Quantitative Aptitude

Percentage

482 Questions
All Successive Percentage Changes 177 Population Growth and Depreciation 103 Fractional Base Multiplication 58 Reverse More-Than and Less-Than Comparisons 38 Income, Expenditure, and Savings 33 Price and Consumption 30 Election Votes and Margins 10 Fake Weight and Faulty Measures 10 Venn Diagram Percentages 9 Passing Marks Shifts 5 Fresh vs. Dry Mixture 2

Percentage Questions

Multiple choice

In a wildlife sanctuary, the total number of herbivores and carnivores increased by 50% from the year 2000 to 2010. During this period, the herbivore population grew by 80%, while the carnivore population increased by 40%. From 2010 to 2020, the carnivore population further increased by 25%. If in the year 2020, the number of carnivores was three times the number of herbivores, what was the percentage increase in the combined animal population from 2000 to 2020?

  1. 45%

  2. 54%

  3. 75%

  4. 82%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let H and C be initial populations. Total = H+C. 2010: H' = 1.8H, C' = 1.4C. Total' = 1.5(H+C). 1.8H + 1.4C = 1.5H + 1.5C => 0.3H = 0.1C => C = 3H. In 2020, C'' = 1.25 * 1.4C = 1.75C = 1.75(3H) = 5.25H. Given C'' = 3H'', so 5.25H = 3H'' => H'' = 1.75H. Total 2020 = H'' + C'' = 1.75H + 5.25H = 7H. Initial total = H+3H = 4H. Increase = (7H-4H)/4H = 3/4 = 75%.

Multiple choice

A print shop has N identical printers. Each printer can produce 1 poster every 4 minutes. The shop replaces 40% of the printers with new printers, each of which can produce 1 poster every 2 minutes. All printers operate continuously at their respective rates. By what percent does the total number of posters that can be produced in 1 hour increase as a result of the replacement?

  1. 25%

  2. 33 1 3 %

  3. 40%

  4. 50%

  5. 66 2 3 %
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let N = 100. Old rate = 100/4 = 25 posters/min. Replace 40% (40 printers) with new ones (rate 1/2). New rate = 60*40/2 + 60*60/4 = 1200 + 900 = 2100 posters/hour. Old rate = 25*60 = 1500 posters/hour. Increase = (2100 - 1500) / 1500 = 600 / 1500 = 40%.

Multiple choice

The population of City A increased by p% last year, and the number of employed residents increased by q%, where p > q. By what percentage did the ratio of total population to employed residents increase, in terms of p and q?

  1. p q %

  2. (p - q)%

  3. [ 100 ( p − q ) ( 100 + p ) ] %

  4. [ 100 ( p − q ) ( 100 + q ) ] %

  5. [ 100 ( p − q ) ( 100 + p + q ) ] %
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P be population and E be employed. Ratio R = P/E. New ratio R' = P(1+p/100) / E(1+q/100). The percentage increase is ((R'-R)/R) * 100, which simplifies to 100(p-q)/(100+q).

Multiple choice

A bookstore owner purchased a set of novels for $120. She set the selling price so that it equaled the cost price plus a markup of 25 percent of the selling price. If the set was sold at the marked price, what was the gross profit made by the owner from the purchase and sale?
  1. $36
  2. $40
  3. $48
  4. $50
  5. $52
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let SP be the selling price. Markup = 0.25 * SP. CP = SP - 0.25 * SP = 0.75 * SP. Given CP = 120, so 0.75 * SP = 120, SP = 160. Profit = SP - CP = 160 - 120 = 40.

Multiple choice

At the end of the first year, student enrollment at a certain college was 25 percent higher than at the beginning of the year. At the end of the second year, enrollment was 50 percent higher than at the beginning of the first year. What was the percent increase in enrollment from the end of the first year to the end of the second year?

  1. 15%

  2. 18%

  3. 20%

  4. 25%

  5. 30%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial enrollment be 100. End of year 1 = 125. End of year 2 = 150 (50% higher than beginning of year 1). Increase from end of year 1 to end of year 2 = (150-125)/125 = 25/125 = 20%.

Multiple choice

Lena owns a boutique in a popular shopping district. She buys 150 scarves for $750 in total. Lena marks up the price of each scarf by 50%, but during a clearance sale, she offers a 30% discount. What is the profit percentage Lena makes on each scarf after the discount?

  1. 20%

  2. 15%

  3. 10%

  4. 5%

  5. 3%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the cost price of one scarf be 100 units. Marked price = 150 units. After a 30% discount, the selling price = 150 * 0.7 = 105 units. Profit = 105 - 100 = 5 units. Profit percentage = 5%.

Multiple choice

In a town of 2000 people, 60% are males. Out of the males, 40% are literate. If 55% of the total population is literate, what percentage of females is literate?

  1. 67.5%

  2. 72.5%

  3. 70.5%

  4. 77.5%

  5. 80.5%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total population is 2000. Males = 60% of 2000 = 1200, so females = 800. Literate males = 40% of 1200 = 480. Total literate = 55% of 2000 = 1100. Literate females = 1100 - 480 = 620. Percentage of females literate = (620 / 800) * 100 = 77.5%.

Multiple choice

Two numbers are 18 percent less and 42 percent less than a third number, respectively. If the third number is increased by 25 percent, what percentage is the second number of the first number now?

  1. 57.14%

  2. 70.73%

  3. 76.73%

  4. 79.14%

  5. 84.73%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the third number be 100. First number = 82, second number = 58. If the third number increases by 25 percent, it becomes 125. The problem asks for the second number as a percentage of the first number, which remains 58/82 = 70.73 percent.

Multiple choice

The population of the town of Paxton continuously increased in the two decades 1960 through 1969 and 1970 through 1979. Was the percentage increase greater in the first decade than in the second decade? (1) The population increase in the first decade was 10,082. (2) The population increased by the same amount in both decades.

  1. if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient;

  2. if statement (2) ALONE is sufficient to answer the question but statement (1) alone is not sufficient.

  3. if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient;

  4. if EACH statement ALONE is sufficient to answer the question;

  5. if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question
Reveal answer Fill a bubble to check yourself
B Correct answer