Q26. A merchant sells an article at Rs. 468 and gains 17½% . Find the cost price.
Formula → C.P. = (100 × S.P.) / (100 + Gain%)
Substitution → (100 × 468) / (100 + 35/2)
Calculation → 46800 / (235/2) = 46800 × 2 / 235 = 93600 / 235 = 398.297... ≈ Rs. 398.30
Final Answer → Rs. 398.30 (≈)
Q27. If C.P. = Rs. 250 and profit is 12½%, find S.P.
Formula → S.P. = C.P. × (100 + Profit%) / 100
Substitution → 250 × (100 + 25/2) / 100
Calculation → 250 × 225/2 ÷ 100 = 250 × 225 / 200 = 250 × 9/8 = 281.25
Final Answer → Rs. 281.25
Q28. An article marked at Rs. 600 is sold at 20% discount. If CP = Rs. 400, find gain or loss %.
Formula → SP = MP × (1 − Discount%) ; Gain% = (SP − CP) / CP × 100
Substitution → SP = 600 × (1 − 1/5) = 600 × 4/5 = 480
Calculation → (480 − 400)/400 ×100 = 80/400 ×100 = 20
Final Answer → 20% profit
Q29. A shopkeeper mixes two varieties of sugar bought at Rs. 20/kg and Rs. 30/kg in equal quantity and sells at Rs. 30/kg. Find profit %.
Formula → Average C.P. = (20 + 30) / 2 ; Profit% = (SP − Avg C.P.) / Avg C.P. ×100
Substitution → Avg C.P. = 50/2 = 25 ; Profit% = (30 − 25)/25 ×100
Calculation → 5/25 ×100 = 20
Final Answer → 20% profit
Q30. An article marked at Rs. 1800 was sold at two successive discounts of 10% and 5%. Find the final selling price.
Formula → SP = MP × (1 − d1) × (1 − d2)
Substitution → SP = 1800 × 9/10 × 19/20
Calculation → 1800 × 171 / 200 = (1800/200) ×171 = 9 × 171 = 1539
Final Answer → Rs. 1,539
Q31. If an article is sold at Rs. 1,980 the seller gains 10%. Find the cost price.
Formula → C.P. = (100 × S.P.) / (100 + Gain%)
Substitution → (100 × 1980) / 110
Calculation → 198000 / 110 = 1800
Final Answer → Rs. 1,800
Q32. A trader allows 5% discount on MP and still gains 10% on CP. If CP = Rs. 800, find MP.
Formula → SP = CP × (1 + Gain%) ; SP = MP × (1 − Discount%) → MP = SP / (1 − d)
Substitution → SP = 800 × 11/10 = 880 ; MP = 880 ÷ 95/100 = 880 × 100/95 = 880 × 20/19
Calculation → 880 × 20 / 19 = 17600 / 19 = 926.315... ≈ Rs. 926.32
Final Answer → Rs. 926.32 (≈)
Q33. A merchant marks his goods 40% above cost and allows 12½% discount. Find profit%.
Formula → MP = 1.40 CP ; SP = MP × (1 − 1/8) = MP × 7/8 ; Profit% = (SP − CP)/CP ×100
Substitution → SP = 1.40 CP × 7/8 = CP × (140/100 × 7/8) = CP × (980/800) = CP × 49/40
Calculation → Profit% = (49/40 −1) ×100 = (9/40)×100 = 22.5
Final Answer → 22.5% profit
Q34. An article bought for Rs. 750 is sold at Rs. 825. Find gain %.
Formula → Profit% = (SP − CP) / CP × 100
Substitution → (825 − 750)/750 × 100
Calculation → 75 / 750 ×100 = 10
Final Answer → 10% profit
Q35. A shopkeeper gives a flat discount of Rs. 40 on an article of marked price Rs. 800. If C.P. = Rs. 600, find profit or loss %.
Formula → SP = MP − Flat discount ; Profit% = (SP−CP)/CP×100
Substitution → SP = 800 − 40 = 760 ; Profit% = (760 − 600)/600 ×100
Calculation → 160 / 600 ×100 = 26 2/3
Final Answer → 26 2/3% profit
Q36. Two articles cost Rs. 400 and Rs. 600. They are sold at Rs. 480 and Rs. 660 respectively. Find overall profit %.
Formula → Total CP = 400 + 600 ; Total SP = 480 + 660 ; Overall profit% = (Total SP − Total CP)/Total CP ×100
Substitution → Total CP = 1000 ; Total SP = 1140 ; Profit = 140
Calculation → 140 / 1000 ×100 = 14
Final Answer → 14% profit
Q37. A shopkeeper sells an item at 20% profit on C.P., but uses a weight of 900 g instead of 1 kg. Find overall gain %.
Formula → Effective gain = [(1 + profit%) ÷ (true fraction sold)] − 1 ; then ×100
Substitution → (1 + 1/5) ÷ (9/10) −1 = (6/5) ÷ (9/10) −1 = (6/5 × 10/9) −1 = (60/45) −1 = 4/3 −1 = 1/3
Calculation → 1/3 ×100 = 33 1/3
Final Answer → 33 1/3% gain
Q38. An article marked Rs. 1600 is sold at two discounts 12% and 8%. Find final selling price.
Formula → SP = MP × (1 − d1) × (1 − d2)
Substitution → SP = 1600 × 88/100 × 92/100 = 1600 × 22/25 × 23/25
Calculation → 1600 × 506 / 625 = (1600/625) × 506 = 2.56 × 506 = 1295.36
Final Answer → Rs. 1,295.36 (≈)
Q39. Cost price of 3 items is Rs. 450. Two are sold at profit 20% and one at loss 10%. Find net gain or loss %.
Formula → Work with total CP and total SP.
Substitution → CP_total = 450. Let each item CP = 150. SP1 = 150 × 6/5 = 180 ; SP2 = 180 ; SP3 = 150 × 9/10 = 135
Calculation → Total SP = 180 + 180 + 135 = 495 ; Profit = 45 ; Profit% = 45/450 ×100 = 10
Final Answer → 10% profit
Q40. A seller gains 25% on an item. What fraction of the S.P. is the profit?
Formula → Profit fraction of SP = Profit / SP = (Gain% × CP)/[CP(1 + Gain%)] = Gain%/(100 + Gain%)
Substitution → (25) / (100 + 25) = 25/125 = 1/5
Calculation → = 1/5 = 0.2
Final Answer → Profit = 1/5 of S.P.
Q41. An article is sold for Rs. 990 at 10% loss. At what price should it be sold to make 10% profit?
Formula → C.P. = (100 × SP_loss) / (100 − Loss%) ; SP_for_profit = C.P. × (1 + Desired%)
Substitution → C.P. = 100 × 990 / 90 = 1100 ; SP_for_10% = 1100 × 11/10 = 1210
Calculation → Rs. 1,210
Final Answer → Rs. 1,210
Q42. A dealer marks up price by 50% and gives 20% discount. Find his profit %.
Formula → MP = 1.50 CP ; SP = MP × 0.80 = 1.50 × 0.80 × CP = 1.20 CP ; Profit% = (1.20 −1)×100
Substitution → Profit% = 0.20 ×100 = 20
Final Answer → 20% profit
Q43. A shopkeeper sells an article at Rs. 1320 after two successive discounts of 10% each on MP. Find MP.
Formula → SP = MP × 0.9 × 0.9 = MP × 81/100
Substitution → MP = SP × 100/81 = 1320 × 100 / 81
Calculation → 1320 × 100 / 81 = 132000 / 81 = 1629.63... ≈ Rs. 1629.63
Final Answer → Rs. 1,629.63 (≈)
Q44. If an article is sold for Rs. 1,400 with 12% discount on MP and CP = Rs. 1,100, find the marked price and profit %.
Formula → SP = MP × 88/100 ; MP = SP × 100/88 ; Profit% = (SP − CP)/CP ×100
Substitution → MP = 1400 × 100 / 88 = 140000 / 88 = 1590.909... ; Profit% = (1400 − 1100)/1100 ×100 = 300/1100 ×100 = 27 3/11%
Calculation → MP ≈ Rs. 1,590.91 ; Profit% ≈ 27.27%
Final Answer → MP ≈ Rs. 1,590.91 ; Profit ≈ 27.27%
Q45. A trader sells two items at Rs. 220 each; one at 10% profit and the other at 10% loss. Find overall profit or loss.
Formula → Use CP = SP/(1 ± rate) ; Total CP = CP1 + CP2 ; Total SP = 440 ; net = SP_total − CP_total
Substitution → CP1 = 220 / 1.10 = 200 ; CP2 = 220 / 0.90 = 244.44... ; Total CP = 444.44...
Calculation → Net = 440 − 444.44... = −4.44... ⇒ Loss ≈ Rs. 4.44 ; Loss% ≈ 4.44/444.44 ×100 ≈ 1%
Final Answer → ≈ 1% loss (≈ Rs. 4.44)
Q46. An item that costs Rs. 750 is sold at Rs. 825. Find profit percent.
Formula → Profit% = (SP−CP)/CP × 100
Substitution → (825 − 750)/750 × 100 = 75/750 ×100
Calculation → = 10
Final Answer → 10% profit
Q47. A shopkeeper offers a customer two successive discounts of 5% and 10% on MP of Rs. 2000. What is final price?
Formula → SP = MP × 95/100 × 90/100
Substitution → 2000 × 19/20 × 9/10 = 2000 × 171/200 = (2000/200)×171 = 10 × 171 = 1710
Calculation → Rs. 1,710
Final Answer → Rs. 1,710
Q48. If the profit on an article is 12% and its S.P. is Rs. 1,120, what is C.P.?
Formula → C.P. = (100 × S.P.) / (100 + Profit%)
Substitution → (100 × 1120)/112 = 112000 / 112 = 1000
Calculation → Rs. 1,000
Final Answer → Rs. 1,000
Q49. An article sold at 8% loss fetched Rs. 460. What should be the selling price to get 12% profit?
Formula → C.P. = (100 × SP_loss) / (100 − Loss%) ; Desired SP = C.P. × (1 + 12/100)
Substitution → C.P. = 100 × 460 / 92 = 500 ; Desired SP = 500 × 112 / 100 = 560
Calculation → Rs. 560
Final Answer → Rs. 560
Q50. A retailer buys at Rs. 360 and marks price 25% above cost. During sale, he allows 20% discount. Find profit %.
Formula → MP = 1.25 CP ; SP = MP × 0.80 ; Profit% = (SP − CP)/CP ×100
Substitution → MP = 360 × 5/4 = 450 ; SP = 450 × 4/5 = 360
Calculation → SP = CP ⇒ Profit = 0%
Final Answer → 0% (break-even)
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