Solved Examples
Profit & Loss · Study material
Solved Examples – Profit & Loss
Solved examples help students understand the practical application of Profit & Loss concepts in competitive examinations. These examples are designed from basic to advanced level and cover important Profit & Loss problems frequently asked in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, and placement aptitude tests.
Topics Covered in Solved Examples
- Basic Profit and Loss Calculations
- Profit Percentage Problems
- Loss Percentage Problems
- Selling Price and Cost Price Problems
- Discount and Marked Price
- Successive Discount Problems
- False Weight Problems
- Equal Profit and Loss Cases
- Percentage-Based Business Problems
- Advanced Commercial Calculations
Example 1: Basic Profit Calculation
Question: A shopkeeper buys an article for 800 and sells it for 950. Find the profit.
Solution:
Profit:
= SP − CP
= 950 − 800
= 150
Therefore:
Profit = 150
Example 2: Basic Loss Calculation
Question: A trader buys a product for 1200 and sells it for 1050. Find the loss.
Solution:
Loss:
= CP − SP
= 1200 − 1050
= 150
Therefore:
Loss = 150
Example 3: Profit Percentage
Question: A merchant buys an article for 500 and sells it for 650. Find the profit percentage.
Solution:
Profit:
= 650 − 500
= 150
Profit percentage:
= (150/500) × 100
= 30%
Therefore:
Profit percentage = 30%
Example 4: Loss Percentage
Question: A trader buys a machine for 4000 and sells it for 3400. Find the loss percentage.
Solution:
Loss:
= 4000 − 3400
= 600
Loss percentage:
= (600/4000) × 100
= 15%
Therefore:
Loss percentage = 15%
Example 5: Selling Price with Profit
Question: The cost price of an article is 2000. If the profit is 25%, find the selling price.
Solution:
Selling price:
= CP × (100 + Profit%)/100
= 2000 × 125/100
= 2500
Therefore:
Selling price = 2500
Example 6: Selling Price with Loss
Question: A product costs 3000. If it is sold at a loss of 20%, find the selling price.
Solution:
Selling price:
= 3000 × (100 − 20)/100
= 3000 × 80/100
= 2400
Therefore:
Selling price = 2400
Example 7: Finding Cost Price
Question: An article is sold for 1800 at a profit of 20%. Find the cost price.
Solution:
Cost price:
= SP × 100/(100 + Profit%)
= 1800 × 100/120
= 1500
Therefore:
Cost price = 1500
Example 8: Finding Cost Price in Loss
Question: An article is sold for 2550 at a loss of 15%. Find the cost price.
Solution:
Cost price:
= SP × 100/(100 − Loss%)
= 2550 × 100/85
= 3000
Therefore:
Cost price = 3000
Example 9: Discount Problem
Question: A shopkeeper gives a 10% discount on an article marked at 5000. Find the selling price.
Solution:
Discount:
= 10% of 5000
= 500
Selling price:
= 5000 − 500
= 4500
Therefore:
Selling price = 4500
Example 10: Discount Percentage
Question: An article marked at 4000 is sold for 3600. Find the discount percentage.
Solution:
Discount:
= 4000 − 3600
= 400
Discount percentage:
= (400/4000) × 100
= 10%
Therefore:
Discount percentage = 10%
Example 11: Successive Discount Problem
Question: Two successive discounts of 20% and 10% are given on an article. Find the net discount percentage.
Solution:
Net discount:
= 20 + 10 − (20 × 10)/100
= 30 − 2
= 28%
Therefore:
Net discount = 28%
Example 12: Equal Profit and Loss
Question: Two articles are sold, one at 20% profit and another at 20% loss. Find the overall percentage result if both have equal cost price.
Solution:
Net loss:
= (20 × 20)/100
= 4%
Therefore:
Overall loss = 4%
Example 13: False Weight Problem
Question: A trader uses 900g weight instead of 1kg while claiming no profit. Find his gain percentage.
Solution:
Error:
= 1000 − 900
= 100g
Gain percentage:
= [100/(1000 − 100)] × 100
= 100/900 × 100
= 11.11%
Therefore:
Gain percentage = 11.11%
Example 14: Marked Price and Profit
Question: A shopkeeper marks an article at 2500 and gives a discount of 20%. If the cost price is 1600, find the profit percentage.
Solution:
Selling price:
= 2500 × 80/100
= 2000
Profit:
= 2000 − 1600
= 400
Profit percentage:
= (400/1600) × 100
= 25%
Therefore:
Profit percentage = 25%
Example 15: Overall Profit Percentage
Question: A trader earns 15% profit on one article and 25% profit on another. If the cost prices are equal, find the average profit percentage.
Solution:
Average profit:
= (15 + 25)/2
= 20%
Therefore:
Average profit percentage = 20%
Example 16: Selling at Double Profit
Question: A trader sells an article at 100% profit for 2400. Find the cost price.
Solution:
100% profit means:
SP = 200% of CP
Cost price:
= 2400 × 100/200
= 1200
Therefore:
Cost price = 1200
Example 17: Profit with Overhead Charges
Question: A trader buys an article for 5000 and spends 500 on transport. If he sells it for 6600, find the profit percentage.
Solution:
Actual cost price:
= 5000 + 500
= 5500
Profit:
= 6600 − 5500
= 1100
Profit percentage:
= (1100/5500) × 100
= 20%
Therefore:
Profit percentage = 20%
Example 18: Mixed Profit and Loss Problem
Question: A trader sells two articles for 500 each. On one he gains 25% and on the other he loses 20%. Find the overall profit or loss percentage.
Solution:
First article:
CP = 500 × 100/125
= 400
Second article:
CP = 500 × 100/80
= 625
Total CP:
= 400 + 625
= 1025
Total SP:
= 500 + 500
= 1000
Loss:
= 1025 − 1000
= 25
Loss percentage:
= (25/1025) × 100
≈ 2.44%
Therefore:
Overall loss ≈ 2.44%
Important Exam Tips
- Always calculate profit and loss on Cost Price.
- Memorize direct SP and CP formulas.
- Use successive discount shortcuts whenever possible.
- Be careful while handling overhead charges.
- Remember equal gain-loss formula.
- Practice false weight problems regularly.
- Verify calculations carefully in percentage-based questions.
Practicing solved examples regularly improves conceptual clarity, calculation speed, and accuracy in solving Profit & Loss questions in competitive examinations.