Profit Loss : Let's Make it Easy with Quiz
Profit and Loss: Concepts, Formulas & Practice Arena
Master cost price, selling price, discounts, and percentage shortcuts with verified board solutions and interactive mock tests.
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1. Essential Terminology
- Cost Price (CP): The exact amount paid to purchase an article, including any overhead expenses (repairs, transport).
- Selling Price (SP): The price at which an article is sold to the consumer.
- Marked Price (MP): The printed or list price tagged on the product before discounts.
- Profit (Gain): Occurs when the Selling Price is strictly greater than the Cost Price ($SP > CP$).
- Loss: Occurs when the Selling Price is less than the Cost Price ($SP < CP$).
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2. Comprehensive Formula Bank
Profit & Loss Amount
Profit = SP − CP
Loss = CP − SP
Loss = CP − SP
Percentage Values
Profit % = (Profit ÷ CP) × 100
Loss % = (Loss ÷ CP) × 100
Loss % = (Loss ÷ CP) × 100
Direct SP Calculation
SP = [ (100 + Gain%) ÷ 100 ] × CP
SP = [ (100 − Loss%) ÷ 100 ] × CP
SP = [ (100 − Loss%) ÷ 100 ] × CP
Direct CP Calculation
CP = [ 100 ÷ (100 + Gain%) ] × SP
CP = [ 100 ÷ (100 − Loss%) ] × SP
CP = [ 100 ÷ (100 − Loss%) ] × SP
Marked Price & Discount
Discount = MP − SP
Discount % = (Discount ÷ MP) × 100
Discount % = (Discount ÷ MP) × 100
Combined Shortcut Ratio
CP × (100 + Gain%) = MP × (100 − Disc%)
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3. Worked Conceptual Example
Problem: An article marked at ₹1,500 is sold at a 20% discount, yielding an overall 20% profit. What was its Cost Price?
Step 1: Determine Selling Price (SP)
Discount = 20% of ₹1,500 = ₹300 &implies; $SP = 1,500 - 300 = ₹1,200$.
Step 2: Determine Cost Price (CP) using Gain %
$CP = [ 100 ÷ (100 + 20) ] \times 1,200 = (100 / 120) \times 1,200 = ₹1,000$.
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