Percentage — Practice MCQs

1. Basics

x% = x/100. To find x% of y, multiply y by x/100. "A is what % of B" = A/B × 100.

2. Fraction–percent table (learn by heart)

3. Key formulas

4. Solved examples

Price rises 25%; cut in consumption to keep expense same = 25/125 = 20%.

Successive increases of 10% and 20% = 10 + 20 + 2 = 32%.

Increase 20% then decrease 20% → 20 − 20 − 4 = 4% loss.

In an election of two candidates, the winner gets 60% and wins by 400 votes → 20% = 400 → total valid votes 2000.

A student needs 33% to pass; gets 125 and fails by 40 → 33% = 165 → max marks 500.

Population 10,000 grows 10% a year: after 2 years 10,000 × 1.21 = 12,100.

A's salary is 25% more than B's → B's is 25/125 = 20% less than A's.

5. Traps

• Always take the percentage on the right base (the "than" quantity).
• Percentage points ≠ percent (rate 10% → 12% is 2 points, but a 20% rise).

Solved examples by question type

Each type that comes in the ASO paper, worked step by step. Try it yourself first, then read the solution.

Basic level

Example 1. What is 45% of 720?
(a) 162   (b) 3,240   (c) 324   (d) 369
Answer: (c) 324
Solution: 45% of 720 = 45/100 × 720 = 324.

Example 2. 270 g is what percent of 3 kg?
(a) 9%   (b) 0.9%   (c) 90%   (d) 10%
Answer: (a) 9%
Solution: Convert to the same unit: 3 kg = 3000 g. 270/3000 × 100 = 9%.

Example 3. 260 g is what percent of 2 kg?
(a) 13%   (b) 14%   (c) 130%   (d) 1.3%
Answer: (a) 13%
Solution: Convert to the same unit: 2 kg = 2000 g. 260/2000 × 100 = 13%.

Example 4. 8⅓% of 432 is:
(a) 33   (b) 72   (c) 48   (d) 36
Answer: (d) 36
Solution: 8⅓% = 1/12. So 1/12 × 432 = 36. Learning these fractions saves time.

Example 5. 6.25% of 768 is:
(a) 64   (b) 45   (c) 48   (d) 96
Answer: (c) 48
Solution: 6.25% = 1/16. So 1/16 × 768 = 48. Learning these fractions saves time.

Example 6. 250% of a number is 500. What is 40% of the number?
(a) 84   (b) 80   (c) 200   (d) 160
Answer: (b) 80
Solution: Number = 500 × 100/250 = 200. 40% of 200 = 80.

Example 7. What is 10% of 40% of 600?
(a) 300   (b) 24   (c) 240   (d) 12
Answer: (b) 24
Solution: 10% of 40% of 600 = 10/100 × 40/100 × 600 = 24.

Example 8. What is 25% of 60% of 800?
(a) 1,200   (b) 120   (c) 60   (d) 680
Answer: (b) 120
Solution: 25% of 60% of 800 = 25/100 × 60/100 × 800 = 120.

Example 9. If 23% of a number exceeds 18% of the same number by 15, the number is:
(a) 600   (b) 300   (c) 150   (d) 400
Answer: (b) 300
Solution: (23 − 18)% of N = 15 → 5% of N = 15 → N = 15 × 100/5 = 300.

Example 10. After a 15% increase, a man's salary is ₹23,000. His original salary was:
(a) 21,000   (b) 20,000   (c) 19,550   (d) 3,000
Answer: (b) 20,000
Solution: Original = 23,000 × 100/115 = ₹20,000. Do not subtract 15% of the new salary.

Example 11. A man spends 35% of his income on rent, 25% on food and 10% on education. He saves ₹6,000. His income is:
(a) 21,000   (b) 20,000   (c) 40,000   (d) 14,000
Answer: (b) 20,000
Solution: Saving = 100 − 35 − 25 − 10 = 30%. Income = 6,000 × 100/30 = ₹20,000.

Example 12. A man spends 35% of his income on rent, 25% on food and 10% on education. He saves ₹6,000. His income is:
(a) 20,000   (b) 40,000   (c) 21,000   (d) 14,000
Answer: (a) 20,000
Solution: Saving = 100 − 35 − 25 − 10 = 30%. Income = 6,000 × 100/30 = ₹20,000.

ASO exam level

Example 13. In an election between two candidates, the winner got 62% of the votes and won by 600 votes. The total number of votes polled was:
(a) 3,100   (b) 967   (c) 2,500   (d) 1,250
Answer: (c) 2,500
Solution: Margin = 62% − 38% = 24% of total = 600. Total = 600 × 100/24 = 2,500.

Example 14. In an election, 25% of the votes were invalid. The winner got 65% of the valid votes. If the total votes were 10,000, how many valid votes did the loser get?
(a) 4,875   (b) 4,900   (c) 2,625   (d) 3,500
Answer: (c) 2,625
Solution: Valid = 75% of 10,000 = 7,500. Loser = 35% of 7,500 = 2,625.

Example 15. A student who gets 25% marks fails by 15 marks. Another who gets 35% marks gets 35 marks more than the pass mark. The maximum marks are:
(a) 600   (b) 250   (c) 140   (d) 500
Answer: (d) 500
Solution: (35 − 25)% of max = 15 + 35 = 50. So max = 50 × 100/10 = 500.

Example 16. The price of an article is first increased by 20% and then decreased by 10%. The net change is:
(a) 10% increase   (b) 8% decrease   (c) 8% increase   (d) 9% increase
Answer: (c) 8% increase
Solution: Net = a + b + ab/100 = 20 + (-10) + (20×-10)/100 = 8%. Successive changes are never simply added.

Example 17. The price of petrol falls by 50%. By what percent can a person increase consumption without changing the expenditure?
(a) 105%   (b) 50%   (c) 96%   (d) 100%
Answer: (d) 100%
Solution: Increase by 50/(100 − 50) × 100 = 100%.

Example 18. If A's salary is 25% more than B's, then B's salary is how much percent less than A's?
(a) 25%   (b) 33.33%   (c) 23%   (d) 20%
Answer: (d) 20%
Solution: B is less by 25/(100 + 25) × 100 = 20%.

Example 19. If A's salary is 20% more than B's, then B's salary is how much percent less than A's?
(a) 25%   (b) 21.67%   (c) 20%   (d) 16.67%
Answer: (d) 16.67%
Solution: B is less by 20/(100 + 20) × 100 = 16.67%.

Example 20. The population of a town is 40,000. It increases by 10% every year. What will it be after 2 years?
(a) 52,400   (b) 47,900   (c) 48,400   (d) 48,000
Answer: (c) 48,400
Solution: 40,000 × (1 + 10/100)^2 = 48,400. Growth is compounded every year.

Example 21. A machine loses 20% of its value every year. Its value after 2 years is ₹51,200. What was its original price?
(a) 90,000   (b) 80,000   (c) 71,680   (d) 73,728
Answer: (b) 80,000
Solution: Original = 51,200 ÷ (80/100)² = ₹80,000. Increasing back by 20% each year gives the wrong answer.

Example 22. The numerator of a fraction is increased by 50% and the denominator is decreased by 25%. The new fraction is 9/11. The original fraction is:
(a) 45/22   (b) 9/22   (c) 9/11   (d) 10/22
Answer: (b) 9/22
Solution: New = original × 150/75. So original = 9/11 × 75/150 = 9/22.

Example 23. While measuring the radius of a circle, an error of 4% in excess is made. The error in the calculated area is:
(a) 8.16%   (b) 9.16%   (c) 4%   (d) 8%
Answer: (a) 8.16%
Solution: Area ∝ radius². Error = 4 + 4 + 4×4/100 = 8.16%.

Example 24. The length of a rectangle is increased by 10%. By what percent must the breadth be decreased to keep the area the same?
(a) 9.09%   (b) 12.09%   (c) 10%   (d) 11.11%
Answer: (a) 9.09%
Solution: Decrease = 10/(100 + 10) × 100 = 9.09%. Same rule as price and consumption.

Example 25. The length of a rectangle is increased by 10%. By what percent must the breadth be decreased to keep the area the same?
(a) 12.09%   (b) 9.09%   (c) 11.11%   (d) 10%
Answer: (b) 9.09%
Solution: Decrease = 10/(100 + 10) × 100 = 9.09%. Same rule as price and consumption.

Example 26. A man spends 75% of his income. His income rises by 25% and his expenditure by 10%. By what percent do his savings change?
(a) 75% decrease   (b) 70% increase   (c) 35% increase   (d) 15% increase
Answer: (b) 70% increase
Solution: Take income = 100. Old: spend 75, save 25. New: income 125, spend 82.5, save 42.5. Change = 17.5/25 × 100 = 70%.

Example 27. A man spends 80% of his income. His income rises by 10% and his expenditure by 5%. By what percent do his savings change?
(a) 5% increase   (b) 30% increase   (c) 15% increase   (d) 35% decrease
Answer: (b) 30% increase
Solution: Take income = 100. Old: spend 80, save 20. New: income 110, spend 84, save 26. Change = 6/20 × 100 = 30%.

Example 28. A 25% fall in the price of rice lets a person buy 2 kg more for ₹240. What was the original price per kg?
(a) ₹40   (b) ₹50   (c) ₹42   (d) ₹30
Answer: (a) ₹40
Solution: Money saved = 25% of 240 = 60, which buys 2 kg → reduced price = ₹30/kg. Original = 30 × 100/75 = ₹40.

Example 29. A 20% fall in the price of rice lets a person buy 4 kg more for ₹600. What was the original price per kg?
(a) ₹30   (b) ₹39.5   (c) ₹45   (d) ₹37.5
Answer: (d) ₹37.5
Solution: Money saved = 20% of 600 = 120, which buys 4 kg → reduced price = ₹30/kg. Original = 30 × 100/80 = ₹37.5.

Example 30. Two numbers are less than a third number by 30% and 37% respectively. By what percent is the second number less than the first?
(a) 12%   (b) 10%   (c) 11.11%   (d) 7%
Answer: (b) 10%
Solution: Third = 100 → first = 70, second = 63. Less by 7/70 × 100 = 10%.

Example 31. A boy read 1/3 of a book on one day and 1/4 of the remaining pages on the next day. If 45 pages are still unread, how many pages does the book have?
(a) 135   (b) 90   (c) 108   (d) 45
Answer: (b) 90
Solution: Unread fraction = (1 − 1/3) × (1 − 1/4) = 1/2. Pages = 45 ÷ 1/2 = 90. The second fraction is of the remainder, not of the whole book.

Example 32. A boy read 1/3 of a book on one day and 1/4 of the remaining pages on the next day. If 60 pages are still unread, how many pages does the book have?
(a) 60   (b) 144   (c) 120   (d) 180
Answer: (c) 120
Solution: Unread fraction = (1 − 1/3) × (1 − 1/4) = 1/2. Pages = 60 ÷ 1/2 = 120. The second fraction is of the remainder, not of the whole book.

Example 33. Two students appeared in an exam. One scored 9 marks more than the other, and his marks were 56% of the sum of their marks. What were their marks?
(a) 33 and 24   (b) 45 and 36   (c) 66 and 57   (d) 42 and 33
Answer: (d) 42 and 33
Solution: Let the lower score be x. x + 9 = 56% of (2x + 9) → x = 33. Scores: 42 and 33. (Asked in OPSC ASO 2025.)

Example 34. Two students appeared in an exam. One scored 18 marks more than the other, and his marks were 56% of the sum of their marks. What were their marks?
(a) 84 and 66   (b) 87 and 69   (c) 66 and 48   (d) 132 and 114
Answer: (a) 84 and 66
Solution: Let the lower score be x. x + 18 = 56% of (2x + 18) → x = 66. Scores: 84 and 66. (Asked in OPSC ASO 2025.)

Example 35. A crate has 1 bruised mango for every 40 mangoes. 1 out of every 2 bruised mangoes cannot be sold. If there are 6 unsaleable mangoes, how many mangoes are in the crate?
(a) 240   (b) 520   (c) 960   (d) 480
Answer: (d) 480
Solution: Bruised = 6 × 2/1 = 12. Total = 12 × 40 = 480. (Same type as OPSC ASO 2025.)

Example 36. The sum of two numbers is 3,000. If 6.5% of one number equals 8.5% of the other, the numbers are:
(a) 1,700 and 1,300   (b) 1,320 and 1,680   (c) 1,530 and 1,470   (d) 1,800 and 1,200
Answer: (a) 1,700 and 1,300
Solution: 6.5% of A = 8.5% of B → A : B = 8.5 : 6.5. A = 3,000 × 8.5/15 = 1,700, B = 1,300.

Advanced level

Example 37. Fresh grapes contain 90% water and dry grapes contain 20% water. How much fresh grapes are needed to get 100 kg of dry grapes?
(a) 200 kg   (b) 400 kg   (c) 190 kg   (d) 800 kg
Answer: (d) 800 kg
Solution: The solid part does not change. Dry solid = 80% of 100 = 80 kg = 10% of fresh. Fresh = 800 kg.

Example 38. Fresh cherries contain 99% water. After drying in the sun, the water becomes 96%. What is the new weight of 1 kg of cherries?
(a) 276 g   (b) 500 g   (c) 970 g   (d) 250 g
Answer: (d) 250 g
Solution: Solid = 1% of 1000 g = 10 g = 4% of new weight → new weight = 250 g. A small change in water % causes a big weight loss.

Example 39. 5% of A's income equals 15% of B's income, and 10% of B's income equals 20% of C's income. If C's income is ₹12,000, A's income is:
(a) ₹84,000   (b) ₹36,000   (c) ₹24,000   (d) ₹72,000
Answer: (d) ₹72,000
Solution: B = 20/10 × 12,000 = 24,000. A = 15/5 × 24,000 = ₹72,000.

Example 40. A number is increased by 50% and then again by 50%. By what percent must the result be reduced to get back the original number?
(a) 50%   (b) 59.56%   (c) 55.56%   (d) 100%
Answer: (c) 55.56%
Solution: After two increases: 100 → 225. Reduce by 125/225 × 100 = 55.56%.

Example 41. A number is increased by 25% and then again by 25%. By what percent must the result be reduced to get back the original number?
(a) 36%   (b) 33.33%   (c) 40%   (d) 50%
Answer: (a) 36%
Solution: After two increases: 100 → 156.25. Reduce by 56.25/156.25 × 100 = 36%.

Example 42. In a school, 40% of the students were boys. Next year the number of boys rose by 10% and the number of girls fell by 10%. What percent of the students are boys now?
(a) 41.9%   (b) 50%   (c) 44.9%   (d) 40%
Answer: (c) 44.9%
Solution: Take 100 students: boys 40 → 44, girls 60 → 54. Boys % = 44/98 × 100 = 44.9%.

Example 43. A school has 5,000 students. Its strength rises by 20% in the first year, falls by 10% in the second and rises by 20% in the third. What is its strength after 3 years?
(a) 6,500   (b) 6,804   (c) 6,450   (d) 6,480
Answer: (d) 6,480
Solution: 5,000 × 120/100 × 90/100 × 120/100 = 6,480.

Example 44. A tax is increased by 25% and consumption of the item falls by 20%. The revenue from the tax:
(a) decreases by 1%   (b) increases by 0%   (c) does not change   (d) decreases by 2%
Answer: (c) does not change
Solution: Revenue = rate × consumption. Change = 25 − 20 − (25×20)/100 = 0%.

Topic-wise practice for Percentage (Quant): Successive change, price-consumption, income-saving, exam pass/fail, election, population. Useful for OPSC ASO, OSSC, OSSSC and other Odisha exams.

Question types covered

• Basic percentage of a number
• x is what per cent of y; A is x% more or less than B
• Successive percentage change and net change
• Effect on area and volume
• Price-consumption-expenditure
• Income, expenditure and savings
• Exam pass and fail marks
• Election votes and invalid votes
• Population growth and depreciation
• Venn diagram based percentage
• Commission and simple tax