Profit, Loss and Discount

Overview

Profit, Loss and Discount forms the core of commercial mathematics in the CG TET Paper I Mathematics section. This topic tests your ability to apply basic arithmetic operations to real-world buying and selling scenarios—skills that primary teachers must impart to young learners through relatable, everyday examples.

For CG TET, questions typically involve straightforward calculations: finding profit or loss percentage, calculating selling price from cost price, or determining the final price after a discount. The focus is on conceptual clarity rather than complex multi-step problems. Understanding this topic also builds the foundation for teaching children about money, transactions, and basic financial literacy.

Mastery requires a firm grip on the relationship between Cost Price, Selling Price, Marked Price, and the percentages linking them. Most errors occur when students confuse which price serves as the base for percentage calculations.

Key Concepts

• **Cost Price (CP)**: The price at which a goods is purchased or manufactured. This is always the reference point for calculating profit or loss.

• **Selling Price (SP)**: The price at which goods are sold to a customer. Compare SP with CP to determine profit or loss.

• **Profit occurs when SP > CP**; the seller gains money. Loss occurs when SP < CP; the seller loses money.

• **Marked Price (MP)**: The price written on the label or tag before any discount. Also called List Price or Catalogue Price.

• **Discount**: Reduction given on the Marked Price. Discount is always calculated on MP, not on CP.

• **Profit and Loss percentages are always calculated on Cost Price** as the base, while Discount percentage is calculated on Marked Price as the base.

• **Successive discounts** are not additive—apply each discount one after the other on the reduced price.

• In break-even situations (no profit, no loss), SP = CP.

Formulas / Key Facts

| Concept | Formula | |---------|---------| | Profit | Profit = SP − CP | | Loss | Loss = CP − SP | | Profit % | Profit % = (Profit / CP) × 100 | | Loss % | Loss % = (Loss / CP) × 100 | | SP when Profit % given | SP = CP × (100 + Profit%) / 100 | | SP when Loss % given | SP = CP × (100 − Loss%) / 100 | | CP from SP and Profit % | CP = SP × 100 / (100 + Profit%) | | CP from SP and Loss % | CP = SP × 100 / (100 − Loss%) | | Discount | Discount = MP − SP | | Discount % | Discount % = (Discount / MP) × 100 | | SP after Discount | SP = MP × (100 − Discount%) / 100 | | Two successive discounts a% and b% | Equivalent single discount = a + b − (ab/100) % |

**Key fact**: When an article is sold at the same price it was bought, Profit % = Loss % = 0.

Worked Examples

### Example 1: Finding Profit and Profit % A shopkeeper buys a toy for ₹80 and sells it for ₹100. Find the profit and profit percentage.

**Solution**:

• CP = ₹80, SP = ₹100
• Profit = SP − CP = 100 − 80 = ₹20
• Profit % = (Profit / CP) × 100 = (20 / 80) × 100 = 25%

**Answer**: Profit = ₹20, Profit % = 25%

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### Example 2: Finding SP when Loss % is given A book was purchased for ₹150 and sold at a loss of 10%. Find the selling price.

**Solution**:

• CP = ₹150, Loss % = 10%
• SP = CP × (100 − Loss%) / 100
• SP = 150 × (100 − 10) / 100 = 150 × 90 / 100 = ₹135

**Answer**: SP = ₹135

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### Example 3: Discount Calculation A shirt has a marked price of ₹500. A discount of 20% is offered. Find the selling price and the discount amount.

**Solution**:

• MP = ₹500, Discount % = 20%
• Discount = MP × Discount% / 100 = 500 × 20 / 100 = ₹100
• SP = MP − Discount = 500 − 100 = ₹400

**Answer**: Discount = ₹100, SP = ₹400

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### Example 4: Successive Discounts A bag with MP ₹1000 is offered discounts of 10% and then 20%. Find the final selling price.

**Solution**:

• After first discount (10%): Price = 1000 × 90 / 100 = ₹900
• After second discount (20% on ₹900): Price = 900 × 80 / 100 = ₹720

**Alternative using formula**:

• Equivalent discount = 10 + 20 − (10 × 20 / 100) = 30 − 2 = 28%
• SP = 1000 × 72 / 100 = ₹720

**Answer**: Final SP = ₹720

Common Mistakes

| Wrong Thinking | Correct Fix | |----------------|-------------| | Calculating Profit % on SP instead of CP | Always use CP as the base for profit/loss percentages. Memory aid: "Profit and Loss live at Cost's house." | | Adding successive discounts directly (10% + 20% = 30%) | Apply discounts sequentially, or use the formula: a + b − ab/100. Successive 10% and 20% gives 28%, not 30%. | | Calculating Discount % on CP | Discount is always on Marked Price (the label price), never on cost price. | | Confusing MP with SP when discount is involved | Remember: MP is before discount, SP is after discount. The relationship is SP = MP − Discount. | | Forgetting to convert percentage to decimal or fraction | When using (100 + x)/100, ensure proper division. Example: 25% profit means multiply CP by 125/100 or 1.25. |

Quick Reference

• **Profit/Loss % base = Cost Price; Discount % base = Marked Price**

• SP > CP → Profit; SP < CP → Loss; SP = CP → No profit, No loss

• SP = CP × (100 ± Profit or Loss %) / 100

• SP = MP × (100 − Discount %) / 100

• Two discounts a% and b% together = (a + b − ab/100)%

• No discount means SP = MP; 100% loss means SP = 0