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Percentages MCQ Quiz - Objective Question with Answer for Percentages - Download Free PDF

Last updated on Jun 9, 2025

Latest Percentages MCQ Objective Questions

Percentages Question 1:

The price of a product increased by 20%. After some time, it decreased by 15%. What is the overall percentage change in the price?

  1. 1%
  2. 2%
  3. 4%
  4. 3%

Answer (Detailed Solution Below)

Option 2 : 2%

Percentages Question 1 Detailed Solution

Given:

First increase (r1) = 20%

Second decrease (r2) = -15%

Formula used:

Overall % change = r1 + r2 + (r1 × r2)/100

Calculations:

Overall % change = 20 + (-15) + (20 × -15)/100

⇒ Overall % change = 20 - 15 - 300/100

⇒ Overall % change = 5 - 3 = 2%

∴ The overall percentage change in the price is 2%.

Percentages Question 2:

A book's price is increased by \(20\%\) and then decreased by \(15\%\). If the original price is \(b\) dollars, what is the final price in terms of \(b\)?

  1. 1.02b
  2. 1.05b
  3. 0.95b
  4. 0.85b

Answer (Detailed Solution Below)

Option 1 : 1.02b

Percentages Question 2 Detailed Solution

The initial price increase of \(20\%\) makes the price \(b + 0.20b = 1.20b\). A subsequent \(15\%\) decrease results in \(1.20b - 0.15(1.20b) = 1.20b - 0.18b = 1.02b\). Therefore, the final price is \(1.02b\), showing that the combination of increases and decreases results in a net increase of \(2\%\).

Percentages Question 3:

In a sale, a jacket's price is reduced to 85% of its original price. If the original price is \( p \), which expression represents the sale price?

  1. 0.85p
  2. 8.5p
  3. 0.085p
  4. 85p

Answer (Detailed Solution Below)

Option 1 : 0.85p

Percentages Question 3 Detailed Solution

The correct answer is option 1. The sale price is 85% of the original price. To find this, multiply \( p \) by 0.85. Hence, the expression is \( 0.85p \). Option 2 implies the sale price is 850% of the original price, which is incorrect. Option 3 implies the sale price is 8.5% of the original price, which is incorrect. Option 4 implies the sale price is 8500% of the original price, which is incorrect.

Percentages Question 4:

If 480 is q% greater than 80, what is the value of q?

  1. 400
  2. 480
  3. 500
  4. 600

Answer (Detailed Solution Below)

Option 3 : 500

Percentages Question 4 Detailed Solution

To find q, we start with the equation: \(480 = (1 + \frac{q}{100}) \cdot 80\). Dividing both sides by 80 gives \(6 = 1 + \frac{q}{100}\). Subtracting 1 from both sides, we have \(5 = \frac{q}{100}\). Multiplying by 100 gives \(q = 500\). Thus, the value of q is 500.

Percentages Question 5:

A population of bacteria decreases by \(30\%\) every hour. If the initial population is \(b\), and after 2 hours the population is increased by \(10\%\), what is the population as a percentage of the original?

  1. 56%
  2. 54%
  3. 64%
  4. 72%

Answer (Detailed Solution Below)

Option 2 : 54%

Percentages Question 5 Detailed Solution

Initially, the population is \(b\). A \(30\%\) reduction each hour means after the first hour, the population is \(0.70b\). After the second hour, it becomes \(0.70 \times 0.70b = 0.49b\). Then, an increase of \(10\%\) means the population is \(0.49b + 0.10 \times 0.49b = 0.49b + 0.049b = 0.539b\). Thus, \(0.539b\) is \(53.9\%\) of the original population, which is approximately \(54\%\).

Top Percentages MCQ Objective Questions

Percentages Question 6

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The value of a collectible comic book increased by 167% from the end of 2011 to the end of 2012 and then decreased by 16% from the end of 2012 to the end of 2013. What was the net percentage increase in the value of the collectible comic book from the end of 2011 to the end of 2013?

  1. 124.28%
  2. 140.28%
  3. 151.00%
  4. 209.72%

Answer (Detailed Solution Below)

Option 1 : 124.28%

Percentages Question 6 Detailed Solution

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Choice A is correct. It's given that the value of the comic book increased by 167% from the end of 2011 to the end of 2012. Therefore, if the value of the comic book at the end of 2011 was a dollars, then the value, in dollars, of the comic book at the end of 2012 was \(x+\left(\frac{167}{100}\right) x\), which can be rewritten as 1x + 1.67x, or 2.67. It's also given that the value of the comic book decreased by 16% from the end of 2012 to the end of 2013. Therefore, the value, in dollars, of the comic book at the end of 2013 was \(2.67 x-2.67 x\left(\frac{16}{100}\right)\), which can be rewritten as 2.67x - (2.67x) (0.16), or 2.2428x. Thus, if the value of the comic book at the end of 2011 was dollars, and the value of the comic book at the end of 2013 was 2.2428x dollars, then from the end of 2011 to the end of 2013, the value of the comic book increased by 2.2428x-1x, or 1.2428x, dollars. Therefore, the increase in the value of the comic book from the end of 2011 to the end of 2013 is equal to 1.2428 times the value of the comic book at the end of 2011. It follows that from the end of 2011 to the end of 2013, the net percentage increase in the value of the comic book was (1.2428) (100) %, or 124.28%.
Choice B is incorrect and may result from conceptual or calculation errors.
Choice C is incorrect. This is the difference between the net percentage increase in the value of the comic book from the end of 2011 to the end of 2012 and the net percentage decrease in the value of the comic book from the end of 2012 to the end of 2013, not the net percentage increase in the value of the comic book from the end of 2011 to the end of 2013.
Choice D is incorrect. This is the net percentage increase in the value of the comic book from the end of 2011 to the end of 2013, if the value of the comic book increased by 167% from the end of 2011 to the end of 2012 and then increased, not decreased, by 16% from the end of 2012 to the end of 2013.
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Percentages Question 7

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The number a is 60% greater than the positive number b. The number c is 45% less than a. The number c is how many times b?

  1. .88, 22/25
  2. .88, 2/25
  3. .88, 22/2
  4. .8, 22/25

Answer (Detailed Solution Below)

Option 1 : .88, 22/25

Percentages Question 7 Detailed Solution

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The correct answer is .88. It's given that the number a is 60% greater than the positive number b. Therefore, \(a=\left(1+\frac{60}{100}\right) b\), which is equivalent to a = (1 + 0.60)b, or a = 1.60b. It's also given that the number c is 45% less than a. Therefore, \(c=\left(1-\frac{45}{100}\right) a\), which is equivalent to c = (1 -0.45)a, or c = 0.55a. Since a = 1.60b, substituting 1.606 for a in the equation c = 0.55a yields c = 0.55(1.60b), or c = 0.886. Thus, the number cis 0.88 times the number b. Note that .88 and 22/25 are examples of ways to enter a correct answer.
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Percentages Question 8

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37% of the items in a box are green. Of those, 37% are also rectangular. Of the green rectangular items, 42% are also metal. Which of the following is closest to the percentage of the items in the box that are not rectangular green metal items?

  1. 1.16%
  2. 57.50%
  3. 94.25%
  4. 98.84%

Answer (Detailed Solution Below)

Option 3 : 94.25%

Percentages Question 8 Detailed Solution

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Choice C is correct. It's given that 37% of the items in a box are green. Let x represent the total number of 100 100 items in the box. It follows that \(\frac{37}{100} x \text {, or } 0.37 x\), items in the box are green. It's also given that of those, 37% are also rectangular. Therefore, \(\frac{37}{100}(0.37 x) \text {, or } 0.1369 x\), items in the box are green rectangular items. It's also given that of the green rectangular items, 42% are also metal. Therefore, \(\frac{42}{100}(0.1369 x) \text {, or } 0.057498 x\), items in the box are rectangular green metal items. The number of the items in the box that are not rectangular green metal items is the total number of items in the box minus the number of rectangular green metal items in the box. Therefore, the number of items in the box that are not rectangular green metal items is - 0.057498x, or 0.942502x. The percentage of items in the box that are not rectangular green metal items is the percentage that 0.942502x is of x. If p% represents this percentage, the value of p is \(100\left(\frac{0.942502 x}{x}\right) \text {, or } 94.2502 \text {. }\)Of the given choices, 94.25% is closest to the percentage of items in the box that are not rectangular green metal items.
Choice A is incorrect and may result from conceptual or calculation errors.
Choice B is incorrect and may result from conceptual or calculation errors.
Choice D is incorrect and may result from conceptual or calculation errors.
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Percentages Question 9

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According to a set of standards, a certain type of substance can contain a maximum of 0.001% phosphorus by mass. If a sample of this substance has a mass of 140 grams, what is the maximum mass, in grams, of phosphorus the sample can contain to meet these standards?

  1. .0014
  2. .001
  3. .014
  4. .04

Answer (Detailed Solution Below)

Option 1 : .0014

Percentages Question 9 Detailed Solution

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The correct answer is .0014. It's given that a certain type of substance can contain a maximum of 0.001% phosphorus by mass to meet a set of standards. If a sample of the substance has a mass of 140 grams, it follows that the maximum mass, in grams, of phosphorus the sample can contain to meet the standards is \(0.001 \% \text { of } 140 \text {, or } \frac{0.001}{100}(140) \text {, }\) which is equivalent to (0.00001)(140), or 0.0014. Note that .0014 and 0.001 are examples of ways to enter a correct answer.
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Percentages Question 10

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The number w is 110% greater than the number z. The number z is 55% less than 50. What is the value of w?

  1. 189/4, 47.25
  2. 18/4, 47.25
  3. 189/4, 4.25
  4. 89/4, 47.25

Answer (Detailed Solution Below)

Option 1 : 189/4, 47.25

Percentages Question 10 Detailed Solution

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The correct answer is 47.25. It's given that the number w is 110% greater than the number z. It follows that \(w=\left(1+\frac{110}{100}\right) z \text {, or } w=2.1 z\). It's also given that the number z is 55% less than 50. It follows that \(z=\left(1-\frac{55}{100}\right)(50) \text {, or } z=0.45(50) \text {, }\)which yields z = 22.5. Substituting 22.5 for z in the equation w = 2.1% yields w = 2.1(22.5), which is equivalent to w = 47.25. Therefore, the value of w is 47.25. Note that 47.25 and 189/4 are examples of ways to enter a correct answer. 
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Percentages Question 11

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The number a is 70% less than the positive number b. The number c is 60% greater than a. The number c is how many times b?

  1. .48, 12/25
  2. .48, 1/25
  3. .48, 12/5
  4. .48, 12/2

Answer (Detailed Solution Below)

Option 1 : .48, 12/25

Percentages Question 11 Detailed Solution

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The correct answer is .48. It's given that the number a is 70% less than the positive number b. Therefore, \(a=\left(1-\frac{70}{100}\right) b\), which is equivalent to a = (1 - 0.70)b, or a = 0.30b. It's also given that the number c is 60% greater than a. Therefore, \(c=\left(1+\frac{60}{100}\right) a\), which is equivalent to c = (1 + 0.60)a, or c = 1.60a. Since a = 0.30b, substituting 0.30b for a in the equation c = 1.60a yields c = 1.60(0.30b), or c = 0.48b. Thus, c is 0.48 times b. Note that .48 and 12/25 are examples of ways to enter a correct answer.
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Percentages Question 12

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According to the 2010 Census, the adult population aged 18 years or greater of the United States in 2010 was 234,564,071. In 2010, a survey was conducted among a randomly chosen sample of adults aged 18 years or greater in the United States about their preference to live in a warm climate or a cool climate. The table below displays a summary of the survey results.

Climate Preferences 

  Warm  Cool No preference Total 
18–35 years old 295  168  45  508 
36–50 years old 246  123  41  410 
51–65 years old 238  117  48  403 
Greater than 65 years old  137  78  64  279 
Total  916  486  198  1,600 

Which of the following is closest to the difference between the percentage of adults aged 18–50 years who responded “warm” and the percentage of adults aged 51 years or greater who responded “warm”?

  1. 4%
  2. 5%
  3. 10% 
  4. 18% 

Answer (Detailed Solution Below)

Option 1 : 4%

Percentages Question 12 Detailed Solution

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Choice A is correct. The percentage of adults aged 18–50 who responded “warm” is \(\frac{295+246}{508+410}=\frac{541}{918} \text {, or }\), or about 58.9%. The percentage of adults aged 51 years or greater who responded “warm” is \(\frac{238+137}{403+279}=\frac{375}{682}\), or about 55.0%. The difference between 58.9% and 55.0% is 3.9%. Of the answer choices, 4% is closest to this number. 
Choices B, C, and D are incorrect and may result from calculation errors. 
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Percentages Question 13

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The number a is 70% less than the positive number b. The number c is 80% greater than a. The number c is how many times b?

  1. .54, 27/5
  2. .54, 27/0
  3. .54, 2/50
  4. .54, 7/50

Answer (Detailed Solution Below)

Option 1 : .54, 27/5

Percentages Question 13 Detailed Solution

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The correct answer is .54. It's given that the number a is 70% less than the positive number b. Therefore, \(a=\left(1-\frac{70}{100}\right) b\), which is equivalent to a = (1 − 0.70)b, or a = 0.306. It's also given that the number c is 80% greater than a. Therefore, \(c=\left(1+\frac{80}{100}\right) a\), which is equivalent to c = (1 + 0.80)a, or c = 1.80a. Since a = 0.306, substituting 0.306 for a in the equation c = 1.80a yields c = 1.80(0.30b), or c = 0.54b. Thus, c is 0.54 times b. Note that .54 and 27/50 are examples of ways to enter a correct answer.
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Percentages Question 14

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Year Subscriptions sold  
2012  5,600 
2013  5,880 

The manager of an online news service received the report above on the number of subscriptions sold by the service. The manager estimated that the percent increase from 2012 to 2013 would be double the percent increase from 2013 to 2014. How many subscriptions did the manager expect would be sold in 2014?

  1. 6,020 
  2. 6,027 
  3. 6,440 
  4. 6,468 

Answer (Detailed Solution Below)

Option 2 : 6,027 

Percentages Question 14 Detailed Solution

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Choice B is correct. The percent increase from 2012 to 2013 was \(\frac{5,880-5,600}{5,600}=0.05\), or 5%. Since the percent increase from 2012 to 2013 was estimated to be double the percent increase from 2013 to 2014, the percent increase from 2013 to 2014 was expected to be 2.5%. 
Therefore, the number of subscriptions sold in 2014 is expected to be the number of subscriptions sold in 2013 multiplied by (1 + 0.025), or 5,880 (1.025) = 6,027.
Choice A is incorrect and is the result of adding half of the value of the increase from 2012 to 2013 to the 2013 result. Choice C is incorrect and is the result adding twice the value of the increase from 2012 to 2013 to the 2013 result. Choice D is incorrect and is the result of interpreting the percent increase from 2013 to 2014 as double the percent increase from 2012 to 2013. 
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Percentages Question 15

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A school district is forming a committee to discuss plans for the construction of a new high school. Of those invited to join the committee, 15% are parents of students, 45% are teachers from the current high school, 25% are school and district administrators, and the remaining 6 individuals are students. How many more teachers were invited to join the committee than school and district administrators?

Answer (Detailed Solution Below) 8

Percentages Question 15 Detailed Solution

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The correct answer is 8. The 6 students represent (100 -15 - 45 - 25)% = 15% of those invited to join the committee. If x people were invited to join the committee, then 0.15x = 6. Thus, there were \(\frac{6}{0.15}=40\) people invited to join the committee. It follows that there were 0.45(40) = 18 teachers and 0.25(40) = 10 school and district administrators invited to join the committee. Therefore, there were 8 more teachers than school and district administrators invited to join the committee.
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