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

A number is first increased by 10% and then it is further increased by 20%. The original number is increased altogether by what percentage?

  1. 28%

  2. 30%

  3. 22%

  4. 32%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

After a 10% increase, the value becomes 1.1 times original. After a further 20% increase, it becomes 1.1 × 1.2 = 1.32 times original. This represents a 32% overall increase. Options A (28%), B (30%), and C (22%) are common errors from adding percentages (10+20=30) or miscalculating the compound effect.

Multiple choice

The monthly income of Ramesh was Rs.16,500 and his monthly expenditure was Rs.10,500. Next year his income increased by 25% and his expenditure increased by 19%. Find the percentage increase in his saving.

  1. 32.4%

  2. 35.5%

  3. 44.4%

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

Original saving = 16500 - 10500 = 6000. New income = 16500 + 25% = 20625. New expenditure = 10500 + 19% = 12495. New saving = 20625 - 12495 = 8130. Percentage increase = (8130 - 6000) / 6000 × 100 = 2130 / 6000 × 100 = 35.5%. The key is to calculate the percentage increase based on the original saving, not the original income.

Multiple choice

A district has 10,24,000 inhabitants. If the population increases at the rate 2.5% per annum, find the number of inhabitants at the end of three years.

  1. 11,20,736

  2. 11,02,736

  3. 10,75,840

  4. 10,64,850
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For population growth at 2.5% per annum, we use compound interest formula: A = P(1 + r)^n. Initial population P = 10,24,000, rate r = 2.5% = 0.025, time n = 3 years. A = 10,24,000 × (1.025)^3 = 10,24,000 × 1.076890625 = 11,02,736. This accounts for compounding effect where population growth builds upon the previous year's population. Option B matches this calculation.

Multiple choice

The price of some wooden furniture increases by 65% when it passes through three hands. If the first and second sellers made a profit of 20% and 25%, respectively, then find the profit percentage of the third seller.

  1. 10%

  2. 12.5%

  3. 16%

  4. 8%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let final price = 165% of original. First seller: 120%, second seller: 125%. Let third seller's profit = p%. Then 1.20 × 1.25 × (1 + p/100) = 1.65. This gives 1.50 × (1 + p/100) = 1.65, so 1 + p/100 = 1.10, therefore p = 10%.

Multiple choice

Harsh's salary is firstly increased by 15 percent and then again increased by 20 percent. What is the overall percentage increase in A’s salary?

  1. 32%

  2. 38%

  3. 45%

  4. 42%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For successive percentage changes, use the multiplier method. First increase of 15%: multiplier = 1.15. Second increase of 20%: multiplier = 1.20. Combined effect = 1.15 × 1.20 = 1.38, which represents a 38% overall increase. The key insight is that successive percentage changes compound, not add simply.

Multiple choice

A shopkeeper bought two articles A and B at two different rates. He marked the article A 50% more and sold it by giving m% of discount. The marked price of the article A is equal to the cost price of B. He sold the article B at a rate twice that of the article A. The total profit percent is 50%. Find the value of m?

  1. 28%

  2. 16.67%

  3. 20%

  4. 25 %

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let CP of A = x, CP of B = y. MP of A = 1.5x = CP of B = y. SP of A = 1.5x(1 - m/100). SP of B = 2 × SP of A. Total CP = x + y = x + 1.5x = 2.5x. Total SP = SP of A + SP of B = 3 × SP of A = 3 × 1.5x(1 - m/100) = 4.5x(1 - m/100). Profit% = 50%, so 1.5 × 2.5x = 4.5x(1 - m/100). Solving gives m = 16.67%.

Multiple choice

A shopkeeper marked the price of a product Rs. 900 more than its cost price and announced successive discounts of 25% and 20% on the marked price, but he suffered a loss of 10%. By what percent should he increase the marked price to earn a profit of Rs. 360 at the same discount?
  1. $\( \frac{50}{7} \)%$
  2. $\( \frac{100}{7} \)%$
  3. $\( \frac{50}{3} \)%$
  4. $\( \frac{100}{3} \)%$

  5. 25%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let CP = x. MP = x + 900. After discounts: SP = (x + 900) × 0.75 × 0.8 = 0.6(x + 900). This is at 10% loss, so 0.6(x + 900) = 0.9x. Solving: 0.6x + 540 = 0.9x, x = 1800. Required SP = 1800 + 360 = 2160. New MP needed: 2160 = 0.6 × New MP, so New MP = 3600. Increase from old MP: (3600 - 2700)/2700 × 100 = 33.33% = 100/3%.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? What is the number of females in the town? I. The population of the town is 100000 and the town has more males than females. II. If the females increases by 10% which is 2% less than the percent increase in male population, the population will be increased by 8.8% and will become 108800

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statements I and II together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement II alone is sufficient. Let females = F and males = M. After 10% increase in females, population becomes 1.088 × 100000 = 108800. The male increase is 2% more than female increase, so males increase by 12%. We have 1.10F + 1.12M = 108800 and F + M = 100000. Solving these gives F ≈ 52273. Statement I only tells us M > F, which is insufficient alone.

Multiple choice

Find the correct relationship between the given quantities: Quantity I: In Town A, 1000 people live, and men & women comprise exactly half the population each. While 70% of the entire population is literate, only 60% men are literate. Q1 = Percent women literates. Quantity II: In Town B, 2000 people live, and men & women comprise exactly half the population each. While 45% of the entire population is literate, only 40% of women are literate. Q2 = Percent men literates.

  1. Quantity II > Quantity I

  2. Quantity I ≥ Quantity II

  3. Quantity I > Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Town A has 1000 people (500 men, 500 women). 70% total literate = 700 literate. Only 60% men literate = 300 literate men. So 400 literate women = 80% of women. Quantity II: Town B has 2000 people (1000 men, 1000 women). 45% total literate = 900 literate. Only 40% women literate = 400 literate women. So 500 literate men = 50% of men. 80% > 50%, so Quantity I > Quantity II.

Multiple choice

Find the correct relationship between the given quantities: Quantity I: In Town A, 1000 people live, and men & women comprise exactly half the population each. While 70% of the entire population is literate, only 60% men are literate.Find percent women literates. Quantity II: In Town B, 2000 people live, and men & women comprise exactly half the population each. While 45% of the entire population is literate, only 40% of women are literate. Find percent men literates. दी गई मात्राओ में सही संबंध ज्ञात कीजिये: मात्रा I: एक क़स्बा A में, 1000 लोग रहते है, जिनमे पुरुष और महिलाये प्रत्येक जनसँख्या का ठीक आधा है| जबकि सम्पूर्ण आबादी का 70% साक्षर है, केवल 60% पुरुष साक्षर है. महिलाओं की साक्षरता प्रतिशत बताइए। मात्रा II: क़स्बे B में, 2000 लोग रहते है, जिनमे पुरुष और महिलाये प्रत्येक जनसँख्या का ठीक आधा है। जबकि सम्पूर्ण आबादी का 45% साक्षर है, केवल 40% महिलाएं साक्षर है। पुरुषो की साक्षरता प्रतिशत बताइए।

  1. Quantity II > Quantity I मात्रा II > मात्रा I

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity I > Quantity II मात्रा I > मात्रा II

  4. Quantity I ≤ Quantity II मात्रा I ≤ मात्रा II

  5. Quantity I = Quantity II मात्रा I = मात्रा II
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Town A has 1000 people (500 men, 500 women). 70% literate = 700 people. 60% men literate = 300 men. Women literate = 700-300 = 400, so women literacy = 400/500 = 80%. Quantity II: Town B has 2000 people (1000 men, 1000 women). 45% literate = 900 people. 40% women literate = 400 women. Men literate = 900-400 = 500, so men literacy = 500/1000 = 50%. Therefore 80% > 50%, making Quantity I greater.

Multiple choice

The population of a city increases at the rate $3\%$ per year. If at time t the population of city is p, then find equation of p in time t.
  1. $p=ce^{\displaystyle\frac{3t}{100}}$
  2. $p=3e^{\displaystyle\frac{3t}{100}}$
  3. $p=e^{\displaystyle\frac{3t}{100}}$
  4. $p=\displaystyle\frac{3}{100}e^{3t}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The rate of change of population is dp/dt = (3/100) * p. This is a separable differential equation: dp/p = (3/100) dt. Integrating both sides: ln(p) = (3t/100) + C. Exponentiating: p = e^(3t/100 + C) = c * e^(3t/100).