Profit and Loss Solved Problems (With Detailed Solutions)
Profit and Loss is one of the most important arithmetic topics used in daily life and competitive examinations. It deals with transactions involving buying and selling of goods and helps understand financial gain or loss.
In this article, we will cover all fundamental concepts of profit and loss and solve multiple problems step by step for better understanding.
Important Definitions
- Cost Price (CP): Price at which an item is purchased
- Selling Price (SP): Price at which an item is sold
- Profit: When SP > CP
- Loss: When SP < CP
- Profit %: (Profit / CP) × 100
- Loss %: (Loss / CP) × 100
Solved Profit & Loss Problems
Problem 1: A shopkeeper buys a pen for ₹20 and sells it for ₹25. Find the profit.
Solution:
Cost Price (CP) = ₹20 Selling Price (SP) = ₹25
Profit = SP − CP = 25 − 20 = ₹5
Profit = ₹5
Problem 2: A book is sold for ₹180 at a loss of ₹20. Find the cost price.
Solution:
Selling Price (SP) = ₹180 Loss = ₹20
Cost Price = SP + Loss = 180 + 20 = ₹200
Cost Price = ₹200
Problem 3: A trader buys an article for ₹400 and sells it at a profit of 10%. Find the selling price.
Solution:
Cost Price (CP) = ₹400 Profit % = 10%
Profit = (10 / 100) × 400 = ₹40
Selling Price = CP + Profit = 400 + 40 = ₹440
Selling Price = ₹440
Problem 4: An article is sold for ₹540 at a loss of 10%. Find the cost price.
Solution:
Loss % = 10% Selling Price = ₹540
CP = (100 / 90) × SP = (100 / 90) × 540 = ₹600
Cost Price = ₹600
Problem 5: If a person gains 20% by selling an article for ₹600, find the cost price.
Solution:
Profit % = 20% Selling Price = ₹600
CP = (100 / 120) × SP = (100 / 120) × 600 = ₹500
Cost Price = ₹500
Common Errors to Avoid
- Using selling price instead of cost price in percentage calculation
- Confusing profit and loss formulas
- Ignoring percentage conversions
- Calculation mistakes with fractions
Exam Tips
✔ Always identify CP and SP clearly
✔ Use shortcut formulas for percentage problems
✔ Double-check percentage base (CP vs SP)
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