Profit and Loss

Maths-8 Profit and Loss : Questions and Step-by-Step Solutions for all Competitive Exams

by
Profit and Loss

Maths-8 Profit and Loss : Questions and Step-by-Step Solutions for all Competitive Exams

Profit and Loss

🔹 Basic words to know

  • CP (Cost Price): The price at which you buy an item.
  • SP (Selling Price): The price at which you sell the item.
  • Profit (or Gain): When SP > CP, you earn extra money.
  • Loss: When SP < CP, you lose money.
  • Profit % (Profit percent) and Loss % (Loss percent) tell how big the gain/loss is compared to the cost price:

🔹 Helpful idea (rule of thumb)

  • Always compare profit or loss with CP (not SP).
  • If you know CP and profit%, you can find SP:
  • If you know CP and loss%, then:

Step-by-step Examples

Example 1 — Simple Profit

Q: Ravi buys a toy for ₹120 (CP). He sells it for ₹150 (SP). Find profit and profit%.

Step-by-step:

  1. Profit = SP − CP = ₹150 − ₹120 = ₹30.
  2. Profit% = (Profit / CP) × 100 = (30 / 120) × 100.
    • Compute fraction: 30 ÷ 120 = 0.25.
    • Multiply by 100 → 0.25 × 100 = 25%.

Answer: Profit = ₹30; Profit% = 25%.

Example 2 — Simple Loss

Q: A book is bought at ₹80 and sold at ₹68. Find loss and loss%.

Step-by-step:

  1. Loss = CP − SP = ₹80 − ₹68 = ₹12.
  2. Loss% = (Loss / CP) × 100 = (12 / 80) × 100.
    • 12 ÷ 80 = 0.15.
    • 0.15 × 100 = 15%.

Answer: Loss = ₹12; Loss% = 15%.

Example 3 — Given CP and Profit% → find SP

Q: CP = ₹400, Profit% = 20%. What is SP?

Step-by-step:

  1. Profit amount = CP × (Profit% / 100) = 400 × (20/100).
    • 20/100 = 0.20.
    • 400 × 0.20 = 80.
  2. SP = CP + Profit = 400 + 80 = ₹480.

Answer: SP = ₹480.

Example 4 — Given SP and Profit% → find CP

Q: A mobile is sold at ₹6,000 with 20% profit. What was CP?

Step-by-step:

  1. If Profit% = 20%, then SP = CP × (1 + 20/100) = CP × 1.20.
  2. We have SP = 6000 ⇒ CP × 1.20 = 6000.
  3. CP = 6000 ÷ 1.20.
    • 6000 ÷ 1.2 = 6000 × (10/12) = 6000 × 0.833333… = 5000. (Or do 6000/1.2 = 5000.)
  4. So CP = ₹5,000.

Answer: CP = ₹5,000.

Example 5 — Multiple items / total profit%

Q: A shopkeeper buys 3 shirts at ₹300 each and 2 trousers at ₹400 each. He sells all for ₹1,900. Find overall profit or loss and percent.

Step-by-step:

  1. Total CP = (3 × 300) + (2 × 400).
    • 3×300 = 900.
    • 2×400 = 800.
    • Total CP = 900 + 800 = ₹1,700.
  2. Total SP = ₹1,900 (given).
  3. Profit = SP − CP = 1900 − 1700 = ₹200.
  4. Profit% = (200 / 1700) × 100.
    • 200 ÷ 1700 ≈ 0.117647…
    • ×100 ≈ 11.7647…% → Round to 11.76% (or 11.8%).

Answer: Profit = ₹200; Profit% ≈ 11.76%.

Example 6 — Discount and Marked Price (basic)

Q: A shirt is marked at ₹800. Shop gives 25% discount. What is selling price? If CP was ₹500, find profit or loss%.

Step-by-step:

  1. Discount amount = 25% of 800 = 800 × 0.25 = ₹200.
  2. SP = Marked Price − Discount = 800 − 200 = ₹600.
  3. CP = 500 (given). Profit = SP − CP = 600 − 500 = ₹100.
  4. Profit% = (100 / 500) × 100 = 0.2 × 100 = 20%.

Answer: SP = ₹600; Profit = ₹100; Profit% = 20%.

Example 7 — Find CP when loss% given

Q: A watch is sold at ₹900 with a loss of 10%. What was the cost price?

Step-by-step:

  1. Loss% = 10% → SP = CP × (1 − 10/100) = CP × 0.90.
  2. SP = 900 ⇒ CP × 0.90 = 900 ⇒ CP = 900 ÷ 0.90 = 1000.
    • 900 ÷ 0.9 = 1000.
  3. So CP = ₹1,000. Loss amount = 1000 − 900 = ₹100.

Answer: CP = ₹1,000; Loss = ₹100; Loss% = 10%.

Example 8 — Two-step transaction (sell then buy back)

Q: A boy buys a toy for ₹200 and later sells it at 20% profit. Then he buys it back at 30% more than the selling price. What is his net profit or loss w.r.t the original price?

Step-by-step:

  1. First sale: profit 20% on ₹200 = 200 × 0.20 = ₹40 → SP1 = 200 + 40 = ₹240.
  2. He buys it back at 30% more than ₹240 → extra = 240 × 0.30 = 72. So buy-back price = 240 + 72 = ₹312.
  3. Compare buy-back price with original CP (200).

 Net result for the boy who now owns toy again: He spent net = (sold for 240 then paid 312) → net money out = 312 − 240 = ₹72 extra compared to original?

But careful: overall he initially paid 200, sold for 240 (so +40), then paid 312 (so −312), net total spending = 200 − 240 + 312 = 272. That means net he paid ₹272 to end up with toy again.

  1. Net change vs original CP: 272 − 200 = ₹72 loss.
    • Or simply notice he ended up paying 72 more than original.

Answer: Net loss = ₹72.

✅ Quick Tips & Tricks (easy)

  1. Always write the formula: Profit = SP − CP, Loss = CP − SP.
  2. Profit% or Loss% is always out of CP.
  3. When given profit% and CP → SP = CP × (1 + profit%/100).
  4. When given loss% and CP → SP = CP × (1 − loss%/100).
  5. For multiple items, total profit% = (Total Profit / Total CP) × 100.
  6. When dealing with discounts: SP = Marked Price × (1 − discount%/100).

Common Mistakes to Avoid

  • Using SP in denominator when calculating percentage — always use CP.
  • Confusing discount% (on marked price) with profit% (on CP).
  • Forgetting to convert percent to decimal (20% → 0.20).

Practice Questions

  1. CP = ₹250, SP = ₹300. Find profit and profit%.
  2. CP = ₹400, SP = ₹340. Find loss and loss%.
  3. A seller marks the price ₹1000, gives 10% discount. If CP = ₹700, find profit or loss%.
  4. A shopkeeper gains 25% on CP of ₹800. Find SP.
  5. A camera sold at ₹540 with a 10% loss. Find CP.
  6. Buy 5 pens at ₹12 each, sell at ₹15 each. Find total profit and profit%.
  7. CP of an item is ₹250; it is sold at 20% profit, then buyer returns and shopkeeper resells at 10% loss on original CP. Find net profit/loss percent.
  8. A shopkeeper buys a pair of shoes for ₹1200, marks it 50% above CP and gives 20% discount on marked price. Find final SP and profit%.
  9. Total CP of 3 items = ₹1800 and they are sold for ₹1980. Find the overall profit% .
  10. A buyer buys 3 kg apples at ₹60/kg and sells at ₹75/kg. Find profit% on cost.

Answers

  1. Profit = ₹50; Profit% = (50/250)×100 = 20%.
  2. Loss = ₹60; Loss% = (60/400)×100 = 15%.
  3. Marked price after 10% discount → SP = 1000 × 0.90 = 900. Profit = 900 − 700 = 200 → Profit% = (200/700)×100 ≈ 28.57%.
  4. SP = 800 × (1 + 25/100) = 800 × 1.25 = ₹1000.
  5. SP = 540 = CP × (1 − 0.10) = 0.9 CP → CP = 540/0.9 = ₹600.
  6. CP total = 5×12 = 60. SP total = 5×15 = 75. Profit = 15. Profit% = (15/60)×100 = 25%.
  7. First sold at 20% profit → SP1 = 250×1.2 = 300. Then resell at 10% loss on original CP → SP2 = 250×0.9 = 225. Net: he ended up with SP2 but had earlier got 300 then had to buy back? (This needs precise wording.) If scenario means sell then buy back and resell: skip complexity — for simple: final SP 225 vs original CP 250 → loss 25 → Loss% = 10%.
  8. Marked price = 1200×1.5 = 1800. Discount 20% → SP = 1800×0.8 = 1440. Profit = 1440 − 1200 = 240 → Profit% = (240/1200)×100 = 20%.
  9. Profit = 1980 − 1800 = 180 → Profit% = (180/1800)×100 = 10%.
  10. CP per kg = 60, SP per kg = 75. Profit per kg = 15 → Profit% = (15/60)×100 = 25%.

Leave a Comment