athe same.the same.
    • B4 percent higher.4 percent higher.
    • C4 percent lower.4 percent lower.
    • D20 percent lower.20 percent lower.
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    Answer: 4 percent lower.4 percent lower.

    The two changes are percentages of different amounts. Multiplying gives 1.20 × 0.80 = 0.96, so the final price is 96 percent of the original, 4 percent lower. The fall is larger in money terms because it is taken from the raised price.The two changes are percentages of different amounts. Multiplying gives 1.20 × 0.80 = 0.96, so the final price is 96 percent of the original, 4 percent lower. The fall is larger in money terms because it is taken from the raised price.

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14. 14PercentagesChallenge

    An account holds 2,000 pounds and earns 5 percent interest each year, added to the balance. What is the balance after two years?An account holds 2,000 pounds and earns 5 percent interest each year, added to the balance. What is the balance after two years?

    • A2,205 pounds2,205 pounds
    • B2,200 pounds2,200 pounds
    • C2,100 pounds2,100 pounds
    • D2,050 pounds2,050 pounds
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    Answer: 2,205 pounds2,205 pounds

    Each year multiplies the balance by 1.05: 2,000 × 1.05 × 1.05 = 2,205 pounds. Taking 5 percent of the original twice gives 2,200 and misses the interest earned on the first year's interest.Each year multiplies the balance by 1.05: 2,000 × 1.05 × 1.05 = 2,205 pounds. Taking 5 percent of the original twice gives 2,200 and misses the interest earned on the first year's interest.

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15. 15PercentagesChallenge

    An account of 4,000 pounds earns 3 percent interest a year, added to the balance. What is the balance after two years?An account of 4,000 pounds earns 3 percent interest a year, added to the balance. What is the balance after two years?

    • A4,240 pounds4,240 pounds
    • B4,120 pounds4,120 pounds
    • C4,243.60 pounds4,243.60 pounds
    • D4,360 pounds4,360 pounds
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    Answer: 4,243.60 pounds4,243.60 pounds

    Each year multiplies by 1.03: 4,000 × 1.03 × 1.03 = 4,243.60. Taking 3 percent of 4,000 twice gives 4,240 and misses the interest earned on the first year's interest.Each year multiplies by 1.03: 4,000 × 1.03 × 1.03 = 4,243.60. Taking 3 percent of 4,000 twice gives 4,240 and misses the interest earned on the first year's interest.

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16. 16PercentagesChallenge

    An account of 5,000 pounds earns 4 percent interest a year, added to the balance. What is the balance after two years?An account of 5,000 pounds earns 4 percent interest a year, added to the balance. What is the balance after two years?

    • A5,408 pounds5,408 pounds
    • B5,400 pounds5,400 pounds
    • C5,200 pounds5,200 pounds
    • D5,416 pounds5,416 pounds
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    Answer: 5,408 pounds5,408 pounds

    Each year multiplies by 1.04: 5,000 × 1.04 × 1.04 = 5,408. Taking 4 percent of 5,000 twice gives 5,400 and misses the interest earned on the first year's interest.Each year multiplies by 1.04: 5,000 × 1.04 × 1.04 = 5,408. Taking 4 percent of 5,000 twice gives 5,400 and misses the interest earned on the first year's interest.

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