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

The table below gives the age-wise population percentage of a city: Age group Percentage Below 30 years 14.00 30-34.99 29.75 35-39.99 26.25 40-44.99 0 45-49.99 18.50 50 years and above 11.50 The number of persons below the age of 40 years is 10.5 lakhs. If the ratio of taxpayers to other persons in the same age group below 30 years is 1 : 2, then what is the number of taxpayers (in lakhs) in that age group?

  1. 0.4

  2. 0.7

  3. 0.85

  4. 1.05
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total population below 40 is 10.5 lakhs. Percentage below 30 is 14%, 30-34.99 is 29.75%, 35-39.99 is 26.25%. Total percentage < 40 = 14 + 29.75 + 26.25 = 70%. 70% = 10.5 lakhs, so 1% = 0.15 lakhs. Below 30 years = 14% = 14 * 0.15 = 2.1 lakhs. Taxpayers ratio 1:2 means 1/3 of 2.1 = 0.7 lakhs.

Multiple choice

The population of Houston dropped to 2,378,146 in the year 2022 from 3,752,125 in the year 2020 due to the outbreak of an epidemic. What was the percentage change in the population of Houston?

  1. 36.61%

  2. 57.77%

  3. 62.13%

  4. 71.98%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The percentage change is calculated as (New Value - Old Value) / Old Value * 100. Here, (2,378,146 - 3,752,125) / 3,752,125 * 100 = -1,373,979 / 3,752,125 * 100 which is approximately -36.619%. The magnitude of the drop is 36.61%.

Multiple choice

g(x) = 30.5(1.08)x The population of a certain species of birds, in thousands, from the years 2000 to 2020 can be modeled by the function g, where x is the number of years after 2000. Which of the following is the best interpretation of the number 1.08 in this context?

  1. On average, the population increased by approximately 0.08 thousand birds per year.

  2. On average, the population increased by approximately 1.08 thousand birds per year.

  3. On average, the population increased by approximately 8% per year.

  4. On average, the population increased by approximately 108% per year.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In the exponential growth model g(x) = a(b)^x, the base b represents (1 + r), where r is the growth rate. Here, 1.08 = 1 + 0.08, which corresponds to an 8% increase per year.

Multiple choice

A man buys 35 kg of sugar and sets a marked price in order to make 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by p percent so as to make an overall profit of 15%. Then p is nearest to

  1. 31

  2. 22

  3. 35

  4. 25
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total cost = 35 * C. Total revenue target = 35 * C * 1.15 = 40.25C. Revenue from first 5 kg = 5 * 1.2C = 6C. Revenue from next 15 kg = 15 * 1.2C * 0.9 = 16.2C. Remaining sugar = 35 - 5 - 15 - 3 = 12 kg. Revenue needed = 40.25C - 6C - 16.2C = 18.05C. Selling price per kg = 18.05C / 12 = 1.504C. Marked price was 1.2C. Increase = (1.504 - 1.2) / 1.2 = 0.253, which is 25%.

Multiple choice

The total of male and female populations in a city increased by 25% from 1970 to 1980. During the same period, the male population increased by 40% while the female population increased by 20%. From 1980 to 1990, the female population increased by 25%. In 1990, if the female population is twice the male population, then the percentage increase in the total of male and female populations in the city from 1970 to 1990 is

  1. 68.25

  2. 68.75

  3. 68.50

  4. 69.25
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Mark organised a group chat for a project, where he received a total of 900 messages from his colleagues Alice, Bob, Carol, and David. Alice and Bob respectively sent 28% and 18% of these messages, while Carol sent half the number of messages as David. Additionally, Mark realised that out of Alice's, Bob's, Carol's, and David's messages, 25%, 50%, 50%, and 25%, respectively, were funny GIFs. What percentage of the funny GIFs received by Mark were not sent by Carol?

  1. 35.78%

  2. 56.67%

  3. 67.89%

  4. 73.53%

  5. 78.65%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total messages = 900. Alice = 252 (28%), Bob = 162 (18%). Remaining = 486. Carol = x, David = 2x. 3x = 486, x = 162. Carol = 162, David = 324. GIFs: Alice = 252*0.25 = 63. Bob = 162*0.5 = 81. Carol = 162*0.5 = 81. David = 324*0.25 = 81. Total GIFs = 63+81+81+81 = 306. GIFs not by Carol = 306 - 81 = 225. Percentage = (225 / 306) * 100 = 73.53%.

Multiple choice

A number is first increased by 40% and then decreased by 25%, again increased by 15% and then decreased by 20%. What is the net increase/decrease per cent in the number?

  1. 7.2% decrease

  2. 6.4% increase

  3. 3.4% increase

  4. 3.4% decrease

  5. None of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the initial number be 100. After 40% increase: 140. After 25% decrease: 140 * 0.75 = 105. After 15% increase: 105 * 1.15 = 120.75. After 20% decrease: 120.75 * 0.8 = 96.6. The net change is 100 - 96.6 = 3.4% decrease.

Multiple choice

In the city of Hilltop, the number of cars increased by 25%, while the number of bicycles decreased by 25% over the past year. If the current number of cars and bicycles in Hilltop are equal to each other, what was the percentage change in the total transportation count of Hilltop over the past year?

  1. 12.5% decrease

  2. 6.25% decrease

  3. No change

  4. 6.25% increase

  5. 12.5% increase
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let C be the number of cars and B be the number of bicycles. Current state: C = B. Last year: C_old = C/1.25 = 0.8C, B_old = B/0.75 = 1.333B. Total old = 0.8C + 1.333B = 2.133C. Total new = 2C. Change = (2C - 2.133C) / 2.133C = -0.133 / 2.133 = -6.25%.

Multiple choice

In a community, there are 200,000 residents, of which 120,000 are homeowners. Out of every 100 homeowners, 90 participate in community events, but only 70% of the total population is involved in community activities. Determine the percentage of renters who participate in community events.

  1. 30%

  2. 34%

  3. 37%

  4. 40%

  5. 43%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total population = 200,000. Homeowners = 120,000. Renters = 80,000. Total participants = 70% of 200,000 = 140,000. Homeowner participants = 90% of 120,000 = 108,000. Renter participants = 140,000 - 108,000 = 32,000. Percentage = 32,000 / 80,000 = 40%.

Multiple choice

A bakery sells specialty cakes for $50 each. During a weekend promotion, the bakery offered a 20% discount on the cakes. Following the weekend, the bakery decided to increase the discounted price by 30% due to high demand. What is the overall percentage change in price from the original price to the new price after the increase?

  1. 2%

  2. 4%

  3. 8%

  4. 10%

  5. 15%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original price = 50. Discounted price = 50 * 0.8 = 40. New price = 40 * 1.3 = 52. Percentage change = ((52-50)/50) * 100 = 4%.