Lesson 1.5: Profit, Loss, Discount
Introduction:
Profit, loss, and discount are basic concepts in arithmetic, frequently tested in SSC exams. These concepts are applied in trade, commerce, and DI (Data Interpretation) questions.
1. Profit
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Definition: Profit occurs when Selling Price (SP) > Cost Price (CP).
Profit=SP−CP\text{Profit} = SP – CP
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Profit Percentage:
Profit %=ProfitCP×100\text{Profit \%} = \frac{\text{Profit}}{\text{CP}} \times 100
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Example:
CP = ₹500, SP = ₹600 → Profit = 600 – 500 = ₹100
Profit % = (100 / 500) × 100 = 20%
2. Loss
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Definition: Loss occurs when CP > SP.
Loss=CP−SP\text{Loss} = CP – SP
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Loss Percentage:
Loss %=LossCP×100\text{Loss \%} = \frac{\text{Loss}}{\text{CP}} \times 100
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Example:
CP = ₹800, SP = ₹700 → Loss = 800 – 700 = ₹100
Loss % = (100 / 800) × 100 = 12.5%
3. Discount
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Definition: Discount is the reduction in price offered by a seller.
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Discount Formula:
Discount=Marked Price (MP)−Selling Price (SP)\text{Discount} = \text{Marked Price (MP)} – \text{Selling Price (SP)}
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Discount Percentage:
Discount %=DiscountMP×100\text{Discount \%} = \frac{\text{Discount}}{\text{MP}} \times 100
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Example:
MP = ₹1000, SP = ₹900 → Discount = 100
Discount % = (100 / 1000) × 100 = 10%
4. Key SSC Tricks
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If Profit % = Loss %, the difference in CP and SP can be found easily using ratio methods.
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Shortcut:
SP=CP×(1+Profit %100)SP = CP \times \left(1 + \frac{\text{Profit \%}}{100}\right) SP=CP×(1−Loss %100)SP = CP \times \left(1 – \frac{\text{Loss \%}}{100}\right)
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For successive discounts:
Net Discount%=D1+D2−D1×D2100Net \, Discount \% = D_1 + D_2 – \frac{D_1 \times D_2}{100}
5. Practice Questions
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CP = ₹250, SP = ₹300. Find profit and profit %.
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CP = ₹800, SP = ₹720. Find loss and loss %.
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MP = ₹500, discount = 10%. Find SP.
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A shopkeeper gives two successive discounts of 10% and 20% on an item of MP ₹1000. Find the net price.
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CP = ₹600, SP = ₹660. Find profit %. If the SP was ₹540, find loss %.