Profit and Loss Aptitude

Profit and Loss are key concepts in financial mathematics, essential in various competitive exams and business scenarios. These concepts revolve around the calculation of the profit or loss made on a transaction. The profit or loss is determined by the difference between the selling price and the cost price. The understanding of these concepts is crucial for effective financial management and decision-making.

1. A shopkeeper buys a gadget for $150 and sells it for $180. What is the profit percentage?

Cost Price (CP) = $150, Selling Price (SP) = $180.
Profit = SP - CP = $180 - $150 = $30.
Profit Percentage = (Profit / CP) * 100 = (30 / 150) * 100 = 20%.

2. If a television is sold at a loss of 10%, and the selling price is $540, what was its cost price?

Selling Price (SP) = $540, Loss Percentage = 10%.
Let Cost Price be CP. Loss = CP - SP.
10% of CP = CP - $540.
0.1 * CP = CP - 540.
CP = $600.

3. A retailer marks up a product by 40% above the cost price. If it is sold at a discount of 15%, what is the profit percentage?

Let Cost Price (CP) = $100.
Marked Price (MP) = CP + 40% of CP = $100 + $40 = $140.
Selling Price (SP) after 15% discount = MP - 15% of MP = $140 - $21 = $119.
Profit = SP - CP = $119 - $100 = $19.
Profit Percentage = ($19 / $100) * 100 = 19%.

4. A book is bought for $250 and sold at a loss of 8%. What is the selling price of the book?

Cost Price (CP) = $250, Loss Percentage = 8%.
Loss = 8% of CP = 0.08 * $250 = $20.
Selling Price (SP) = CP - Loss = $250 - $20 = $230.

5. A trader sells two smartphones for $1200 each. On one, he gains 20% and on the other, he loses 20%. What is the total gain or loss percentage?

Selling Price of each smartphone = $1200.
For 20% profit, CP = SP / (1 + Profit%) = $1200 / 1.20 = $1000.
For 20% loss, CP = SP / (1 - Loss%) = $1200 / 0.80 = $1500.
Total CP = $1000 + $1500 = $2500, Total SP = $1200 + $1200 = $2400.
Loss = Total CP - Total SP = $2500 - $2400 = $100.
Loss Percentage = ($100 / $2500) * 100 = 2%.

6. A shopkeeper sells a shirt at a profit of 15%. If the selling price is $230, what was the cost price?

Selling Price (SP) = $230, Profit Percentage = 15%.
Let Cost Price be CP. Profit = SP - CP.
15% of CP = $230 - CP.
0.15 * CP = $230 - CP.
CP = $230 / 1.15 = $200.

7. An article is sold at a loss of 25%. If the selling price is $150, find the cost price.

Selling Price (SP) = $150, Loss Percentage = 25%.
Let Cost Price be CP. Loss = CP - SP.
25% of CP = CP - $150.
0.25 * CP = CP - 150.
CP = $150 / 0.75 = $200.

8. A shopkeeper marks his goods 30% above the cost price and then gives a discount of 10%. What is his profit percent?

Let Cost Price (CP) = $100.
Marked Price (MP) = CP + 30% of CP = $100 + $30 = $130.
Selling Price (SP) after 10% discount = MP - 10% of MP = $130 - $13 = $117.
Profit = SP - CP = $117 - $100 = $17.
Profit Percentage = ($17 / $100) * 100 = 17%.

9. A man buys an item for $1200 and sells it at a loss of 15%. What is the selling price of the item?

Cost Price (CP) = $1200, Loss Percentage = 15%.
Loss = 15% of CP = 0.15 * $1200 = $180.
Selling Price (SP) = CP - Loss = $1200 - $180 = $1020.

10. A dealer sells an article for $540 and makes a profit of 20%. What would be the profit percentage if it were sold for $630?

Cost Price (CP) = SP / (1 + Profit%) = $540 / 1.20 = $450.
New Selling Price (SP) = $630.
Profit = New SP - CP = $630 - $450 = $180.
Profit Percentage = ($180 / $450) * 100 = 35%.

11. A retailer buys a radio for $400 and sells it for $520. What is the profit percentage?

Cost Price (CP) = $400, Selling Price (SP) = $520.
Profit = SP - CP = $520 - $400 = $120.
Profit Percentage = (Profit / CP) * 100 = (120 / 400) * 100 = 30%.

12. If a car is sold for $15,000 with a profit of 25%, what is the cost price of the car?

Selling Price (SP) = $15,000, Profit Percentage = 25%.
Cost Price (CP) = SP / (1 + Profit%) = 15000 / 1.25 = $12,000.

13. A shopkeeper marks up a book by 50% above its cost price. If he sells it at a discount of 20%, what is the profit or loss percentage?

Let Cost Price (CP) = $100.
Marked Price (MP) = CP + 50% of CP = $100 + $50 = $150.
Selling Price (SP) after 20% discount = MP - 20% of MP = $150 - $30 = $120.
Profit = SP - CP = $120 - $100 = $20.
Profit Percentage = ($20 / $100) * 100 = 10%.

14. An article is bought for $500 and sold at a profit of 15%. What is the selling price?

Cost Price (CP) = $500, Profit Percentage = 15%.
Selling Price (SP) = CP + Profit = $500 + 15% of $500 = $500 + $75 = $575.

15. A shopkeeper suffers a 10% loss by selling a toy for $180. At what price should he sell the toy to gain a 10% profit?

Selling Price for 10% loss = $180.
Cost Price (CP) = Selling Price / (1 - Loss%) = $180 / 0.90 = $200.
Selling Price for 10% profit = CP + 10% of CP = $200 + $20 = $220.

16. A person sells two watches for $200 each. On one he gains 25% and on the other he loses 25%. What is his overall gain or loss percent?

Selling Price of each watch = $200.
For 25% profit, CP = SP / (1 + Profit%) = $200 / 1.25 = $160.
For 25% loss, CP = SP / (1 - Loss%) = $200 / 0.75 = $266.67.
Total CP = $160 + $266.67 = $426.67, Total SP = $200 + $200 = $400.
Loss = Total CP - Total SP = $426.67 - $400 = $26.67.
Loss Percentage = ($26.67 / $426.67) * 100 ≈ 6.25%.

17. If a bicycle is sold for $480 with a profit of 20%, what is its cost price?

Selling Price (SP) = $480, Profit Percentage = 20%.
Cost Price (CP) = SP / (1 + Profit%) = $480 / 1.20 = $400.

18. A merchant sells an item at a 10% discount on the marked price and makes a 20% profit. If the selling price is $360, what is the marked price?

Selling Price (SP) = $360, Profit Percentage = 20%.
Cost Price (CP) = SP / (1 + Profit%) = $360 / 1.20 = $300.
Marked Price (MP) = SP / (1 - Discount%) = $360 / 0.90 = $400.

19. A trader marks his goods 25% above his cost price and allows a discount of 10%. If the cost price is $500, what is the selling price?

Cost Price (CP) = $500.
Marked Price (MP) = CP + 25% of CP = $500 + $125 = $625.
Selling Price (SP) = MP - 10% of MP = $625 - $62.50 = $562.50.

20. A book is bought for $320 and sold at a profit of 25%. What is the selling price of the book?

Cost Price (CP) = $320, Profit Percentage = 25%.
Profit = 25% of CP = 0.25 * $320 = $80.
Selling Price (SP) = CP + Profit = $320 + $80 = $400.