Q51. A man buys a book for Rs. 120 and sells it for Rs. 150. Find profit and profit percent.
Formula: Profit = S.P. − C.P.; Profit% = (Profit ÷ C.P.) × 100
Substitution: S.P. = 150; C.P. = 120 → Profit = 150 − 120 = 30
Calculation: Profit% = (30 ÷ 120) × 100 = 25
Final Answer: Profit = Rs. 30; Profit% = 25%
Q52. A shopkeeper marks an article 20% above cost and gives 10% discount on marked price. Find his gain %.
Formula: MP = 1.20×C.P.; S.P. = MP×(1 − 10/100); Profit% = (S.P. − C.P.)÷C.P.×100
Substitution: S.P. = 1.20C.P. × 9/10 = 1.08C.P.
Calculation: Profit% = (1.08C.P. − 1.00C.P.)÷1.00C.P.×100 = 0.08×100 = 8
Final Answer: 8% profit
Q53. A trader sells an item at Rs. 315 after 10% discount on marked price. If cost price is Rs. 250, find the marked price.
Formula: S.P. = M.P. × (1 − d); M.P. = S.P. ÷ (1 − d)
Substitution: M.P. = 315 ÷ (1 − 10/100) = 315 ÷ 9/10
Calculation: M.P. = 315 × 10/9 = 350
Final Answer: Marked Price = Rs. 350
Q54. An article sold for Rs. 405 gives 10% profit. Find cost price.
Formula: C.P. = (100 ÷ (100 + profit%)) × S.P.
Substitution: C.P. = (100 ÷ 110) × 405
Calculation: C.P. = (100/110)×405 = (10/11)×405 = 4050/11 = 368.1818…
Final Answer: C.P. ≈ Rs. 368.18
Q55. A merchant allows two successive discounts of 20% and 10% on M.P. of Rs. 2000. Find final price.
Formula: S.P. = M.P. × (1 − d1) × (1 − d2)
Substitution: S.P. = 2000 × 4/5 × 9/10
Calculation: S.P. = 2000 × (36/50) = 2000 × 18/25 = (2000/25)×18 = 80×18 = 1440
Final Answer: Rs. 1,440
Q56. If an item is sold at 12% loss for Rs. 440, what would be the selling price to gain 8%?
Formula: C.P. = (100 ÷ (100 − loss%)) × S.P._loss; Desired S.P. = C.P. × (1 + 8/100)
Substitution: C.P. = (100 ÷ 88) × 440 = (25/22)×440 = 25×20 = 500
Calculation: Desired S.P. = 500 × 108/100 = 500 × 27/25 = 540
Final Answer: Rs. 540
Q57. A dealer sells at 5% profit after giving 10% discount on M.P. Find markup% on cost price.
Formula: S.P. = M.P. × 9/10 and S.P. = C.P. × 1.05 ⇒ M.P. = (1.05 ÷ 9/10) × C.P.
Substitution: M.P. = (1.05 × 10/9) × C.P. = (105/90)×C.P. = (7/6)×C.P.
Calculation: Markup% = ((7/6 − 1) × 100) = (1/6)×100 = 16 2/3
Final Answer: 16⅔% markup
Q58. Two items cost Rs. 250 and Rs. 350. They are sold at Rs. 300 and Rs. 410 respectively. Find overall profit %.
Formula: Overall profit% = (Total S.P. − Total C.P.) ÷ Total C.P. × 100
Substitution: Total C.P. = 250 + 350 = 600; Total S.P. = 300 + 410 = 710
Calculation: Profit = 110; Profit% = 110 ÷ 600 ×100 = 11000/600 = 18 1/3
Final Answer: 18⅓% profit
Q59. A shopkeeper claims 25% profit but uses weight 900 g as 1 kg. What is his actual gain %?
Formula: Effective factor = (1 + claimed profit) ÷ (true fraction sold); Gain% = (factor − 1) ×100
Substitution: factor = 1.25 ÷ 0.9 = (5/4) ÷ (9/10) = (5/4)×(10/9) = 50/36 = 25/18
Calculation: Gain% = (25/18 −1)×100 = (7/18)×100 ≈ 38.888... = 38 8/9
Final Answer: ≈ 38⅘? (precisely 38 8/9% gain)
Q60. An article bought at Rs. 720 is sold at 15% profit. Find selling price.
Formula: S.P. = C.P. × (1 + profit%)
Substitution: S.P. = 720 × 115/100 = 720 × 23/20
Calculation: S.P. = (720/20)×23 = 36×23 = 828
Final Answer: Rs. 828
Q61. Two successive discounts of 5% each are given. Find single equivalent discount.
Formula: Equivalent = 1 − (1 − d1)(1 − d2)
Substitution: = 1 − (95/100 × 95/100) = 1 − 9025/10000
Calculation: = 1 − 0.9025 = 0.0975 = 9.75%
Final Answer: 9.75% discount
Q62. If C.P. = Rs. 800 and S.P. = Rs. 920, find profit and profit percent.
Formula: Profit = S.P. − C.P.; Profit% = Profit ÷ C.P. × 100
Substitution: Profit = 920 − 800 = 120
Calculation: Profit% = 120 ÷ 800 ×100 = 15%
Final Answer: Profit = Rs. 120; Profit% = 15%
Q63. M.P. is 40% above cost and article is sold at 30% profit. Find discount% applied (if any).
Formula: MP = 1.40C.P.; SP (for 30%) = 1.30C.P.; Discount% = (1 − SP/MP)×100
Substitution: SP/MP = 1.30/1.40 = 13/14
Calculation: Discount% = (1 − 13/14)×100 = (1/14)×100 = 100/14 = 7 1/7%
Final Answer: 7 1/7% discount
Q64. A trader marks price 25% above cost and gives 12% discount. Find profit%.
Formula: MP = 1.25C.P.; S.P. = MP × 88/100 = 1.25 × 88/100 × C.P.
Substitution: S.P. = 1.25 × 22/25 × C.P. = (1.25×0.88)C.P. = 1.10C.P.
Calculation: Profit% = (1.10 −1)×100 = 10%
Final Answer: 10% profit
Q65. If a seller gives 10% discount and yet gains 20%, what is the markup percent (percentage above cost)?
Formula: SP = 1.20C.P.; SP = M.P. × 0.90 ⇒ M.P. = SP ÷ 0.90
Substitution: M.P. = 1.20C.P. ÷ 9/10 = 1.20 × 10/9 × C.P. = 4/3 × C.P.
Calculation: Markup% = (4/3 −1)×100 = 1/3×100 = 33 1/3%
Final Answer: 33⅓% markup
Q66. A commodity purchased at Rs. 540 is sold in two equal lots; one at 10% profit and the other at 10% loss. Find net result.
Formula: For equal halves, CP_half = 540/2 = 270. SP1 = 270×1.10; SP2 = 270×0.90
Substitution: SP1 = 297; SP2 = 243
Calculation: Total SP = 540; Total CP = 540 ⇒ Net = 0
Final Answer: No profit, no loss (0%)
Q67. A shopkeeper gives flat discount Rs. 60 on MP Rs. 600. If CP = Rs. 450, find profit%.
Formula: S.P. = M.P. − flat_discount; Profit% = (S.P. − C.P.)÷C.P.×100
Substitution: S.P. = 600 − 60 = 540
Calculation: Profit% = (540 − 450)÷450 ×100 = 90/450×100 = 20%
Final Answer: 20% profit
Q68. An article bought at Rs. 400 is sold for Rs. 360. Find loss%.
Formula: Loss% = (C.P. − S.P.)÷C.P.×100
Substitution: Loss = 400 − 360 = 40
Calculation: Loss% = 40 ÷ 400 ×100 = 10%
Final Answer: 10% loss
Q69. If an article is sold for Rs. 825 at 10% gain, what should be its marked price so that after 10% discount seller still gets 10% gain?
Formula: First find C.P.: C.P. = (100 ÷ 110) × 825. Desired S.P. for 10% gain = 1.10×C.P. MP = Desired S.P. ÷ (1 − 10/100)
Substitution: C.P. = (100/110)×825 = 750; Desired S.P. = 1.10×750 = 825; MP = 825 ÷ 9/10
Calculation: MP = 825 × 10/9 = 916.666…
Final Answer: ≈ Rs. 916.67
Q70. A retailer marks goods 50% above cost and sells at 20% discount. Find profit%.
Formula: MP = 1.50C.P.; S.P. = MP × 4/5 = 1.50×4/5×C.P.
Substitution: S.P. = 1.50 × 4/5 × C.P. = 1.20 C.P.
Calculation: Profit% = (1.20 −1)×100 = 20%
Final Answer: 20% profit
Q71. An item is sold at Rs. 770 after successive discounts of 10% and 5% on marked price. Find marked price.
Formula: S.P. = M.P. × 9/10 × 19/20 = M.P. × 171/200 ⇒ M.P. = S.P. × 200/171
Substitution: M.P. = 770 × 200 / 171
Calculation: = 154000 /171 ≈ 900.5848…
Final Answer: ≈ Rs. 900.58
Q72. A trader sells at Rs. 540 making 20% profit after allowing 10% discount on MP. Find MP.
Formula: S.P. = M.P. × 9/10; Also S.P. = C.P. × 1.20; But C.P. =? Use S.P. to find MP.
Substitution: Since S.P. = 540 and S.P. = M.P.×9/10 ⇒ M.P. = 540 ÷ 9/10 = 540 ×10/9 = 600
Calculation: MP = Rs. 600
Final Answer: Rs. 600
Q73. An item bought for Rs. 840 is sold in two parts at Rs. 420 each. Find overall gain or loss%.
Formula: Total C.P. = 840; Total S.P. = 420 + 420 = 840
Substitution: Profit = 840 − 840 = 0
Calculation: Profit% = 0 ÷ 840 ×100 = 0
Final Answer: No profit, no loss (0%)
Q74. A shopkeeper's cost is Rs. 250. He marks price 60% above cost and sells at 15% discount. Find profit%.
Formula: MP = 1.60C.P.; S.P. = MP×85/100 = 1.60×85/100×C.P.
Substitution: S.P. = 1.60 × 17/20 × C.P. = 1.36 C.P.
Calculation: Profit% = (1.36 −1)×100 = 36%
Final Answer: 36% profit
Q75. If the S.P. of an article is Rs. 900 and the seller gains 20%, find the cost price and the marked price if he marks 25% above cost.
Formula: C.P. = S.P. ÷ (1 + gain%); M.P. = C.P. × (1 + markup%)
Substitution: C.P. = 900 ÷ 1.20 = 900 × 5/6 = 750; M.P. = 750 × 125/100 = 750 × 5/4
Calculation: M.P. = 750 × 5/4 = 937.5
Final Answer: C.P. = Rs. 750; M.P. = Rs. 937.50
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