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

Directions: The item contains a question and two statements I and II, giving certain data. Select the correct answer from the given alternatives depending on the sufficiency of data given in the statements to answer the question. A salesman sells shirts and by selling these shirts he gains 25%. By what percent is marked price more than the cost price? Statement I: He gives a discount of 4% on the marked price. Statement II: The cost price is 20% less than the selling price.

  1. I alone is sufficient and II alone is not sufficient to answer the question.

  2. II alone is sufficient and I alone is not sufficient to answer the question.

  3. Both I and II together are sufficient, but neither statement alone is sufficient to answer the question.

  4. Both I and II together are not sufficient to answer the question and additional data specific to the question is needed.

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

Let CP = 100, SP = 125. MP = x. Statement I: 0.96x = 125, so x is known. Statement II: CP = 0.8 * SP, which is 100 = 0.8 * 125, which is always true and provides no info on MP. Statement I is sufficient.

Multiple choice

Population of a town increases 2.5\% annually but is decreased by 0.5\% every year due to migration. What will be the percentage of increase in 2 years?

  1. 5

  2. 4.04

  3. 4

  4. 3.96
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The net annual increase is 2.5% - 0.5% = 2%. However, percentage increase compounds annually. After 2 years, the factor is (1.02)^2 = 1.0404, giving a 4.04% total increase. Option A (5%) incorrectly adds the rates, while C (4%) uses simple interest instead of compound.

Multiple choice

The length and breadth of a rectangle are increased by 30% and 20% respectively. Find the net percentage change in its area.

  1. 23

  2. 34

  3. 50

  4. 12

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

Original area = L × B. New length = 1.3L (30% increase), new breadth = 1.2B (20% increase). New area = 1.3L × 1.2B = 1.56LB. Percentage change = (1.56 - 1) × 100 = 56% increase. None of the given options (23, 34, 50, 12) equal 56%, so 'None of these' (E) is correct. The correct answer should be 56% increase.

Multiple choice

A man spends 75\% of his income, when his income is increased by 20\%, he increases his expenditure by 10\%. By how much per cent has his savings increased?

  1. 31.25%

  2. 33.25%

  3. 32.50%

  4. 50.00%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let initial income be 100. Initial expenditure = 75, savings = 25. New income = 120 (20% increase). New expenditure = 82.5 (10% increase on 75). New savings = 120 - 82.5 = 37.5. Percentage increase in savings = (37.5 - 25)/25 × 100 = 50%.

Multiple choice

If the price of an article is increased by 20%, by what percentage should its consumption be decreased by a family if the family's expenditure is increased by 8%?

  1. 8%

  2. 10%

  3. 20%

  4. 15%

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

Let original price = 100, consumption = 100 units. New price = 120. New expenditure = 108. New consumption = 108/120 = 0.9 of original. Percentage decrease = (1 - 0.9) x 100 = 10%. The consumption must decrease by 10% to keep expenditure increase at only 8%.

Multiple choice

If the radius of circle is increased by 4 times,what will be the percentage increase in its area?

  1. 300%

  2. 400%

  3. 1600%

  4. 1500%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Area of a circle = pi r^2. When radius increases 4 times, new area = pi(4r)^2 = 16 pi r^2. The area increases by 16 times, which is a 1500% increase (calculated as (16-1) x 100%). 300% would mean 4 times area, 400% would mean 5 times, and 1600% would mean 17 times the original area. Only 1500% correctly represents a 16-fold increase.

Multiple choice

For the past two years, it is observed that the population of a place is increasing by 10% per year. If the present population is 6171 the population two years ago was - पिछले दो वर्षो में यह देखा गया कि किसी जगह की जनसंख्या प्रतिवर्ष 10% बढ़ रही है। अगर वर्तमान जनसंख्या 6171 है तो दो वर्ष पहले जनसंख्या क्या थी ?

  1. 4000

  2. 4500

  3. 5000

  4. 5100
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work backwards from present to past by reversing the compound growth. If population grew 10% each year for 2 years to reach 6171, divide by 1.10 twice: 6171 ÷ 1.21 = 5100. Answer D is correct.

Multiple choice

A shopkeeper purchased a chair marked at Rs 600 at two successive discounts of 15% and 20% respectively. He spent Rs 28 on transportation and sold the chair for Rs 545. His gain percent was - एक दुकानदार ने रू 600 के अंकित मूल्य की एक कुर्सी क्रमशः 15% तथा 20% की दो क्रमिक छूटों पर खरीदी। उसने उस कुर्सी के परिवहन पर रू 28 खर्च किए, तत्पश्चात् उसे रू 545 में बेच दिया। तदनुसार, उसके लाभ का प्रतिशत कितना था?

  1. 25%

  2. 30%

  3. 35%

  4. 20%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Marked price = Rs 600. After first discount of 15%: 600 × 0.85 = 510. After second discount of 20%: 510 × 0.80 = 408 (CP). Add transport: 408 + 28 = 436 (total cost). SP = 545. Gain = 545 - 436 = 109. Gain% = (109/436) × 100 = 25%.

Multiple choice

10% of the inhabitants of a certain city left that city. Later on 15% of the remaining inhabitants of that city again left the city. What is the remaining percentage of population of that city? एक निश्चित शहर के 10% निवासियों ने उस शहर को छोड़ दिया। बाद में शहर के बचे हुये निवासियों को 15% निवासी पुनः शहर छोड़ गये। शहर की जनसंख्या का कितना प्रतिशत शेष है?

  1. 76.5%

  2. 80%

  3. 80.4%

  4. 81%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

After 10% leave: 90% remain. From this remaining 90%, another 15% leave: 15% of 90% = 13.5%. Total remaining = 90% - 13.5% = 76.5%. Option B (80%) incorrectly adds the percentages (10% + 15% = 25%, so 100-25=75) or treats them independently.