Profit, Loss & Discount: Complete Notes, Formulas, Examples, and Practice Questions

 

Profit, Loss & Discount: Complete Notes, Formulas, Examples, and Practice Questions

1. Key Concepts and Formulas

A. Cost Price (CP), Selling Price (SP), Marked Price (MP)

• Cost Price (CP): The price at which an article is purchased.

• Selling Price (SP): The price at which the article is sold.

• Marked Price (MP): The price marked/tagged on the article (before any discount).

B. Profit and Loss

• Profit (P): When SP > CP
  $\text{Profit}=\text{SP}-\text{CP}$

• Loss (L): When CP > SP
  $\text{Loss}=\text{CP}-\text{SP}$

• Profit Percentage (P%):
  $\text{Profit \%}=\left(\frac{\text{Profit}}{\text{CP}}\right)\times 100$

• Loss Percentage (L%):
  $\text{Loss \%}=\left(\frac{\text{Loss}}{\text{CP}}\right)\times 100$

C. Selling Price and Cost Price Formulas

• SP (when profit % known):
  $\text{SP}=\left(\frac{100+P\mathrm{\%}}{100}\right)\times \text{CP}$

• SP (when loss % known):
  $\text{SP}=\left(\frac{100-L\mathrm{\%}}{100}\right)\times \text{CP}$

• CP (when profit % and SP known):
  $\text{CP}=\left(\frac{100}{100+P\mathrm{\%}}\right)\times \text{SP}$

• CP (when loss % and SP known):
  $\text{CP}=\left(\frac{100}{100-L\mathrm{\%}}\right)\times \text{SP}$

D. Discount

• Discount:
  $\text{Discount}=\text{MP}-\text{SP}$

• Discount Percentage:
  $\text{Discount \%}=\left(\frac{\text{Discount}}{\text{MP}}\right)\times 100$

• SP (after discount):
  $\text{SP}=\text{MP}-\text{Discount}$

E. Successive Discounts

• If two discounts of $x\mathrm{\%}$ and $y\mathrm{\%}$ are given successively,
  Net Discount % = $x+y-\frac{xy}{100}$

F. Successive Profits or Losses

• If two profits of $m\mathrm{\%}$ and $n\mathrm{\%}$ are given successively,
  Net Profit % = $m+n+\frac{mn}{100}$

• If one is profit and one is loss,
  Net % = $m-n-\frac{mn}{100}$

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2. Examples

Example 1:
CP = ₹100, SP = ₹120
Profit = ₹20, Profit % = $\frac{20}{100}\times 100=20\mathrm{\%}$

Example 2:
CP = ₹300, SP = ₹250
Loss = ₹50, Loss % = $\frac{50}{300}\times 100=16.67\mathrm{\%}$

Example 3:
MP = ₹240, Discount = 25%
Discount = ₹60, SP = ₹180

Example 4:
Successive discounts of 20% and 20%
Net discount = 20 + 20 - (20×20)/100 = 36%

Example 5:
If CP of 5 oranges = SP of 4 oranges,
Profit % = $\frac{5-4}{4}\times 100=25\mathrm{\%}$

Example 6:
Jane sells a table for $987 at a 6% loss.
CP = $\frac{100}{94}\times 987=\mathrm{\$}1050$

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3. Practice Questions (with answers for first 20)

Questions 1–20 (with answers)

1. CP = ₹80, SP = ₹100. Find profit and profit percentage.
   Ans: Profit = ₹20, Profit % = 25%

2. CP = ₹250, SP = ₹200. Find loss and loss percentage.
   Ans: Loss = ₹50, Loss % = 20%

3. MP = ₹500, Discount = 10%. Find selling price.
   Ans: SP = ₹450

4. CP = ₹400, Profit % = 15%. Find selling price.
   Ans: SP = ₹460

5. CP = ₹600, Loss % = 20%. Find selling price.
   Ans: SP = ₹480

6. MP = ₹800, Discount % = 25%. Find discount and SP.
   Ans: Discount = ₹200, SP = ₹600

7. CP = ₹120, SP = ₹144. Find profit percentage.
   Ans: 20%

8. SP = ₹180, Loss % = 10%. Find cost price.
   Ans: CP = ₹200

9. MP = ₹1,000, Discount = ₹150. Find discount percentage.
   Ans: 15%

10. CP = ₹500, Profit % = 20%. Find SP.
    Ans: ₹600

11. SP = ₹900, Profit % = 25%. Find CP.
    Ans: ₹720

12. MP = ₹400, Discount = 20%, SP = ?
    Ans: ₹320

13. CP = ₹240, SP = ₹216. Find loss percentage.
    Ans: 10%

14. MP = ₹600, Discount = 10%, SP = ?
    Ans: ₹540

15. CP = ₹150, Loss % = 8%. Find SP.
    Ans: ₹138

16. SP = ₹660, Loss % = 12%. Find CP.
    Ans: ₹750

17. MP = ₹1,200, Discount % = 15%. Find SP.
    Ans: ₹1,020

18. CP = ₹350, Profit % = 30%. Find SP.
    Ans: ₹455

19. MP = ₹2,000, Discount = ₹400. Find SP and discount %.
    Ans: SP = ₹1,600, Discount % = 20%

20. CP = ₹800, SP = ₹880. Find profit percentage.
    Ans: 10%

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Questions 21–100 (Practice Only)

21. CP = ₹90, SP = ₹108. Find profit and profit %.

22. CP = ₹400, SP = ₹340. Find loss and loss %.

23. MP = ₹600, Discount = 20%. Find SP.

24. CP = ₹500, Profit % = 25%. Find SP.

25. CP = ₹750, Loss % = 10%. Find SP.

26. MP = ₹900, Discount % = 30%. Find discount and SP.

27. CP = ₹200, SP = ₹250. Find profit %.

28. SP = ₹360, Loss % = 20%. Find CP.

29. MP = ₹800, Discount = ₹120. Find discount %.

30. CP = ₹350, Profit % = 15%. Find SP.

31. SP = ₹1,200, Profit % = 25%. Find CP.

32. MP = ₹500, Discount = 15%, SP = ?

33. CP = ₹320, SP = ₹288. Find loss %.

34. MP = ₹700, Discount = 10%, SP = ?

35. CP = ₹400, Loss % = 12%. Find SP.

36. SP = ₹528, Loss % = 8%. Find CP.

37. MP = ₹1,500, Discount % = 20%. Find SP.

38. CP = ₹600, Profit % = 20%. Find SP.

39. MP = ₹2,400, Discount = ₹480. Find SP and discount %.

40. CP = ₹900, SP = ₹990. Find profit %.

41. CP = ₹100, SP = ₹120. Find profit %.

42. CP = ₹300, SP = ₹240. Find loss %.

43. MP = ₹1,200, Discount = 20%. Find SP.

44. CP = ₹450, Profit % = 10%. Find SP.

45. CP = ₹500, Loss % = 20%. Find SP.

46. MP = ₹1,000, Discount % = 25%. Find discount and SP.

47. CP = ₹180, SP = ₹216. Find profit %.

48. SP = ₹270, Loss % = 10%. Find CP.

49. MP = ₹2,000, Discount = ₹400. Find discount %.

50. CP = ₹600, Profit % = 30%. Find SP.

51. Successive discounts of 10% and 20% on ₹1,000. Find net discount % and SP.

52. Successive discounts of 15% and 10% on ₹2,000. Find net discount % and SP.

53. Successive discounts of 20% and 5% on ₹500. Find net discount % and SP.

54. Successive profits of 10% and 20% on ₹1,000. Find net profit %.

55. Successive profits of 15% and 10% on ₹2,000. Find net profit %.

56. Successive profits of 20% and 5% on ₹500. Find net profit %.

57. Successive profit 10% and loss 5% on ₹1,000. Find net %.

58. Successive profit 15% and loss 10% on ₹2,000. Find net %.

59. Successive profit 20% and loss 5% on ₹500. Find net %.

60. If CP of 7 apples = SP of 5 apples, find profit %.

61. If CP of 12 pens = SP of 10 pens, find profit %.

62. If CP of 8 books = SP of 6 books, find profit %.

63. If CP of 5 kg rice = SP of 4 kg rice, find profit %.

64. If CP of 9 oranges = SP of 7 oranges, find profit %.

65. If CP of 6 pencils = SP of 5 pencils, find profit %.

66. If CP of 10 chocolates = SP of 8 chocolates, find profit %.

67. If CP of 15 bottles = SP of 12 bottles, find profit %.

68. If CP of 20 apples = SP of 16 apples, find profit %.

69. If CP of 25 pens = SP of 20 pens, find profit %.

70. If CP of 30 books = SP of 24 books, find profit %.

71. A shopkeeper marks a product at ₹1,000 and sells at ₹800. Find discount %.

72. MP = ₹2,000, Discount = ₹400. Find SP and discount %.

73. MP = ₹1,500, Discount = 20%. Find SP.

74. MP = ₹1,200, Discount = 10%. Find SP.

75. MP = ₹2,500, Discount = 25%. Find SP.

76. MP = ₹3,000, Discount = 30%. Find SP.

77. MP = ₹1,800, Discount = 15%. Find SP.

78. MP = ₹2,200, Discount = 20%. Find SP.

79. MP = ₹2,800, Discount = 25%. Find SP.

80. MP = ₹3,500, Discount = 30%. Find SP.

81. A product is sold at 10% profit. If CP = ₹500, find SP.

82. A product is sold at 20% profit. If CP = ₹600, find SP.

83. A product is sold at 30% profit. If CP = ₹700, find SP.

84. A product is sold at 40% profit. If CP = ₹800, find SP.

85. A product is sold at 50% profit. If CP = ₹900, find SP.

86. A product is sold at 10% loss. If CP = ₹1,000, find SP.

87. A product is sold at 20% loss. If CP = ₹1,100, find SP.

88. A product is sold at 30% loss. If CP = ₹1,200, find SP.

89. A product is sold at 40% loss. If CP = ₹1,300, find SP.

90. A product is sold at 50% loss. If CP = ₹1,400, find SP.

91. SP = ₹1,200, Profit % = 20%. Find CP.

92. SP = ₹1,300, Profit % = 30%. Find CP.

93. SP = ₹1,400, Profit % = 40%. Find CP.

94. SP = ₹1,500, Profit % = 50%. Find CP.

95. SP = ₹900, Loss % = 10%. Find CP.

96. SP = ₹800, Loss % = 20%. Find CP.

97. SP = ₹700, Loss % = 30%. Find CP.

98. SP = ₹600, Loss % = 40%. Find CP.

99. SP = ₹500, Loss % = 50%. Find CP.

100. CP = ₹1,000, SP = ₹1,200. Find profit %.

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Use these formulas, tricks, and questions to master profit, loss, and discount for all competitive exams. Practice regularly for speed and accuracy.
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