Basic Terms You Must Know
- Cost Price (CP): The price at which an item is purchased.
- Selling Price (SP): The price at which an item is sold.
- Profit (P): When SP > CP, Profit = SP – CP.
- Loss (L): When CP > SP, Loss = CP – SP.
- Profit Percentage: (Profit / CP) × 100.
- Loss Percentage: (Loss / CP) × 100.
Vedic Math Tricks for Profit and Loss
1. Quick Percentage Calculations
Vedic math simplifies percentage calculations. For example:
- To find 12.5% of a number, divide it by 8.
- To find 37.5% of a number, multiply it by 3/8.
2. Profit and Loss Using Ratios
If the profit percentage is P%, then:
SP / CP = (100 + P) / 100
CP / SP = 100 / (100 + P)
3. Successive Profit and Loss
When there are multiple profits or losses:
Net Effect = a + b + (a × b / 100)
4. Dishonest Dealers and Faulty Weights
If a dealer uses a faulty weight:
Profit % = (Error / (True Weight - Error)) × 100
Real-Life Examples and Applications
1. Discounts and Marked Price
Marked Price (MP): The original price of an item.
Selling Price (SP): MP – Discount.
2. Profit and Loss in Business Partnerships
When two partners invest different amounts for the same time:
Profit Sharing Ratio = Investment Ratio
Shortcuts for Competitive Exams
1. Direct Formula for Profit/Loss Percentage
Profit % = ((SP - CP) / CP) × 100
Loss % = ((CP - SP) / CP) × 100
2. Finding CP When SP and Profit % Are Given
CP = (SP × 100) / (100 + Profit %)
3. Finding SP When CP and Loss % Are Given
SP = (CP × (100 - Loss %)) / 100
Practice Problems with Solutions
Problem 1
A shopkeeper sells a toy at a 10% profit. If the CP is ₹500, find the SP.
Solution:
SP = CP × (1 + Profit % / 100)
SP = 500 × (1 + 10 / 100) = 500 × 1.10 = ₹550
Problem 2
A trader sells a watch at a 20% loss. If the SP is ₹1600, find the CP.
Solution:
CP = SP / (1 - Loss % / 100)
CP = 1600 / (1 - 20 / 100) = 1600 / 0.80 = ₹2000
Problem 3
A dishonest dealer sells goods at a 10% profit but uses a faulty weight of 900g instead of 1kg. Find his actual profit %.
Solution:
Profit % = (Error / (True Weight - Error)) × 100
Profit % = (100 / (1000 - 100)) × 100 = 11.11%
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