Percentage: Detailed Notes, Examples, and Practice Questions

 

Percentage: Detailed Notes, Examples, and Practice Questions

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1. Percentage Calculations

A. What is a Percentage?

• A percentage is a way of expressing a number as a fraction of 100. It is denoted using the symbol “%”.

• Formula:

  $$\text{Percentage}=\left(\frac{\text{Part}}{\text{Whole}}\right)\times 100$$

• Example:
  If there are 10 girls in a class of 40 students,

  $$\text{Percentage of girls}=\frac{10}{40}\times 100=25\mathrm{\%}$$

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B. Calculating Percentage of a Number

• To find $P\mathrm{\%}$ of a number $X$:

  $$P\mathrm{\%}\times X=\frac{P}{100}\times X$$

• Example:
  What is 10% of 80?

  $$10\mathrm{\%}\times 80=\frac{10}{100}\times 80=8$$

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C. Calculating the Whole from a Percentage

• If you know the part and the percentage,

  $$\text{Whole}=\frac{\text{Part}}{\text{Percentage}\mathrm{/}100}$$

• Example:
  If 30% of a number is 120, what is the number?

  $$\text{Number}=\frac{120}{0.3}=400$$

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D. Finding What Percent One Number Is of Another

• $$\text{Percent}=\left(\frac{\text{Part}}{\text{Whole}}\right)\times 100$$

• Example:
  What percent of 80 is 56?

  $$\frac{56}{80}\times 100=70\mathrm{\%}$$

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2. Percentage Increase and Decrease

A. Percentage Increase

• $$\mathrm{\%}\text{ Increase}=\frac{\text{New Number}-\text{Original Number}}{\text{Original Number}}\times 100$$

• Example:
  Salary increases from $70,000 to $73,500.
  Increase = $3,500.

  $$\frac{3,500}{70,000}\times 100=5\mathrm{\%}$$

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B. Percentage Decrease

• $$\mathrm{\%}\text{ Decrease}=\frac{\text{Original Number}-\text{New Number}}{\text{Original Number}}\times 100$$

• Example:
  Price drops from $90 to $87.3.
  Decrease = $2.7.

  $$\frac{2.7}{90}\times 100=3\mathrm{\%}$$

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3. Applications in Profit & Loss, Data Interpretation (DI)

A. Profit and Loss

• Profit %:

  $$\frac{\text{Profit}}{\text{Cost Price}}\times 100$$

• Loss %:

  $$\frac{\text{Loss}}{\text{Cost Price}}\times 100$$

• Example:
  If CP = ₹100, SP = ₹120,
  Profit = ₹20,
  Profit % = $\frac{20}{100}\times 100=20\mathrm{\%}$

B. Discount

• Discount %:

  $$\frac{\text{Discount}}{\text{Marked Price}}\times 100$$

• Example:
  Marked Price = ₹200, Discount = ₹40
  Discount % = $\frac{40}{200}\times 100=20\mathrm{\%}$

C. Data Interpretation

• Percentages are used to compare data, find growth rates, and analyze pie charts, bar graphs, and tables.

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4. Examples

Example 1:
What is 15% of 200?

$$\frac{15}{100}\times 200=30$$

Example 2:
A product’s price increases from ₹500 to ₹600. What is the percentage increase?

$$\frac{600-500}{500}\times 100=20\mathrm{\%}$$

Example 3:
If the selling price is ₹150 and the cost price is ₹120, what is the profit percentage?

$$\frac{150-120}{120}\times 100=25\mathrm{\%}$$

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5. Practice Questions (with answers for the first 20)

Questions 1–20 (with answers)

1. What is 25% of 80?
   Ans: 20

2. What percent of 200 is 50?
   Ans: 25%

3. Increase 300 by 10%.
   Ans: 330

4. Decrease 400 by 20%.
   Ans: 320

5. If a product costs ₹500 and is sold for ₹600, what is the profit percentage?
   Ans: 20%

6. If a product costs ₹800 and is sold for ₹600, what is the loss percentage?
   Ans: 25%

7. What is the percentage increase from 40 to 50?
   Ans: 25%

8. What is the percentage decrease from 120 to 90?
   Ans: 25%

9. If 75 is 30% of a number, what is the number?
   Ans: 250

10. If 20% of a number is 18, what is the number?
    Ans: 90

11. A shopkeeper marks an item at ₹250 and sells it at a 20% discount. What is the selling price?
    Ans: ₹200

12. If a student scores 45 out of 60, what percentage did they score?
    Ans: 75%

13. If a population increases from 1,200 to 1,500, what is the percentage increase?
    Ans: 25%

14. If a salary decreases from ₹50,000 to ₹45,000, what is the percentage decrease?
    Ans: 10%

15. What is 12.5% of 320?
    Ans: 40

16. If the cost price is ₹400 and the profit is ₹60, what is the selling price?
    Ans: ₹460

17. If the marked price is ₹500 and the discount is 10%, what is the selling price?
    Ans: ₹450

18. If a student gets 36 out of 48 correct answers, what is the percentage score?
    Ans: 75%

19. A car’s value drops from ₹10,000 to ₹8,000. What is the percentage decrease?
    Ans: 20%

20. If 5% of a number is 25, what is the number?
    Ans: 500

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Questions 21–100 (Practice Only)

21. What is 40% of 150?

22. What percent of 250 is 75?

23. Increase 120 by 15%.

24. Decrease 800 by 25%.

25. If CP = ₹600, SP = ₹750, find profit %.

26. If CP = ₹900, SP = ₹720, find loss %.

27. What is the percentage increase from 80 to 100?

28. What is the percentage decrease from 200 to 160?

29. If 48 is 60% of a number, what is the number?

30. If 15% of a number is 21, what is the number?

31. Marked price = ₹400, discount = 15%. Find SP.

32. If a student scores 32 out of 40, what percent did they score?

33. Population increases from 2,000 to 2,500. Find % increase.

34. Salary decreases from ₹60,000 to ₹54,000. Find % decrease.

35. What is 30% of 270?

36. If CP = ₹350, profit = ₹70, find SP.

37. MP = ₹600, discount = 25%. Find SP.

38. If 27 out of 36 answers are correct, what percent is this?

39. Value drops from ₹18,000 to ₹15,000. Find % decrease.

40. If 8% of a number is 40, what is the number?

41. What is 75% of 240?

42. What percent of 320 is 48?

43. Increase 250 by 20%.

44. Decrease 500 by 12%.

45. If CP = ₹480, SP = ₹600, find profit %.

46. If CP = ₹700, SP = ₹560, find loss %.

47. What is the percentage increase from 150 to 180?

48. What is the percentage decrease from 90 to 72?

49. If 36 is 80% of a number, what is the number?

50. If 25% of a number is 55, what is the number?

51. MP = ₹1,000, discount = 10%. Find SP.

52. If a student scores 54 out of 60, what percent did they score?

53. Population increases from 3,500 to 4,200. Find % increase.

54. Salary decreases from ₹75,000 to ₹67,500. Find % decrease.

55. What is 22% of 400?

56. If CP = ₹1,200, profit = ₹180, find SP.

57. MP = ₹2,000, discount = 20%. Find SP.

58. If 45 out of 50 answers are correct, what percent is this?

59. Value drops from ₹25,000 to ₹20,000. Find % decrease.

60. If 12% of a number is 36, what is the number?

61. What is 60% of 500?

62. What percent of 700 is 210?

63. Increase 400 by 18%.

64. Decrease 900 by 22%.

65. If CP = ₹2,000, SP = ₹2,400, find profit %.

66. If CP = ₹1,500, SP = ₹1,200, find loss %.

67. What is the percentage increase from 60 to 90?

68. What is the percentage decrease from 300 to 255?

69. If 72 is 90% of a number, what is the number?

70. If 40% of a number is 88, what is the number?

71. MP = ₹3,000, discount = 25%. Find SP.

72. If a student scores 90 out of 120, what percent did they score?

73. Population increases from 5,000 to 6,500. Find % increase.

74. Salary decreases from ₹90,000 to ₹81,000. Find % decrease.

75. What is 16% of 350?

76. If CP = ₹2,500, profit = ₹375, find SP.

77. MP = ₹1,200, discount = 15%. Find SP.

78. If 60 out of 75 answers are correct, what percent is this?

79. Value drops from ₹30,000 to ₹24,000. Find % decrease.

80. If 6% of a number is 24, what is the number?

81. What is 33⅓% of 180?

82. What percent of 360 is 54?

83. Increase 720 by 25%.

84. Decrease 1,200 by 10%.

85. If CP = ₹3,000, SP = ₹3,600, find profit %.

86. If CP = ₹2,000, SP = ₹1,500, find loss %.

87. What is the percentage increase from 250 to 300?

88. What is the percentage decrease from 1,000 to 850?

89. If 108 is 90% of a number, what is the number?

90. If 55% of a number is 165, what is the number?

91. MP = ₹2,500, discount = 8%. Find SP.

92. If a student scores 72 out of 80, what percent did they score?

93. Population increases from 8,000 to 10,000. Find % increase.

94. Salary decreases from ₹1,20,000 to ₹1,08,000. Find % decrease.

95. What is 12.5% of 640?

96. If CP = ₹4,000, profit = ₹600, find SP.

97. MP = ₹2,400, discount = 12.5%. Find SP.

98. If 84 out of 105 answers are correct, what percent is this?

99. Value drops from ₹50,000 to ₹40,000. Find % decrease.

100. If 7% of a number is 56, what is the number?

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Practice these questions and master percentage calculations, increase/decrease, and their applications in profit & loss and data interpretation for all competitive exams.