Profit, Loss and Discount

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

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

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