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 shopkeeper purchased an article at Rs.800, at two successive discounts of 10% and 15% respectively. He spent Rs.28 on transportation and sold the article for Rs.800. His gain percent is

  1. 20%

  2. 40%

  3. 30%

  4. 25%

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

After 10% discount: 800 × 0.9 = 720. After additional 15% discount: 720 × 0.85 = 612. This is the purchase price. Adding transportation: 612 + 28 = 640 (total cost). Selling at 800 gives profit = 800 - 640 = 160. Gain percent = (160/640) × 100 = 25%. Wait, gain is calculated on cost price, not marked price. The question says 'sold for Rs.800' - this must be the selling price, not marked price. My calculation is correct: 25% gain on cost of 640.

Multiple choice

A tree was planted 2 years ago. It increases at the rate of 20% per annum. If at present, the height of the tree 680 cm, what was it when the tree was planted? एक पेड़ 2 वर्ष पहले लगाया गया था। यह 20% वार्षिक वृद्धि दर से बढ़ता हैं। यदि इसकी वर्तमान ऊंचाई 680 सेमी है। तो लगाते समय पेड़ की ऊंचाई क्या थी?

  1. 472 cm./सेमी

  2. 380 cm./सेमी

  3. 379 cm./सेमी

  4. 439 cm./सेमी
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Tree grows at 20% per annum for 2 years. If initial height was h, present height = h × (1 + 20/100)² = h × (1.2)² = h × 1.44 = 680 cm. So initial height h = 680/1.44 = 472 cm (approximately). Verification: 472 × 1.2 = 566.4, then 566.4 × 1.2 = 679.68 ≈ 680.

Multiple choice

A student got 60% average marks in five compulsory subjects. He got equal marks in each of the two optional subjects and If the marks of these two subjects are added to the marks of the compulsory subjects, the average of marks is reduced by 4%. What percentage of marks did he get in each of the optional subjects ?

  1. 46%

  2. 50%

  3. 52%

  4. 56%

  5. 58%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the total percentage from 5 compulsory subjects = 5 × 60 = 300%. Let each optional subject be x%. New average with 7 subjects = 60 - 4 = 56%, so total = 7 × 56 = 392%. Therefore: 300 + 2x = 392, which gives 2x = 92 and x = 46%. The student scored 46% in each optional subject.

Multiple choice

In a city (\frac{2}{3})rd of the total population are male population and rest are females, 80% of the males and 70% of the females are literate. 40% of the literate males and 30% of the literate females are graduate. 20% of the graduate males and 25% of the graduate females are government employee. Find the percentage of the total government employee with respect to the total populations.
  1. $5.94$
  2. $5.8$
  3. $6.20$
  4. $6.50$

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Working through percentages sequentially: Males = 2/3 of population. Literate males = 80% of 2/3 = 53.33%. Graduate males = 40% of 53.33% = 21.33%. Government male employees = 20% of 21.33% = 4.27% of total. Similarly, females = 1/3, literate females = 23.33%, graduate females = 7%, government female employees = 1.75%. Total = 4.27 + 1.75 = 6.02%. However, without knowing the actual population numbers, we cannot determine the exact percentage.

Multiple choice

In two successive years, 80 and 60 students of a school appeared at the final examination of which 60% and 80% passed respectively. The average rate of students passed (in percent) is दो क्रमागत वर्षों में, एक स्कूल के 80 और 60 बच्चे निर्णायक परीक्षा में भाग लेते हैं जिसमें से क्रमशः 60% और 80% उत्तीर्ण हुए | छात्रों की औसत उत्तीर्ण दर (प्रतिशत) में है |

  1. 68%

  2. 68(4/7)%

  3. 70%

  4. 72(3/7)%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

First year: 80 students, 60% passed = 48 passed. Second year: 60 students, 80% passed = 48 passed. Total passed = 96 out of 140 total students. Average percentage = (96/140) × 100 = 480/7 = 68(4/7)%.

Multiple choice

Population of a city increase 2.5% annually but is decreased by 0.5 % every year due to migration. What will be the percentage increase in 3 years? एक शहर की जनसंख्या में 2.5% की वृद्धि होती है लेकिन प्रवास के कारण प्रत्येक वर्ष इसमें 0.5 % की कमी हो जाती है | 3 वर्षों में प्रतिशत वृद्धि क्या होगी ?

  1. 4.04%

  2. 6.128%

  3. 6.1208%

  4. 7.1208%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Net annual increase = birth rate - migration rate = 2.5% - 0.5% = 2% per year. Since population grows by 2% each year, we use compound growth formula. After 3 years: P(1.02)^3 = P × 1.061208. Total increase = 6.1208%. Simply adding 2% + 2% + 2% = 6% would be incorrect because population growth compounds on the increased base each year.

Multiple choice

Two trains are running on parallel tracks in the same direction. The length of the two trains is an integral multiple of the number of the bogies. If the difference of their speeds is increased by 20%; and the total number of the bogies of both the trains is decreased by 10%. Find the percentage change in the time of crossing of the slower train by the faster train.

  1. 30%

  2. 25%

  3. 12%

  4. 20%

  5. 22.5%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Crossing time = total length/relative speed. When relative speed increases by 20% (factor 1.2) and total length decreases by 10% (factor 0.9), new time = (0.9L)/(1.2Δv) = 0.75 × (L/Δv) = 0.75T. This is a 25% decrease.

Multiple choice

A man's wage was reduced by 50%. The reduced wage was then increased by 50%. His loss in percentage term is

  1. 10%

  2. 20%

  3. 25%

  4. 50%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Starting with wage W, after 50% reduction: W × 0.5 = 0.5W. After 50% increase: 0.5W × 1.5 = 0.75W. Final wage is 75% of original, meaning a 25% loss. This demonstrates that percentage changes are not reversible when applied sequentially - a 50% loss requires a 100% gain to recover, not a 50% gain.

Multiple choice

(\text{If the radius of sphere increased by 20\%, then how much percentage increase in volume?})
  1. $33.1%$
  2. $71.8%$
  3. $57.44$
  4. $60%$
  5. $None of these$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Volume of a sphere is proportional to the cube of its radius (V = 4/3 πr³). When radius increases by 20%, new radius = 1.2r. New volume = (1.2)³ times original = 1.728 times original. Percentage increase = (1.728 - 1) × 100 = 72.8%. Option A (33.1%) incorrectly uses linear scaling. Option B (71.8%) is close but not exact. Option D (60%) mistakenly uses 3 × 20%. Since 72.8% is not listed, E is correct.

Multiple choice

A shopkeeper marks price of his articles 12% above the cost price and then allows 12% discount on the marked price. What is his loss percent?
  1. $0%$
  2. $1%$
  3. $1.44%$
  4. $2.4%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP = 100. Marked Price = 100 + 12% = 112. Selling Price = 112 - 12% of 112 = 112 - 13.44 = 98.56. Loss = 100 - 98.56 = 1.44. Loss percent = 1.44%. Option A (0%) would be true only if the markup and discount percentages were equal, but the base changes after markup. Option B (1%) is close but not exact. Option D (2.4%) would result from incorrectly subtracting percentages directly.

Multiple choice

A shopkeeper offered an article at a discount of 5% but marked 20% higher than the cost price. Find the profit percent. एक दुकानदार एक वस्तु पर 5% की छूट देता है लेकिन इसके क्रय मूल्य से 20% अधिक अंकित करता है। लाभ प्रतिशत ज्ञात कीजिये।

  1. 12%

  2. 13%

  3. 14%

  4. 15%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP = 100. Marked price = 120 (20% above CP). Selling price after 5% discount = 120 × 0.95 = 114. Profit = 114 - 100 = 14%.

Multiple choice

The population of a certain town increased at a certain rate per annum. Now it is 456976, four years ago it was 390625. What was it been 2 years before? किसी एक कस्बे की जनसंख्या प्रतिवर्ष एक निश्चित दर से बढ़ती है। अब यह 456976 है। चार वर्ष पहले, यह 390625 थी। 2 वर्ष पूर्व यह कितनी रही होगी?

  1. 452200

  2. 425200

  3. 422200

  4. 422500
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Population 4 years ago = 390625, current population = 456976. Ratio = 456976/390625 = 1.17. Let growth rate be r. (1 + r)⁴ = 1.17. Therefore, 1 + r = (1.17)^(1/4) ≈ 1.04, so r ≈ 4%. Population 2 years ago = 390625 × (1.04)² ≈ 390625 × 1.0816 ≈ 422500. Alternatively: 390625 = 625² and 456976 = 676², giving growth factor 676/625 = 1.0816. Two years before = 390625 × 1.0816 = 422500. Option A (452200), B (425200), and C (422200) are incorrect calculations.