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 salary of A increases by 50% every year, whereas the salary of B increases by 25% every year. If in 2008, their salaries are equal, what percentage of Bs salary was As salary in 2005?

  1. 75%

  2. 58%

  3. 50%

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

Let A(t) and B(t) be the salaries in year t. Given A(2008) = B(2008), we have A(2005)(1.5)^3 = B(2005)(1.25)^3. The ratio A(2005)/B(2005) = (1.25/1.5)^3 = (5/6)^3 = 125/216, which is approximately 0.5787 or 58%.

Multiple choice

A man buys a pair of gloves having the price of Rs. 150 at Rs. 105. He is given two successive discounts. If he receives the second discount of 12.5%, then find the percentage of the first discount.

  1. 12.5%

  2. 15%

  3. 20%

  4. 17.5%

  5. 18%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the first discount be x%. The price after the first discount is 150 * (1 - x/100). After the second 12.5% discount, the price is 150 * (1 - x/100) * (1 - 0.125) = 105. Solving 150 * (1 - x/100) * 0.875 = 105 gives 1 - x/100 = 105 / (150 * 0.875) = 105 / 131.25 = 0.8. Thus, x = 20%.

Multiple choice

In each of the years 1997 and 1998, Development Tax Software sold 3.4 million copies more than in the previous year. Quantity A Percent increase in the number of copies sold in 1997 over the previous year Quantity B Percent increase in the number of copies sold in 1998 over the previous year

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. Two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let S be sales in 1996. Sales in 1997 = S + 3.4. Sales in 1998 = S + 6.8. Percent increase 1997 = (3.4/S) * 100. Percent increase 1998 = (3.4/(S+3.4)) * 100. Since S < S+3.4, the fraction 3.4/S is greater than 3.4/(S+3.4).

Multiple choice

Directions: Answer the questions independently of each other. Of the adult population in a certain village 45% men and 25% women are married. Assuming that no man marries more than one women and vice-versa, the percentage of the total population of adult who are married, is?

  1. 30%

  2. 32.14%

  3. 33.33%

  4. 31.8%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let M be the number of men and W be the number of women. Since the number of married men equals the number of married women, 0.45M = 0.25W, so W = 1.8M. The total population is M + 1.8M = 2.8M, and the total married people is 0.45M + 0.25(1.8M) = 0.9M. The percentage is (0.9M / 2.8M) * 100 which is approximately 32.14%.

Multiple choice

DIRECTIONS : Select the correct alterative from the given choices. Find the percentage increase in the volume of a sphere, if its radius increases by 200%.

  1. 700%

  2. 800%

  3. 2600%

  4. 2700%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If the radius increases by 200%, the new radius is r + 2r = 3r. The volume of a sphere is proportional to the cube of the radius, so the new volume is (3r)^3 = 27r^3. The increase is 27r^3 - r^3 = 26r^3, which is 2600% of the original volume.

Multiple choice

The total population of boys and girls in a town showed a 35% rise from 2000 to 2010. During this span, the number of boys increased by 50%, while the girls saw a 30% growth. Moving on to the period between 2010 and 2020, the girl population experienced another notable 35% increase. If in the year 2020, the girl population was five times that of the boys, what was the percentage growth in the overall population of boys and girls in the town from 2000 to 2020?

  1. 88

  2. 68

  3. 58

  4. 38

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

Let B and G be the initial populations. 1.35(B+G) = 1.5B + 1.3G => 1.35B + 1.35G = 1.5B + 1.3G => 0.05G = 0.15B => G = 3B. In 2010, B_2010 = 1.5B, G_2010 = 1.3G = 3.9B. In 2020, G_2020 = 1.35 * 3.9B = 5.265B. Given G_2020 = 5 * B_2020, then B_2020 = 1.053B. Total 2020 = 6.318B. Total 2000 = 4B. Growth = (6.318-4)/4 = 2.318/4 = 0.5795, or approx 58%.

Multiple choice

Karan's annual CTC (Cost to the Company) has two parts – a fixed part and a variable part. His annual CTC increased by 25% and the fixed part in it increased by 20% in 2013 when compared with that of 2012. In 2014, both his annual CTC as well as the variable part in it increased by 33⅓%. If Karan did not receive any bonus from the company in the three given years, then, by what percentage did the fixed part of his annual CTC increase in 2014 when compared with that of 2013?

  1. 40%

  2. 33⅓%

  3. 32.5%

  4. 43⅔%
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

The assistant of a shopkeeper sold an article at a profit of 𝑎%. But in the ledger, he swapped the values of CP and SP of the article owing to which, the ledger showed a loss which was 5 percentage points less than the actual profit. By what percentage should the new SP be increased so that the profit percentage remains the same?

  1. 50%

  2. 52.5%

  3. 43.33%

  4. 56.25%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let CP=x, SP=y. Profit = (y-x)/x = a/100. Swapped: Loss = (x-y)/y = (a-5)/100. Solving these equations for y/x leads to the required increase in SP to restore the original profit margin.

Multiple choice

In the year 2002, the population of a town increased by 𝑝% with respect to its population in 2001, but due to the breakout of a communicable disease, the population of the town dropped by (𝑝 + 5)% in the year 2003 with respect to its population in 2002. If the total population of the town dropped by 8% in 2003 with respect to that in 2001 and, after it revived from the communicable disease, its population increased by 25% in 2004 with respect to that in 2003, then by what percent did the population of the town change in 2004 with respect to that in 2002?

  1. 0

  2. 5

  3. 7.5

  4. 10
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

A student was asked to find the product of three real numbers 𝑎, 𝑏 and c. He committed a mistake in copying all the three numbers and ended up in a result where the value of a got increased by 33⅓%, the product of a and b got increased by 20% and the product of 𝑎,𝑏 and c got increased by 35%. Which of the following gives the percentage change in the value of c?

  1. 10%

  2. 12.5%

  3. 15%

  4. 16.5%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P = abc. New P' = 1.35P. New a' = 1.333a = (4/3)a. New (ab)' = 1.2ab. Since (ab)' = a'b', b' = 1.2ab / (4/3)a = 0.9b. Now P' = a'b'c' = 1.2ab * c' = 1.35abc. So c' = 1.35/1.2 * c = 1.125c. This is a 12.5% increase.

Multiple choice

After two successive increments, Gopal's salary became 187.5% of his initial salary. If the percentage of salary increase in the second increment was twice of that in the first increment, then the percentage of salary increase in the first increment was

  1. 20

  2. 25

  3. 27.5

  4. 30
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the first increment be x%. The second is 2x%. (1 + x/100)(1 + 2x/100) = 1.875. Let y = x/100. (1+y)(1+2y) = 1.875. 1 + 3y + 2y^2 = 1.875. 2y^2 + 3y - 0.875 = 0. Using the quadratic formula, y = 0.25. So x = 25%.

Multiple choice

After two successive increases, the rent of an apartment became 209.44% of its original amount. If the percentage increase in second increment was 1.5 times the first, what was the percentage increase in the first hike?

  1. 32

  2. 34

  3. 36

  4. 40

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

Let the first increase be x%. The second increase is 1.5x%. The final amount is 209.44% of the original, meaning (1 + x/100) * (1 + 1.5x/100) = 2.0944. Solving the quadratic equation x^2 + 166.67x - 7333.33 = 0 gives x = 36.

Multiple choice

A company increased the price of a product by 20 percent. After the price increase, the sales volume dropped to three-fourths of its original value. What was the percentage change in the company's total revenue?

  1. -10%

  2. -5%

  3. 0%

  4. 5%

  5. 10%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Revenue = Price * Quantity. Let initial price be P and quantity be Q. New price is 1.2P and new quantity is 0.75Q. New revenue = 1.2P * 0.75Q = 0.9PQ. This is a 10% decrease from the original revenue.