Profit and Loss: Concepts, Formulas, and Questions

Basic Profit and Loss Questions:

1. A man bought an item for ₹400 and sold it for ₹500. Find his profit.
   • Answer:
     Profit = Selling Price – Cost Price = ₹500 – ₹400 = ₹100
2. If a product is sold for ₹180 after a 10% loss, what is its cost price?
   • Answer:
     Let the Cost Price be $x$x.
     $\text{Selling Price} = x – 10\% \text{ of } x = x – \frac{10}{100} \times x$Selling Price=x−10% of x=x−10010​×x
     $180 = \frac{90}{100} \times x$180=10090​×x
     $x = \frac{180 \times 100}{90} = ₹200$x=90180×100​=₹200
     Cost Price = ₹200
3. A person bought an article for ₹1200 and sold it for ₹1400. Find his profit percentage.
   • Answer:
     Profit = ₹1400 – ₹1200 = ₹200
     Profit Percentage = $\frac{200}{1200} \times 100 = 16.67\%$1200200​×100=16.67%
4. The cost price of a shirt is ₹800. If a 20% profit is earned, what is the selling price?
   • Answer:
     Profit = 20% of ₹800 = $\frac{20}{100} \times 800 = ₹160$10020​×800=₹160
     Selling Price = ₹800 + ₹160 = ₹960
5. A man sold a book for ₹1500, making a profit of 25%. What was the cost price?
   • Answer:
     Let the Cost Price be $x$x.
     Selling Price = $x + 25\% \text{ of } x = x + \frac{25}{100} \times x = 1500$x+25% of x=x+10025​×x=1500
     $1.25x = 1500$1.25x=1500
     $x = \frac{1500}{1.25} = ₹1200$x=1.251500​=₹1200
     Cost Price = ₹1200

Profit and Loss Percentage Questions:

6. A person buys a product for ₹500 and sells it for ₹600. What is the percentage profit?
   • Answer:
     Profit = ₹600 – ₹500 = ₹100
     Profit Percentage = $\frac{100}{500} \times 100 = 20\%$500100​×100=20%
7. A shopkeeper bought an article for ₹700 and sold it for ₹900. What is the profit percentage?
   • Answer:
     Profit = ₹900 – ₹700 = ₹200
     Profit Percentage = $\frac{200}{700} \times 100 = 28.57\%$700200​×100=28.57%
8. A man sold an article for ₹1500, incurring a loss of 20%. Find the cost price.
   • Answer:
     Let the Cost Price be $x$x.
     Selling Price = $x – 20\% \text{ of } x = x – \frac{20}{100} \times x$x−20% of x=x−10020​×x
     $1500 = \frac{80}{100} \times x$1500=10080​×x
     $x = \frac{1500 \times 100}{80} = ₹1875$x=801500×100​=₹1875
     Cost Price = ₹1875
9. If the cost price of a product is ₹800, and the selling price is ₹960, what is the percentage gain?
   • Answer:
     Gain = ₹960 – ₹800 = ₹160
     Percentage Gain = $\frac{160}{800} \times 100 = 20\%$800160​×100=20%
10. A trader incurs a loss of 12%. If the selling price is ₹200, find the cost price.

• Answer:
  Let the Cost Price be $x$x.
  Selling Price = $x – 12\% \text{ of } x = x – \frac{12}{100} \times x$x−12% of x=x−10012​×x
  $200 = \frac{88}{100} \times x$200=10088​×x
  $x = \frac{200 \times 100}{88} = ₹227.27$x=88200×100​=₹227.27
  Cost Price = ₹227.27

Discount and Mark Price Questions:

11. A shirt is sold for ₹1800 after offering a 10% discount. What was the marked price?

• Answer:
  Let the Marked Price be $x$x.
  Selling Price = $x – 10\% \text{ of } x = x – \frac{10}{100} \times x$x−10% of x=x−10010​×x
  $1800 = \frac{90}{100} \times x$1800=10090​×x
  $x = \frac{1800 \times 100}{90} = ₹2000$x=901800×100​=₹2000
  Marked Price = ₹2000

12. A man buys an item for ₹1200 and sells it for ₹1000. Find the percentage loss.

• Answer:
  Loss = ₹1200 – ₹1000 = ₹200
  Loss Percentage = $\frac{200}{1200} \times 100 = 16.67\%$1200200​×100=16.67%

13. An item is marked at ₹500. If a 20% discount is given, what is the selling price?

• Answer:
  Discount = 20% of ₹500 = $\frac{20}{100} \times 500 = ₹100$10020​×500=₹100
  Selling Price = ₹500 – ₹100 = ₹400

14. A shopkeeper gives a 25% discount on a marked price of ₹2000. What is the selling price?

• Answer:
  Discount = 25% of ₹2000 = $\frac{25}{100} \times 2000 = ₹500$10025​×2000=₹500
  Selling Price = ₹2000 – ₹500 = ₹1500

15. A product is sold for ₹2400 after a 10% discount. What is the marked price?

• Answer:
  Let the Marked Price be $x$x.
  Selling Price = $x – 10\% \text{ of } x = x – \frac{10}{100} \times x$x−10% of x=x−10010​×x
  $2400 = \frac{90}{100} \times x$2400=10090​×x
  $x = \frac{2400 \times 100}{90} = ₹2666.67$x=902400×100​=₹2666.67
  Marked Price = ₹2666.67

Successive Profit and Loss Questions:

16. A trader earns a 10% profit on the cost price of a product and then gives a 5% discount. What is the overall profit percentage?

• Answer:
  Total Profit Percentage = $\left( 1 + \frac{10}{100} \right) \times \left( 1 – \frac{5}{100} \right) – 1$(1+10010​)×(1−1005​)−1
  Total Profit Percentage = $1.1 \times 0.95 – 1 = 1.045 – 1 = 0.045 \times 100 = 4.5\%$1.1×0.95−1=1.045−1=0.045×100=4.5%

17. A person buys an article for ₹500 and sells it for ₹600. Then, he gave a 10% discount on the selling price. What is the overall profit percentage?

• Answer:
  New Selling Price = ₹600 – 10% of ₹600 = ₹600 – ₹60 = ₹540
  Profit = ₹540 – ₹500 = ₹40
  Profit Percentage = $\frac{40}{500} \times 100 = 8\%$50040​×100=8%

18. A man sold an item at a loss of 10%, and then after a discount of 5% on the selling price, what was the overall percentage loss?

• Answer:
  Total Loss Percentage = $\left( 1 – \frac{10}{100} \right) \times \left( 1 – \frac{5}{100} \right) – 1$(1−10010​)×(1−1005​)−1
  Total Loss Percentage = $0.90 \times 0.95 – 1 = 0.855 – 1 = -0.145 \times 100 = -14.5\%$0.90×0.95−1=0.855−1=−0.145×100=−14.5%
  Overall Loss = 14.5%

19. A trader offers two successive discounts of 10% and 20%. If the marked price is ₹500, what is the selling price?

• Answer:
  First Discounted Price = ₹500 × (1 – 0.10) = ₹500 × 0.90 = ₹450
  Second Discounted Price = ₹450 × (1 – 0.20) = ₹450 × 0.80 = ₹360
  Selling Price = ₹360

20. A dealer gives successive discounts of 5%, 10%, and 15% on the marked price of ₹2000. What is the final selling price?

• Answer:
  First Discounted Price = ₹2000 × (1 – 0.05) = ₹2000 × 0.95 = ₹1900
  Second Discounted Price = ₹1900 × (1 – 0.10) = ₹1900 × 0.90 = ₹1710
  Third Discounted Price = ₹1710 × (1 – 0.15) = ₹1710 × 0.85 = ₹1453.50
  Final Selling Price = ₹1453.50

Advanced Profit and Loss Problems:

21. A man bought an item for ₹1000 and sold it at a profit of 25%. Then, he bought another item with the entire amount. If he sold the second item at 20% profit, what is the total profit percentage?

• Answer:
  First Profit = ₹1000 + 25% = ₹1000 + ₹250 = ₹1250
  Second Profit = ₹1250 × 20% = ₹1250 + ₹250 = ₹1500
  Total Profit = ₹1500 – ₹1000 = ₹500
  Total Profit Percentage = $\frac{500}{1000} \times 100 = 50\%$1000500​×100=50%

22. A person buys 10 articles at ₹100 each and sells each for ₹120. What is the profit percentage?

• Answer:
  Cost Price = 10 × ₹100 = ₹1000
  Selling Price = 10 × ₹120 = ₹1200
  Profit = ₹1200 – ₹1000 = ₹200
  Profit Percentage = $\frac{200}{1000} \times 100 = 20\%$1000200​×100=20%

23. A product was bought for ₹1800 and sold for ₹1500. What is the percentage loss?

• Answer:
  Loss = ₹1800 – ₹1500 = ₹300
  Loss Percentage = $\frac{300}{1800} \times 100 = 16.67\%$1800300​×100=16.67%

24. A shopkeeper buys an item for ₹1200 and sells it at ₹1600. After giving a discount of 5%, find the original selling price.

• Answer:
  Selling Price after Discount = ₹1600
  Let the original selling price be $x$x.
  $x – 5\% \text{ of } x = ₹1600$x−5% of x=₹1600
  $0.95x = ₹1600$0.95x=₹1600
  $x = \frac{1600}{0.95} = ₹1684.21$x=0.951600​=₹1684.21
  Original Selling Price = ₹1684.21

25. A businessman bought 100 shirts at ₹200 each and sold them at ₹250 each. After offering a 10% discount on each shirt, what is his total profit?

Answer:
Total Cost Price = 100 × ₹200 = ₹20,000
Selling Price without Discount = 100 × ₹250 = ₹25,000
Discount per Shirt = 10% of ₹250 = ₹25
Discounted Selling Price per Shirt = ₹250 – ₹25 = ₹225
Total Selling Price = 100 × ₹225 = ₹22,500
Total Profit = ₹22,500 – ₹20,000 = ₹2,500
Total Profit = ₹2,500