Definition: Solving percent applications involves using the percent equation: Part=PercentΓWhole, often written as P=Rβ B (Part = Rate Γ Base). Convert percentages to decimals (e.g., 25% = 0.25) and solve for the unknown using algebra.
Working: To find 20% of 50, write P=0.20Γ50=10. To find what percent 15 is of 60, write 15=RΓ60, so R=15/60=0.25=25%. To find the whole when 12 is 40%, write 12=0.40ΓB, so B=12/0.40=30.
Example: Problem: 'What is 15% of 200?' P=0.15Γ200=30.
Reason: Percent applications are widely used in finance, statistics, and everyday situations like discounts, taxes, and grades.
3
Easy
7
Medium
5
Hard
π All How to Solve Percent Applications MCQs
Q1. A store marks a jacket at \$80 and advertises a 25% discount. Which expression correctly represents the sale price?
A.80+0.25(80)
B.80β0.25(80) β
C.0.25(80)
D.80Γ·0.25
π‘ Difficulty: easy | β Correct: B
π Explanation: A discount reduces the original price, so the correct model is 80β0.25(80). This gives a sale price of \$60. The other expressions either increase the price, calculate only the discount, or incorrectly divide by the percentage.
Q2. A quantity is increased by 15%. Which statement best describes the relationship between the original value x and the new value?
A.The new value is x+15
B.The new value is 1.15x β
C.The new value is 0.15x
D.The new value is 15x
π‘ Difficulty: easy | β Correct: B
π Explanation: An increase of 15% means the original amount remains and an additional 0.15x is added. Therefore the new value is x+0.15x=1.15x. This distinction prevents the common mistake of treating 15% as a fixed amount.
Q3. A school has 640 students. After a campaign, enrollment increases by 12%. The principal estimates that about 700 students will attend next year. Is the estimate reasonable?
A.Yes, because 12% is approximately 60 students
B.No, because the increase is exactly 76.8 students, giving 716.8 students β
C.No, because 12% must be subtracted
D.Yes, because 12% of 640 is exactly 120 students
π‘ Difficulty: medium | β Correct: B
π Explanation: The increase is 0.12(640)=76.8, so the model gives 716.8 students. Since students are counted in whole numbers, the prediction is about 717 students. An estimate of 700 is somewhat low and does not closely reflect the calculated percentage increase.
Q4. A phone originally costs \500.Itisdiscountedby20400
B.\$420
C.\$430
D.\$440 β
π‘ Difficulty: medium | β Correct: D
π Explanation: The 20% discount gives 500(0.80)=400. The 10% tax is then calculated on \400, not on the original \500. Thus the tax is \' in math mode at position 27: β¦final price is \Μ²(Μ²400+40=\" style="color:#cc0000">40 and the final price is \(400+40=\440.
Q5. A worker's salary rises from \48,000 to \54,000. Which calculation correctly determines the percentage increase?
A.6000Γ·54000
B.48000Γ·6000
C.6000Γ·48000 β
D.54000Γ·48000
π‘ Difficulty: medium | β Correct: C
π Explanation: The increase is 54,000β48,000=6,000. Percentage increase is measured relative to the original salary, so the correct calculation is 6,000Γ·48,000=0.125, or 12.5%. Using the new salary as the denominator gives the wrong reference base.
Q6. A city's water consumption falls from 2.4 million liters per day to 2.04 million liters per day. Officials claim consumption decreased by 20%. What is the best evaluation?
A.The claim is correct because 2.4β2.04=0.36 million
B.The claim is correct because 0.36 is 20% of 2.04
C.The claim is incorrect because the decrease is 15% of the original amount β
D.The claim is incorrect because the decrease is 36%
π‘ Difficulty: medium | β Correct: C
π Explanation: The decrease is 2.4β2.04=0.36 million liters. Relative to the original 2.4 million, the percentage decrease is 0.36Γ·2.4=0.15, or 15%. The denominator must be the starting quantity when finding a decrease from an original amount.
Q7. A retailer buys an item for \120andwantsa30150
B.\$156 β
C.\$160
D.\$180
π‘ Difficulty: medium | β Correct: B
π Explanation: A 30% profit means the profit equals 0.30(120)=36. Adding this to the \' in math mode at position 16: 120 cost gives \Μ²(Μ²120+36=156. Aβ¦" style="color:#cc0000">120 cost gives 120+36=156. A common error is interpreting 30% as \30 or using the desired selling price as the percentage base instead of the original cost.
Q8. A student solves a problem as follows: 'A \250bicycleisdiscounted3030 and the sale price is \$220.' What is the student's main error?
A.The student multiplied by 30 instead of 0.30 β
B.The student should have added the discount
C.The original price should be divided by 30
D.The sale price should be \$280
π‘ Difficulty: easy | β Correct: A
π Explanation: Thirty percent means 0.30, not 30 dollars. The correct discount is 0.30(250)=75, making the sale price 250β75=175. The student's arithmetic uses the numerical percent incorrectly by treating the percent number as a dollar amount.
Q9. A restaurant bill is \72.Acustomerleavesan1818.00
B.\$20.25
C.\$21.24 β
D.\$22.50
π‘ Difficulty: hard | β Correct: C
π Explanation: The tip is 0.18(72)=12.96, so the total is 72+12.96=84.96. Dividing by four gives 84.96Γ·4=21.24. Therefore option C is mathematically correct; the distractors represent common errors involving ignoring the tip or applying the percentage incorrectly.
Q10. A graph of a company's revenue shows \200,000 in January and \230,000 in February. The vertical scale is measured in thousands of dollars. What percentage increase does the graph represent?
A.0.1
B.0.12
C.0.15 β
D.0.3
π‘ Difficulty: medium | β Correct: C
π Explanation: The graph indicates an increase of 230,000β200,000=30,000. Relative to January revenue, the increase is 30,000Γ·200,000=0.15, or 15%. The graph's vertical scale does not change the percentage calculation; it only affects how the values are displayed.
Q11. Two stores advertise the same \1,000laptop.StoreAgivesone30700
B.Store B, because its final price is \$700
C.Store A, because its final price is \$720 β
D.Both stores have the same final price
π‘ Difficulty: hard | β Correct: C
π Explanation: Store A gives 1000(0.70)=700. Store B gives 1000(0.80)(0.90)=720. Therefore Store A has the lower final price. Successive percentage changes should be applied to the changing balance rather than simply adding or subtracting the percentages.
Q12. A population increases by 25% during one year and then decreases by 20% the next year. Compared with the original population, what is the final result?
A.It is unchanged β
B.It is 5% greater
C.It is 5% smaller
D.It is 10% greater
π‘ Difficulty: hard | β Correct: A
π Explanation: Starting with P, the first change gives 1.25P. The 20% decrease is applied to that new value, producing 1.25P(0.80)=P. Thus the population returns exactly to its original value, so option A is correct; the apparent 5% increase comes from incorrectly combining percentage changes additively.
Q13. A charity wants to increase its monthly donations from \8,000 to \10,000. One volunteer says the required increase is 20% because 10,000 is 20% less than 8,000. Another says it is 25%. Who is correct and why?
A.The first volunteer, because 2,000 is 20% of 10,000
B.The second volunteer, because 2,000 is 25% of 8,000 β
C.Both are correct because the percentage difference is always the same
D.Neither is correct because percentage changes cannot compare two amounts
π‘ Difficulty: medium | β Correct: B
π Explanation: The required increase is 10,000β8,000=2,000. Since the change starts from \' in math mode at position 35: β¦ge increase is \Μ²(Μ²2,000\div8,000=β¦" style="color:#cc0000">8,000, the percentage increase is \(2,000\div8,000=0.25, or 25%. Percent increase must use the original amount as the reference, whereas 20% describes the decrease from \10,000 to \$8,000.
Q14. A product's price is increased by 40% and later reduced by 40%. A manager concludes that the final price must equal the original price because the percentages cancel. Which conclusion is correct?
A.The manager is correct for every original price
B.The final price is 16% lower than the original β
C.The final price is 16% higher than the original
D.The final price is 40% lower than the original
π‘ Difficulty: hard | β Correct: B
π Explanation: Let the original price be P. After a 40% increase it becomes 1.40P. A 40% reduction then gives 1.40P(0.60)=0.84P. Therefore the final price is 84% of the original, meaning it is 16% lower. Equal percentage increases and decreases do not cancel because they use different bases.
Q15. A number is increased by p% and then decreased by p%. For which positive value of p will the final number be exactly 91% of the original?
A.0.09
B.0.1
C.0.3 β
D.0.7
π‘ Difficulty: hard | β Correct: C
π Explanation: If the original value is x, the final value is x(1+p)(1βp)=x(1βp2), where p is written as a decimal. Requiring the final value to be 0.91x gives 1βp2=0.91, so p2=0.09 and p=0.30. Therefore the correct answer is C, or 30%.