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📝 Find percent decrease (16 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 16 questions available

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What is Find percent decrease?

Definition:
Percent decrease measures the relative reduction from an original amount to a new, smaller amount. The formula is $\text{Percent Decrease} = \frac{\text{Original Amount} - \text{New Amount}}{\text{Original Amount}} \times 100\%$ . It shows how much a quantity has decreased.

Working:
If a price drops from $80 to$ 60, the decrease is $80 - 60 = 20$ . Percent decrease = $(20/80) \times 100 = 25\%$ .

Example:
Problem: 'A store's sales fell from 500 to 400. Find the percent decrease.' Decrease = 100, so $(100/500) \times 100 = 20\%$ .

Reason:
Percent decrease is crucial for analyzing losses, discounts, and declines in various fields like finance and retail.

Easy

Medium

Hard

📝 All Find percent decrease MCQs

Q1. A price falls from $240$ to $204$ . Which expression correctly represents the percent decrease, and why must the original value be used as the denominator?

36/204\times100

36/240\times100

✅

204/240\times100

240/204\times100

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The decrease is $240-204=36$ . Percent decrease compares the amount lost with the original quantity, so the correct calculation is $36/240\times100=15\%$ . Using the new value as the denominator changes the reference point.

Q2. A quantity decreases from $500$ to $425$ . Without calculating every intermediate step, which statement correctly describes the change?

A.It decreased by

12.5\%

B.It decreased by

15\%

. ✅

C.It decreased by

17.5\%

D.It decreased by

20\%

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The absolute decrease is $500-425=75$ . Comparing $75$ with the original $500$ gives $75/500=0.15$ , or $15\%$ . The percentage must always describe the decrease relative to the starting amount.

Q3. Two stores reduce a jacket from $800$ to $680$ and a pair of shoes from $600$ to $510$ . Which conclusion is mathematically justified?

A.The jacket has the larger percent decrease.

B.The shoes have the larger percent decrease.

C.Both items have the same percent decrease. ✅

D.The items have different percentage decreases because their original prices differ.

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The jacket decreases by $120$ , giving $120/800=15\%$ . The shoes decrease by $90$ , giving $90/600=15\%$ . Although the dollar decreases differ, both reductions represent exactly the same percentage of their original prices.

Q4. A school reduces its daily electricity use from $1,200$ kWh to $900$ kWh. A student says the decrease is $25\%$ because $900$ is $75\%$ of $1,200$ . How should the statement be evaluated?

A.Correct, because the remaining amount is

75\%

. ✅

B.Incorrect, because the decrease is

75\%

C.Correct, because

900-1,200=300

D.Incorrect, because the decrease is

30\%

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The student is correct. If $900$ is $75\%$ of the original $1,200$ , then the amount removed is the remaining $100\%-75\%=25\%$ . The absolute decrease is $300$ , and $300/1,200=25\%$ .

Q5. A town's water consumption drops from $2.4$ million liters per day to $2.04$ million liters. Which reasoning best determines the percent decrease?

A.Subtract first, then divide the decrease by

2.04

B.Divide

2.04

2.4

, then interpret the result as the decrease.

C.Subtract

2.04

from

2.4

, divide by

2.4

, and multiply by

100

. ✅

D.Divide the original amount by the new amount and multiply by

100

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The decrease is $2.4-2.04=0.36$ million liters. Because percent decrease uses the original amount as the reference, calculate $0.36/2.4\times100=15\%$ . This approach correctly separates absolute change from relative change.

Q6. A factory reduces defects from $80$ per $1,000$ products to $56$ per $1,000$ . Management reports a $30\%$ decrease. Which interpretation is correct?

A.The report is correct because

24/80=30\%

. ✅

B.The report is incorrect because the decrease is

24\%

C.The report is correct because

56/80=70\%

D.The report is incorrect because

56/1,000=5.6\%

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The number of defects decreases by $80-56=24$ . Relative to the original $80$ defects, the decrease is $24/80=0.30$ , or $30\%$ . The rate per $1,000$ does not change the percent decrease calculation.

Q7. A phone battery capacity is modeled as $100\%$ at the beginning of a test. After several hours, the graph shows $62\%$ remaining. What percent decrease has occurred?

A.0.38 ✅

B.0.62

C.0.48

D.1.62

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: The graph shows that $62\%$ of the original capacity remains. Therefore the portion that has disappeared is $100\%-62\%=38\%$ . The percent decrease is thus $38\%$ , not $62\%$ , because $62\%$ represents the remaining amount.

Q8. A graph shows monthly water use falling from $40,000$ liters in January to $30,000$ liters in April. Another student estimates a $10\%$ decrease by subtracting the two values and ignoring the original amount. What is the correct result?

A.0.1

B.0.2

C.0.25 ✅

D.0.33299999999999996

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The decrease is $40,000-30,000=10,000$ liters. Relative to January's original $40,000$ liters, the percentage decrease is $10,000/40,000\times100=25\%$ . The student's $10\%$ confuses an absolute difference with a percentage.

Q9. A graph indicates that a company's annual waste fell from $75$ tons to $60$ tons. The company then claims the waste decreased by $15\%$ . Which assessment is most accurate?

A.The claim is correct because

75-60=15

B.The claim is correct because

60/75=80\%

C.The claim is incorrect; the decrease is

20\%

. ✅

D.The claim is incorrect; the decrease is

25\%

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The graph shows an absolute decrease of $15$ tons. Dividing by the original $75$ tons gives $15/75=0.20$ , so the percent decrease is $20\%$ . The reported $15\%$ incorrectly treats the numerical difference as the percentage.

Q10. A company's customer complaints decrease from $360$ per month to $270$ . A manager calculates $270/360\times100=75\%$ and reports a $75\%$ decrease. What error did the manager make?

A.They used the wrong subtraction operation.

B.They calculated the percent remaining instead of the percent decrease. ✅

C.They should divide by the new value.

D.They should multiply the original value by

75

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The calculation $270/360\times100=75\%$ correctly describes the percentage of complaints remaining. The decrease is the complement: $100\%-75\%=25\%$ . The manager confused the percentage remaining with the percentage decrease.

Q11. A student's score falls from $92$ to $69$ . She calculates $(92-69)/69\times100$ and gets about $33.3\%$ . Why is this not the correct percent decrease?

A.The numerator should be

69-92

B.The denominator should be

92

, the original score. ✅

C.The denominator should be

23

, the amount of decrease.

D.No correction is needed because

33.3\%

is correct.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The decrease is $23$ points, but percent decrease compares that loss with the original score of $92$ . Thus $23/92\times100=25\%$ . Using $69$ , the final score, as the denominator produces a different and inappropriate reference.

Q12. A retailer lowers a product's price from $1,500$ to $1,200$ , then applies another $10\%$ reduction to the new price. What is the overall percent decrease from the original price?

A.0.3 ✅

B.0.32

C.0.35

D.0.4

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: The first reduction gives $1,200$ , which is $80\%$ of the original. The second reduction makes the price $1,080$ , or $72\%$ of the original. Therefore the total decrease is $100\%-72\%=28\%$ , not 32%.

Q13. A population decreases from $50,000$ to $45,000$ . Later it decreases by another $10\%$ of its new value. Which statement best describes the final population and total percent decrease from the original?

A.Final

40,000

, total decrease

20\%

B.Final

40,500

, total decrease

19\%

. ✅

C.Final

40,500

, total decrease

18\%

D.Final

41,000

, total decrease

18\%

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The first decrease produces $45,000$ , a $10\%$ reduction. The second reduction is $10\%$ of $45,000$ , or $4,500$ , leaving $40,500$ . The total decrease is $9,500$ , and $9,500/50,000=19\%$ .

Q14. A quantity decreases by the same fixed percentage each year. It is $800$ initially and $648$ after two years. What was the annual percent decrease?

A.0.08

B.0.09

C.0.1 ✅

D.0.12

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: If the annual decrease is $r$ , the amount after two years is $800(1-r)^2=648$ . Thus $(1-r)^2=0.81$ , so $1-r=0.9$ and $r=0.10$ . Therefore the annual decrease is $10\%$ , showing that repeated percentage changes are multiplicative.

Q15. Two quantities both decrease by $20\%$ . The first starts at $150$ , while the second starts at $900$ . Which statement is necessarily true after the decreases?

A.Both decrease by the same numerical amount.

B.The first loses more units than the second.

C.The second loses

120

more units than the first. ✅

D.Both end at the same value.

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: A $20\%$ decrease removes $30$ from $150$ and $180$ from $900$ . Therefore the second quantity loses $180-30=150$ more units, not $120$ . Both percentages are equal, but the numerical decreases depend on the original values.

Q16. A sensor reading falls from $1,000$ units to $640$ units. A proposed shortcut says that because $640$ is $64\%$ of $1,000$ , the percent decrease is $64\%$ . Which corrected reasoning is strongest?

A.The shortcut is correct because the final value is

64\%

B.The decrease is

36\%

because the remaining

64\%

must be subtracted from

100\%

. ✅

C.The decrease is

56\%

because

640-100=540

D.The decrease is

40\%

because

640

is close to

600

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Since $640/1,000=64\%$ , the final reading represents $64\%$ of the original. The portion lost is therefore $100\%-64\%=36\%$ . This complement method is efficient when the new value is already easily expressed as a percentage of the original.

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