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Profit & Loss — Extra Practice Bank · Chapter 1

Profit and Loss — Complete Guide

Table of Contents

  1. Introduction to the Topic
  2. Basic Concepts and Terminology
  3. Core Formulas
  4. Type 1: Basic Profit/Loss Calculation
  5. Type 2: Marked Price and Discount
  6. Type 3: Successive Discounts
  7. Type 4: False Weight/Measure Problems
  8. Type 5: Multiple Transactions (Buying/Selling in Bulk, Mixed Profit/Loss)
  9. Type 6: Cost Price/Selling Price Ratio Problems
  10. Common Shortcuts and Tricks
  11. Common Mistakes to Avoid
  12. Solved Examples (25 fully worked problems)
  13. Practice Question Bank (50 questions)
  14. Answer Key with Quick Solutions

1. Introduction to the Topic

Profit and Loss is a percentage-heavy chapter built almost entirely on the relationship between Cost Price (CP), Selling Price (SP), and Marked Price (MP). SSC, RRB, and banking exams typically ask 2-4 questions from this chapter, and mastery here is largely about applying the base formula correctly with the right reference value (CP is always the base for profit/loss %, MP is always the base for discount %).

2. Basic Concepts and Terminology

Cost Price (CP): The price at which an item is purchased/produced.

Selling Price (SP): The price at which an item is sold.

Marked Price (MP) / List Price: The price displayed/labeled on the item, before any discount.

Profit: SP − CP (when SP > CP)

Loss: CP − SP (when CP > SP)

Discount: MP − SP (the reduction offered on the marked price)

3. Core Formulas

Figure: How Cost Price, Selling Price, and Marked Price relate to each other.

Formula 1: Profit % = (Profit/CP) × 100 = [(SP−CP)/CP] × 100

Formula 2: Loss % = (Loss/CP) × 100 = [(CP−SP)/CP] × 100

Formula 3: SP = CP × (100+Profit%)/100 [when there’s a profit] SP = CP × (100−Loss%)/100 [when there’s a loss]

Formula 4: CP = SP × 100/(100+Profit%) [when there’s a profit] CP = SP × 100/(100−Loss%) [when there’s a loss]

Formula 5: Discount % = (Discount/MP) × 100 = [(MP−SP)/MP] × 100

Formula 6: SP = MP × (100−Discount%)/100

Formula 7 (successive discounts): Net discount % = a+b−(ab/100) [for two successive discounts a% and b%] — note this is subtracted, unlike successive profit% which adds the cross term.

Formula 8 (false weight): If a dishonest shopkeeper uses a false weight of x grams instead of the true weight of y grams (claiming to sell y grams but actually giving x grams), while charging for y grams: Profit % = [(y−x)/x] × 100 (when cost price is based on actual weight given)

Formula 9 (equal SP, different profit/loss %): If two items are sold at the same SP, one at a% profit and other at a% loss, there is always a NET LOSS of (a²/100)% on the total transaction (regardless of the actual SP value).

4. Type 1: Basic Profit/Loss Calculation

Pattern: “A man buys an article for ₹800 and sells it for ₹920. Find his profit percentage.” - Profit=120. Profit%=(120/800)×100=15%

Pattern: “An article is sold at a loss of 12%. If it was bought for ₹500, find the selling price.” - SP=500×(100−12)/100=500×0.88=₹440

5. Type 2: Marked Price and Discount

Figure: Discount is subtracted from the Marked Price to get the Selling Price.

Pattern: “A shopkeeper marks an article at ₹1200 and sells it after a discount of 15%. Find the SP.” - SP=1200×0.85=₹1020

Pattern: “An article marked at ₹2000 is sold for ₹1700. Find the discount percentage.” - Discount=300. Discount%=(300/2000)×100=15%

Pattern (finding MP from CP, profit%, and discount%): “A shopkeeper wants to make a profit of 20% after giving a discount of 10%. If the CP is ₹900, find the MP.” - Required SP=900×1.2=1080. MP×0.9=1080 ⇒ MP=1080/0.9=₹1200

6. Type 3: Successive Discounts

Pattern: “Find the single equivalent discount for successive discounts of 20% and 10%.” - Net=20+10−(20×10)/100=30−2=28%

Pattern (three successive discounts): “Find the single equivalent discount for 10%, 10%, and 10% successive discounts.” - First combine 10% and 10%: 10+10−1=19%. Then combine 19% and 10%: 19+10−1.9=27.1%

7. Type 4: False Weight/Measure Problems

Pattern: “A shopkeeper claims to sell rice at cost price but uses a weight of 900g instead of 1kg. Find his profit percentage.” - Profit%=[(1000−900)/900]×100=(100/900)×100=11.11%

8. Type 5: Multiple Transactions (Mixed Profit/Loss)

Pattern: “A man sells two watches for ₹1980 each, one at a profit of 10% and the other at a loss of 10%. Find his overall gain or loss percentage.” - Using the shortcut: net loss=(10²/100)%=1% loss. - Let’s verify: CP1=1980/1.1=1800; CP2=1980/0.9=2200. Total CP=4000. Total SP=3960. Loss=40. Loss%=(40/4000)×100=1% loss ✓ (matches shortcut)

9. Type 6: Cost Price/Selling Price Ratio Problems

Pattern: “If the SP of 15 articles equals the CP of 18 articles, find the profit percentage.” - Let CP of 1 article=1. SP of 15 articles=CP of 18 articles=18. SP of 1 article=18/15=1.2. - Profit%=(1.2−1)/1×100=20%

10. Common Shortcuts and Tricks

  1. Always use CP as the base for profit/loss %, and MP as the base for discount % — mixing these up is the single most common error in this chapter.
  2. Successive discount formula uses subtraction (a+b−ab/100), while successive profit/growth formula uses addition (a+b+ab/100) — memorize both directions clearly.
  3. Equal SP, equal profit%/loss%: net result is ALWAYS a loss of (common%)²/100 — this shortcut avoids computing individual CPs.
  4. For CP/SP ratio-of-articles problems (“SP of x articles = CP of y articles”), directly compute profit% = [(y−x)/x]×100 (a very fast shortcut derived from Type 6’s method).
  5. False weight profit% = [(true weight − false weight)/false weight] × 100 — treat this exactly like the CP/SP ratio shortcut.
  6. When a problem gives marked price, discount%, and desired profit%, work backward from CP: find required SP first (from profit%), then find MP (from discount% applied to MP giving that SP).
  7. Discount is always calculated on MP, never on CP — a frequent source of confusion when problems mention both values.
  8. For three or more successive discounts, combine two at a time repeatedly using the pairwise formula rather than trying to compute all at once.

11. Common Mistakes to Avoid

  • Using SP as the base for profit%/loss% instead of CP.
  • Using CP as the base for discount% instead of MP.
  • Adding successive discounts directly (20%+10%=30%) instead of using the correct net-discount formula (28%, not 30%).
  • Forgetting the “always a loss” result in the equal-SP-equal-%-profit/loss scenario, and instead assuming the net result is zero.
  • Sign errors in false weight problems — the profit is based on the goods actually given (false/lower quantity), not the claimed quantity.
  • Confusing “discount on MP” with “reduction from CP” — these are different bases entirely.
  • Not accounting for compounding when discounts or profits are applied in sequence, rather than added directly.

12. Solved Examples (25 Fully Worked Problems)

Example 1. A man buys an article for ₹450 and sells it for ₹540. Find his profit percentage. Solution: Profit=90. Profit%=(90/450)×100=20%.

Example 2. An article is sold at a loss of 8%. If the CP is ₹625, find the SP. Solution: SP=625×0.92=₹575.

Example 3. A shopkeeper sells an article for ₹690, incurring a loss of 8%. Find the CP. Solution: CP=690×100/92=₹750.

Example 4. Find the SP of an article whose CP is ₹1200, to earn a profit of 25%. Solution: SP=1200×1.25=₹1500.

Example 5. An article marked at ₹1500 is sold after a discount of 20%. Find the SP. Solution: SP=1500×0.8=₹1200.

Example 6. Find the discount percentage if an article marked at ₹800 is sold for ₹680. Solution: Discount=120. Discount%=(120/800)×100=15%.

Example 7. A shopkeeper wants a profit of 15% after offering a discount of 10%. If CP=₹1020, find the MP. Solution: Required SP=1020×1.15=1173. MP=1173/0.9=₹1303.33.

Example 8. Find the single equivalent discount for successive discounts of 25% and 20%. Solution: 25+20−(25×20)/100=45−5=40%.

Example 9. Find the single equivalent discount for three successive discounts of 10%, 20%, 10%. Solution: Combine10&20: 10+20−2=28%. Combine28&10:28+10−2.8=35.2%.

Example 10. A dishonest trader claims to sell goods at cost price but uses a weight of 800g for every 1kg. Find his profit percentage. Solution: Profit%=[(1000−800)/800]×100=(200/800)×100=25%.

Example 11. A man sells two articles for ₹2400 each, one at 20% profit and the other at 20% loss. Find his overall gain/loss percentage. Solution: Net loss=(20²)/100=4% loss.

Example 12. If the SP of 20 articles equals the CP of 25 articles, find the profit percentage. Solution: Profit%=[(25−20)/20]×100=25%.

Example 13. A shopkeeper allows a discount of 10% and still makes a profit of 26%. Find the profit percentage if no discount were allowed (i.e., find profit% on the marked price sale directly). Solution: Let CP=100. SP(with 10% discount)=100×1.26=126=MP×0.9 ⇒ MP=140. Without discount, SP=MP=140. Profit%=(140−100)/100×100=40%.

Example 14. A trader marks his goods 40% above cost price and allows a discount of 15%. Find his profit percentage. Solution: Let CP=100. MP=140. SP=140×0.85=119. Profit%=19%.

Example 15. By selling an article for ₹960, a man loses 4%. At what price should he sell it to gain 10%? Solution: CP=960×100/96=1000. Required SP=1000×1.1=₹1100.

Example 16. A man buys 12 pens for ₹100 and sells them at 8 pens for ₹100. Find his profit or loss percentage. Solution: CP per pen=100/12. SP per pen=100/8. Profit%=[(100/8−100/12)/(100/12)]×100=[(12.5−8.33)/8.33]×100≈50%.

Example 17. A shopkeeper sells an article at a 10% loss. Had he sold it for ₹66 more, he would have gained 5%. Find the CP. Solution: Let CP=x. SP1=0.9x. SP2=1.05x. Difference=1.05x−0.9x=0.15x=66. x=₹440.

Example 18. Find the marked price of an article if it’s sold after a 25% discount for ₹1500. Solution: MP=1500/0.75=₹2000.

Example 19. A trader buys 100 kg of rice for ₹6000 and sells 60 kg at 10% profit and the rest at 5% loss. Find his overall profit/loss percentage. Solution: CP per kg=60. SP of 60kg=60×60×1.1=3960. SP of 40kg=40×60×0.95=2280. Total SP=3960+2280=6240. Total CP=6000. Profit=240. Profit%=(240/6000)×100=4%.

Example 20. A man sold an article at a loss of 15%. Had he sold it for ₹450 more, he would have gained 5%. Find the CP. Solution: 0.05x−(−0.15x)=450⇒0.2x=450⇒x=₹2250.

Example 21. Find the CP of an article that is sold for ₹1955 at a profit of 15%. Solution: CP=1955×100/115=₹1700.

Example 22. A shopkeeper offers successive discounts of 20% and 5% on an article marked at ₹2500. Find the effective SP and the single equivalent discount. Solution: SP=2500×0.8×0.95=2500×0.76=₹1900. Equivalent discount%=(2500−1900)/2500×100=24% (matches 20+5−1=24 ✓).

Example 23. A retailer buys goods at 20% discount on MP and sells them at MP. Find his profit percentage. Solution: Let MP=100. CP=80. SP=100. Profit%=(20/80)×100=25%.

Example 24. By selling 45 lemons for ₹40, a woman loses 20%. How many lemons should she sell for ₹24 to gain 20% on the whole? Solution: SP for 45 lemons=40, this is at 20% loss ⇒ CP for 45=40/0.8=50 ⇒ CP per lemon=50/45=10/9. To gain 20%, SP per lemon=(10/9)×1.2=12/9=4/3. Number of lemons for ₹24=24/(4/3)=24×3/4=18 lemons.

Example 25. A shopkeeper marks his goods at 50% above CP and allows successive discounts of 20% and 10%. Find his profit or loss percentage. Solution: Let CP=100. MP=150. SP=150×0.8×0.9=150×0.72=108. Profit%=8%.

13. Practice Question Bank (50 Questions)

Set A — Basic Profit/Loss (Q1–Q12) 1. A man buys an article for ₹720 and sells it for ₹864. Find his profit%. 2. An article is sold at 12% loss for ₹528. Find the CP. 3. Find the SP of an article with CP ₹950 to gain 18%. 4. An article sold at ₹1440 incurs a loss of 10%. Find the CP. 5. A man sells an article for ₹690 at a profit of 15%. Find the CP. 6. Find the loss percentage if an article bought for ₹800 is sold for ₹680. 7. A man buys an item for ₹550 and wants a profit of 30%. Find the required SP. 8. An article’s CP is ₹1250. It’s sold for ₹1000. Find the loss%. 9. A trader sells goods at ₹2760, gaining 15%. Find the CP. 10. Find CP if SP=₹918 and loss%=15%. 11. A man buys a bicycle for ₹2500 and sells it at a loss of 8%. Find the SP. 12. An article is bought for ₹640 and sold for a profit of 25%. Find the SP.

Set B — Marked Price & Discount (Q13–Q22) 13. Find the SP of an article marked ₹2500 with a 12% discount. 14. An article marked at ₹1800 is sold for ₹1530. Find the discount%. 15. Find the MP if SP=₹850 after a 15% discount. 16. A shopkeeper wants 20% profit after a 10% discount on CP=₹900. Find MP. 17. Find the single equivalent discount for successive discounts of 30% and 10%. 18. Find the single equivalent discount for 15%, 15%, and 15% successive discounts. 19. A trader marks goods 60% above CP and allows a 25% discount. Find profit%. 20. An article marked ₹3000 is sold after two successive discounts of 10% and 5%. Find the SP. 21. Find the MP of an article sold for ₹1360 after a discount of 20%. 22. A shopkeeper allows a discount of 12% and still gains 32%. Find the profit% if sold at MP without discount.

Set C — False Weight (Q23–Q28) 23. A trader uses a weight of 950g instead of 1kg. Find his profit%. 24. A shopkeeper claims to sell at CP but uses a 900g weight for 1kg. Find profit%. 25. A dishonest dealer professes to sell at CP but uses a false weight and gains 25%. Find the weight he uses instead of 1kg. 26. A trader uses a weight of 720g for 750g. Find his profit%. 27. A grocer sells rice at CP using a weight of 950g for 1000g claimed. Find profit%. 28. A trader gains 20% by using a false weight instead of the true one. Find the false weight (in grams, out of 1000g true weight).

Set D — Multiple Transactions (Q29–Q36) 29. A man sells two articles for ₹1200 each, one at 25% profit and other at 25% loss. Find overall %. 30. Find the overall profit/loss% if a shopkeeper sells 2 items at ₹3000 each, one at 15% loss and other at 15% profit. 31. A man sells 150kg wheat, 90kg at 8% profit and 60kg at 4% loss, CP=₹40/kg. Find overall profit%. 32. A shopkeeper buys 50 chairs at ₹800 each. He sells 30 at 20% profit and 20 at 10% loss. Find overall profit%. 33. Two horses are sold at ₹9975 each, one at 15% profit and one at 15% loss. Find the total profit or loss. 34. A trader buys 200 items, sells 120 at 15% profit and 80 at 5% loss, at a uniform CP. Find overall profit%. 35. A man sold 2 watches at ₹1596 each, one at 12% profit, other at 12% loss. Find overall gain/loss. 36. A shopkeeper sells two TVs at the same price, one at 30% profit and other at 30% loss. Find overall loss%.

Set E — Ratio & Advanced (Q37–Q44) 37. If SP of 25 articles = CP of 30 articles, find profit%. 38. If SP of 12 articles = CP of 15 articles, find profit%. 39. If SP of 40 articles = CP of 32 articles, find loss%. 40. A man buys 8 articles for ₹10 and sells 10 for ₹8. Find profit/loss%. 41. A shopkeeper sells an article at a loss of 12%. Had he sold it for ₹80 more, he’d have gained 8%. Find the CP. 42. By selling an article for ₹1520, a man gains 12%. Find the SP for a 20% gain. 43. A man buys apples at 6 for ₹10 and sells at 5 for ₹10. Find profit%. 44. A dealer sold an article at 8% loss. Had he sold it for ₹800 more, he would have gained 12%. Find CP.

Set F — Mixed/Advanced (Q45–Q50) 45. A shopkeeper marks goods 25% above CP and gives a discount such that he still makes a 10% profit. Find the discount%. 46. Find the CP of an article sold at ₹4025 with a 15% profit, then find the SP needed for a 25% profit on the same CP. 47. A retailer buys an article at 15% discount on MP=₹2000 and sells at 10% above MP. Find his profit%. 48. A man sells an article at a profit of 20%. If he had bought it at 10% less and sold it for ₹36 less, he would have gained 30%. Find the CP. 49. A shopkeeper sold two articles, each for ₹2970, one at a profit of 10% and the other at a loss of 10%. Find whether there’s an overall profit or loss, and by how much. 50. A merchant marks his goods at a price that allows him a 25% profit after giving a 20% discount. Find the CP as a percentage of MP.

14. Answer Key with Quick Solutions

Set A 1. profit=144;profit%=(144/720)×100=20% 2. CP=528×100/88=₹600 3. SP=950×1.18=₹1121 4. CP=1440×100/90=₹1600 5. CP=690×100/115=₹600 6. loss=120;loss%=(120/800)×100=15% 7. SP=550×1.3=₹715 8. loss%=(250/1250)×100=20% 9. CP=2760×100/115=₹2400 10. CP=918×100/85=₹1080 11. SP=2500×0.92=₹2300 12. SP=640×1.25=₹800

Set B 13. SP=2500×0.88=₹2200 14. discount=270;discount%=(270/1800)×100=15% 15. MP=850/0.85=₹1000 16. requiredSP=900×1.2=1080;MP=1080/0.9=₹1200 17. 30+10−3=37% 18. combine15&15:15+15−2.25=27.75;combine27.75&15:27.75+15−4.1625=38.5875% 19. CP=100,MP=160,SP=160×0.75=120;profit%=20% 20. SP=3000×0.9×0.95=₹2565 21. MP=1360/0.8=₹1700 22. CP=100,SP(discounted)=132=MP×0.88⇒MP=150;withoutdiscount SP=150;profit%=50%

Set C 23. profit%=[(1000−950)/950]×100≈5.26% 24. profit%=[(1000−900)/900]×100≈11.11% 25. 25%gain⇒(1000−x)/x=0.25⇒1000−x=0.25x⇒1000=1.25x⇒x=800g 26. profit%=[(750−720)/720]×100≈4.17% 27. profit%=[(1000−950)/950]×100≈5.26% 28. (1000−x)/x=0.2⇒1000−x=0.2x⇒x=1000/1.2≈833.33g

Set D 29. net loss=(25²)/100=6.25% loss 30. net loss=(15²)/100=2.25% loss 31. CP total=150×40=6000;SP=90×40×1.08+60×40×0.96=3888+2304=6192;profit=192;profit%=(192/6000)×100=3.2% 32. CP=50×800=40000;SP=30×800×1.2+20×800×0.9=28800+14400=43200;profit=3200;profit%=(3200/40000)×100=8% 33. net loss=(15²)/100=2.25%;CP total=9975/1.15+9975/0.85=8673.9+11735.3=20409.2;loss=20409.2×0.0225≈₹459.2 loss(approx, matching%method) 34. CP=1(per item,200total);SP=120×1.15+80×0.95=138+76=214;total CP=200;profit=14;profit%=(14/200)×100=7% 35. net loss=(12²)/100=1.44% loss 36. net loss=(30²)/100=9% loss

Set E 37. profit%=[(30−25)/25]×100=20% 38. profit%=[(15−12)/12]×100=25% 39. loss%=[(40−32)/40]×100=20% 40. CPperarticle=10/8=1.25;SPperarticle=8/10=0.8;loss%=[(1.25−0.8)/1.25]×100=36% 41. 0.08x+0.12x=80⇒0.2x=80⇒x=₹400 42. CP=1520/1.12≈1357.14;SP(20%)=1357.14×1.2≈₹1628.57 43. CPperapple=10/6=1.667;SPperapple=10/5=2;profit%=[(2−1.667)/1.667]×100=20% 44. 0.08x+0.12x=800⇒0.2x=800⇒x=₹4000 45. CP=100,MP=125;requiredSP=110;discount=15;discount%=(15/125)×100=12% 46. CP=4025/1.15=3500;SP(25%)=3500×1.25=₹4375 47. CP=2000×0.85=1700;SP=2000×1.1=2200;profit=500;profit%=(500/1700)×100≈29.41% 48. let CP=x,newCP=0.9x,SP1=1.2x,SP2=SP1−36=1.2x−36,and SP2=0.9x×1.3=1.17x.So1.2x−36=1.17x⇒0.03x=36⇒x=₹1200 49. net loss=(10²)/100=1% loss;CP total=2970/1.1+2970/0.9=2700+3300=6000;total SP=5940;loss=60(matches1%of6000=60✓) 50. CP=100(base),SP(with25%profit)=125=MP×0.8⇒MP=156.25;CP as % of MP=(100/156.25)×100=64%

End of Profit and Loss study material. This chapter’s percentage-base logic (CP vs MP) connects directly to the Mixtures and Alligation module that follows.

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