Class 8 Mathematics – NCERT (Ganita Prakash) Part 2 Chapter 1: FRACTIONS IN DISGUISE
Complete Question Bank
πΉ SECTION A: Multiple Choice Questions (20 Questions)
1. 75% expressed as a fraction is:
(a) \(\frac{3}{4}\)
(b) \(\frac{7}{5}\)
(c) \(\frac{4}{3}\)
(d) \(\frac{1}{4}\)
(Conceptual Understanding)
2. If 20% of a number is 30, the number is:
(a) 150
(b) 120
(c) 180
(d) 60
(Problem Solving)
3. A discount of 25% on ₹400 means the discount amount is:
(a) ₹25
(b) ₹100
(c) ₹300
(d) ₹375
(Financial Literacy)
4. If the price of a book increases from ₹80 to ₹100, the percentage increase is:
(a) 20%
(b) 25%
(c) 30%
(d) 40%
(Numeracy)
5. 200% of 50 is:
(a) 50
(b) 100
(c) 150
(d) 200
(Basic Computation)
6. \(\frac{2}{5}\) as a percentage is:
(a) 20%
(b) 40%
(c) 60%
(d) 80%
(Conceptual Understanding)
7. If 10% of x = 15, then 30% of x is:
(a) 15
(b) 30
(c) 45
(d) 60
(Logical Reasoning)
8. A shopkeeper sells an item at a profit of 20% on CP. If CP = ₹250, SP is:
(a) ₹270
(b) ₹300
(c) ₹350
(d) ₹200
(Problem Solving)
9. In a class of 40, 60% are girls. Number of boys is:
(a) 16
(b) 24
(c) 32
(d) 20
(Analytical Thinking)
10. Simple Interest on ₹2000 at 5% p.a. for 2 years is:
(a) ₹100
(b) ₹200
(c) ₹250
(d) ₹300
(Numeracy)
11. If 40% of a number is 120, then the number is:
(a) 300
(b) 240
(c) 360
(d) 480
(Problem Solving)
12. Which is greater: 30% of 200 or 40% of 150?
(a) 30% of 200
(b) 40% of 150
(c) Both equal
(d) Cannot compare
(Analytical Thinking)
13. A number increased by 20% gives 180. The original number is:
(a) 150
(b) 160
(c) 140
(d) 200
(Logical Reasoning)
14. 5% of 2 hours (in minutes) is:
(a) 5 minutes
(b) 6 minutes
(c) 8 minutes
(d) 10 minutes
(Real-Life Application)
15. If 25% of students in a school are absent and 450 are present, total students:
(a) 600
(b) 500
(c) 750
(d) 800
(Problem Solving)
16. Compound Interest on ₹1000 at 10% p.a. for 2 years:
(a) ₹100
(b) ₹210
(c) ₹200
(d) ₹1210
(Financial Literacy)
17. A TV bought for ₹15,000 depreciates by 10% in one year. Its value after 1 year:
(a) ₹13,500
(b) ₹13,000
(c) ₹14,000
(d) ₹12,500
(Real-Life Application)
18. If \(\frac{a}{b} = \frac{3}{4}\), then what % of a is b?
(a) 75%
(b) 133.33%
(c) 120%
(d) 80%
(Analytical Thinking)
19. In a mixture of milk and water, milk is 70%. In 50 litres, milk is:
(a) 30 litres
(b) 35 litres
(c) 40 litres
(d) 45 litres
(Spatial Understanding)
20. Successive discounts of 20% and 10% are equivalent to a single discount of:
(a) 28%
(b) 30%
(c) 25%
(d) 32%
(Logical Reasoning)
πΉ SECTION B: Assertion & Reasoning (20 Questions)
21. Assertion (A): 50% of a quantity is the same as half of that quantity.
Reason (R): 50% = \(\frac{50}{100} = \frac{1}{2}\).
(a) Both A and R are true and R explains A.
(b) Both A and R are true but R does not explain A.
(c) A is true but R is false.
(d) A is false but R is true.
(Conceptual Understanding)
22. Assertion (A): Percentages greater than 100% are meaningless.
Reason (R): Percentage is always out of 100, so cannot exceed 100.
(a) Both A and R are true and R explains A.
(b) Both A and R are true but R does not explain A.
(c) A is false, R is true.
(d) Both are false.
(Logical Reasoning)
23. Assertion (A): If 20% of x = 30, then x = 150.
Reason (R): 20% = \(\frac{1}{5}\), so x = 30 × 5 = 150.
(a) Both true and R explains A.
(b) Both true but R does not explain A.
(c) A true, R false.
(d) Both false.
(Analytical Thinking)
24. Assertion (A): Profit % is always calculated on Cost Price.
Reason (R): Profit = SP – CP.
(a) Both true and R explains A.
(b) Both true but R does not explain A.
(c) A true, R false.
(d) A false, R true.
(Financial Literacy)
25. Assertion (A): Simple interest for 2 years is double that of 1 year for same rate.
Reason (R): Simple interest is directly proportional to time.
(a) Both true and R explains A.
(b) Both true but R does not explain A.
(c) A true, R false.
(d) A false, R true.
(Logical Reasoning)
26. Assertion (A): A discount of 50% followed by another 50% is the same as 100% discount.
Reason (R): Percentages are additive.
(a) Both A and R are true and R explains A.
(b) Both A and R are true but R does not explain A.
(c) A is false, R is true.
(d) Both are false.
(Problem Solving)
27. Assertion (A): If length increases by 10% and breadth decreases by 10%, area remains same.
Reason (R): Area = length × breadth.
(a) Both A and R are true and R explains A.
(b) Both A and R are true but R does not explain A.
(c) A is false, R is true.
(d) Both are false.
(Spatial Understanding)
28. Assertion (A): 1% of 1 day = 14.4 minutes.
Reason (R): 1 day = 1440 minutes.
(a) Both true and R explains A.
(b) Both true but R does not explain A.
(c) A true, R false.
(d) Both false.
(Real-Life Application)
29. Assertion (A): Compound Interest is always greater than Simple Interest for the same rate and time (>1 year).
Reason (R): In CI, interest is calculated on increasing principal each year.
(a) Both true and R explains A.
(b) Both true but R does not explain A.
(c) A true, R false.
(d) A false, R true.
(Financial Literacy)
30. Assertion (A): If CP = SP, then profit % = 0%.
Reason (R): Profit % = \(\frac{SP-CP}{CP} × 100\).
(a) Both true and R explains A.
(b) Both true but R does not explain A.
(c) A true, R false.
(d) Both false.
(Analytical Thinking)
31. Assertion (A): 30% of 50 = 50% of 30.
Reason (R): \(x\% \text{ of } y = y\% \text{ of } x\).
(a) Both true and R explains A.
(b) Both true but R does not explain A.
(c) A true, R false.
(d) Both false.
(Logical Reasoning)
32. Assertion (A): To compare two ratios, converting them to percentages is helpful.
Reason (R): Percentages have a common denominator of 100.
(a) Both true and R explains A.
(b) Both true but R does not explain A.
(c) A true, R false.
(d) A false, R true.
(Conceptual Understanding)
33. Assertion (A): Depreciation means value decreases by a fixed percentage each year.
Reason (R): Depreciation is the opposite of compound interest.
(a) Both true and R explains A.
(b) Both true but R does not explain A.
(c) A true, R false.
(d) Both false.
(Financial Literacy)
34. Assertion (A): If population increases by 10% each year, it doubles in 7 years.
Reason (R): Compound growth formula is \(A = P(1+r)^t\).
(a) Both true and R explains A.
(b) Both true but R does not explain A.
(c) A is false, R is true.
(d) Both false.
(Analytical Thinking)
35. Assertion (A): GST is always calculated on the selling price.
Reason (R): GST is an indirect tax added to the cost of goods.
(a) Both true and R explains A.
(b) Both true but R does not explain A.
(c) A true, R false.
(d) A false, R true.
(Financial Literacy)
36. Assertion (A): 0.5 = 5%.
Reason (R): To convert decimal to percentage, multiply by 100.
(a) Both true and R explains A.
(b) Both true but R does not explain A.
(c) A is false, R is true.
(d) Both false.
(Numeracy)
37. Assertion (A): If an item is sold at a loss of 20%, then SP = 80% of CP.
Reason (R): Loss % = \(\frac{CP-SP}{CP} × 100\).
(a) Both true and R explains A.
(b) Both true but R does not explain A.
(c) A true, R false.
(d) A false, R true.
(Problem Solving)
38. Assertion (A): In a pie chart, each sector's angle is proportional to its percentage.
Reason (R): Total angle in a circle is 360°.
(a) Both true and R explains A.
(b) Both true but R does not explain A.
(c) A true, R false.
(d) Both false.
(Spatial Understanding)
39. Assertion (A): If 30% of a number is added to itself, the result is 130% of the number.
Reason (R): Adding 30% means multiplying by 1.30.
(a) Both true and R explains A.
(b) Both true but R does not explain A.
(c) A true, R false.
(d) Both false.
(Logical Reasoning)
40. Assertion (A): 10% of ₹500 is equal to 50% of ₹100.
Reason (R): Both equal ₹50.
(a) Both true and R explains A.
(b) Both true but R does not explain A.
(c) A true, R false.
(d) Both false.
(Analytical Thinking)
πΉ SECTION C: True/False (10 Questions)
41. 3/4 = 75%. (True) (Conceptual Understanding)
42. 200% of 60 is 120. (True) (Basic Computation)
43. If CP = ₹100, SP = ₹120, then profit % = 20%. (True) (Financial Literacy)
44. 10% of 1 hour = 6 minutes. (True) (Real-Life Application)
45. Discount is calculated on Marked Price. (True) (Conceptual Understanding)
46. Simple interest for 3 years at 10% p.a. on ₹1000 is ₹400. (False) (Numeracy)
47. If a number is increased by 20% and then decreased by 20%, it returns to original. (False) (Logical Reasoning)
48. 0.05 = 5%. (True) (Numeracy)
49. If milk is 40% of a mixture, water is 60%. (True) (Spatial Understanding)
50. Compound interest is always less than simple interest. (False) (Financial Literacy)
πΉ SECTION D: Short Answer I (2 Marks – 15 Questions)
51. Convert 5/8 into percentage. (Numeracy)
52. Find 40% of 250 km. (Problem Solving)
53. If 35% of students in a class are girls and there are 65 girls, find total students. (Logical Reasoning)
54. A shirt marked ₹800 is sold at ₹680. Find discount percentage. (Financial Literacy)
55. A number decreased by 15% becomes 340. Find the number. (Analytical Thinking)
56. Express 0.125 as a percentage. (Numeracy)
57. Find 12.5% of 64. (Basic Computation)
58. If 30% of x is 45, find x. (Problem Solving)
59. In a test, Ravi scored 42 out of 50. Find his percentage. (Real-Life Application)
60. A cycle bought for ₹2000 is sold at a loss of 15%. Find selling price. (Financial Literacy)
61. What percent of 80 is 20? (Analytical Thinking)
62. Increase ₹500 by 20%. (Numeracy)
63. Decrease 150 by 30%. (Basic Computation)
64. If 20% of a number is 60, what is 40% of the same number? (Logical Reasoning)
65. Convert 33⅓% into fraction. (Conceptual Understanding)
πΉ SECTION E: Short Answer II (3 Marks – 10 Questions)
66. In a school, 45% of students are boys. If there are 440 girls, find total students and number of boys. (Problem Solving)
67. The price of sugar increases from ₹40/kg to ₹50/kg. Find percentage increase. (Real-Life Application)
68. A car’s value depreciates by 12% each year. If purchased for ₹6,00,000, find its value after 1 year. (Financial Literacy)
69. If 20% of (x + 50) = 30, find x. (Algebraic Thinking)
70. A mixture contains milk and water in ratio 3:2. Find percentage of milk. (Spatial Understanding)
71. A man saves 30% of his monthly income of ₹25,000. How much does he spend? (Real-Life Application)
72. Find simple interest on ₹5000 at 8% p.a. for 3 years. Also find amount. (Numeracy)
73. In an election, candidate A got 48% votes and lost by 1600 votes. Find total votes. (Logical Reasoning)
74. A number is first increased by 25% and then decreased by 20%. Find net percentage change. (Analytical Thinking)
75. If selling price of 10 articles = cost price of 12 articles, find profit %. (Financial Literacy)
πΉ SECTION F: Long Answer (5 Marks – 10 Questions)
76. A shopkeeper buys 80 articles for ₹2400. He sells 25% at a profit of 10% and the rest at a profit of 20%. Find total selling price and overall profit %. (Problem Solving & Financial Literacy)
77. The population of a town increases by 5% annually. If present population is 84,000, find population after 2 years. Also find population 2 years ago. (Logical Reasoning & Real-Life Application)
78. By selling a book for ₹225, a shopkeeper loses 10%. At what price should he sell to gain 15%? (Analytical Thinking)
79. A sum of money doubles itself in 5 years at simple interest. Find rate % p.a. (Financial Literacy)
80. In an election, candidate A got 55% votes and won by 6000 votes. Find total votes polled. (Logical Reasoning)
81. A trader marks his goods 30% above CP and gives 10% discount. Find his profit %. (Problem Solving)
82. Compound interest on a certain sum for 2 years at 10% p.a. is ₹420. Find the sum. (Analytical Thinking)
83. The length of a rectangle is increased by 20% and breadth decreased by 10%. Find net % change in area. (Spatial Understanding)
84. A milkman mixes water equal to 20% of milk. Find percentage of milk in the mixture. (Problem Solving)
85. If 20% of A = 30% of B = 40% of C, find A:B:C. (Algebraic Thinking)
πΉ SECTION G: Case-Based Questions (5 Cases × 4 Sub-Questions)
CASE 1: Discount Festival
A shop offers successive discounts: 20% + 10% + 5% on marked price of ₹2000.
(i) Price after first discount:
(a) ₹1600
(b) ₹1800
(c) ₹1500
(d) ₹1400
(ii) Price after second discount:
(a) ₹1440
(b) ₹1620
(c) ₹1520
(d) ₹1360
(iii) Final selling price:
(a) ₹1368
(b) ₹1450
(c) ₹1300
(d) ₹1400
(iv) Single equivalent discount %:
(a) 31.6%
(b) 35%
(c) 30%
(d) 32.4%
(Competency: Problem Solving, Financial Literacy)
CASE 2: Bank Interest
Riya deposits ₹10,000 in a bank at 8% p.a. for 3 years.
(i) Simple interest earned:
(a) ₹2400
(b) ₹1800
(c) ₹2000
(d) ₹2200
(ii) Amount after 3 years under simple interest:
(a) ₹12,400
(b) ₹12,000
(c) ₹12,800
(d) ₹11,600
(iii) Compound interest for 3 years:
(a) ₹2597.12
(b) ₹2400
(c) ₹2800
(d) ₹3000
(iv) Difference between CI and SI:
(a) ₹197.12
(b) ₹200
(c) ₹250
(d) ₹300
(Competency: Financial Literacy, Analytical Thinking)
CASE 3: Population Change
The population of a city was 5,00,000 in 2020. It increased by 10% in 2021, decreased by 5% in 2022, and increased by 8% in 2023.
(i) Population in 2021:
(a) 5,50,000
(b) 5,25,000
(c) 5,75,000
(d) 5,10,000
(ii) Population in 2022:
(a) 5,22,500
(b) 5,47,500
(c) 5,37,500
(d) 5,40,000
(iii) Population in 2023:
(a) 5,80,600
(b) 5,85,000
(c) 5,90,200
(d) 5,70,500
(iv) Overall percentage increase from 2020 to 2023:
(a) 13%
(b) 14.2%
(c) 12.5%
(d) 15.8%
(Competency: Logical Reasoning, Real-Life Application)
CASE 4: Exam Scores Comparison
Three students scored as follows in two subjects:
| Student | Math (out of 80) | Science (out of 100) |
||||
| A | 64 | 85 |
| B | 72 | 90 |
| C | 56 | 75 |
(i) Percentage of A in Math:
(a) 80%
(b) 75%
(c) 70%
(d) 85%
(ii) Percentage of B in Science:
(a) 85%
(b) 90%
(c) 92%
(d) 88%
(iii) Who performed better overall (average of two subjects by percentage)?
(a) A
(b) B
(c) C
(d) B and C tied
(iv) If to qualify, a student needs 70% in each subject, who qualified?
(a) Only A
(b) Only B
(c) B and C
(d) A and B
(Competency: Analytical Thinking, Problem Solving)
CASE 5: Profit-Loss Scenario
Kishan buys 50 shirts at ₹300 each. He sells 30 at ₹400 each and the remaining at ₹250 each.
(i) Total Cost Price:
(a) ₹15,000
(b) ₹12,000
(c) ₹18,000
(d) ₹20,000
(ii) Total Selling Price:
(a) ₹16,500
(b) ₹17,000
(c) ₹18,500
(d) ₹19,000
(iii) Overall profit/loss amount:
(a) ₹1500 profit
(b) ₹1500 loss
(c) ₹2000 profit
(d) ₹2000 loss
(iv) Overall profit/loss percentage:
(a) 10% profit
(b) 10% loss
(c) 8% profit
(d) 8% loss
(Competency: Financial Literacy, Problem Solving)
COMPETENCIES COVERED
Logical Reasoning
Problem Solving
Numerical Ability
Financial Literacy
Analytical Thinking
Spatial Understanding
Real-Life Application
Conceptual Understanding
Algebraic Thinking
Data Interpretation
