Profit, Loss and Discount

Overview

Profit, Loss and Discount form the cornerstone of commercial mathematics at the primary level. These concepts connect classroom learning directly to real-life transactions—buying vegetables at the market, festival sales, or running a small shop. For Assam TET Paper I, this topic tests your ability to calculate gains and losses in simple transactions and apply percentage-based discounts.

Questions typically involve straightforward numerical problems requiring you to find cost price, selling price, profit or loss percentage, or the final price after discount. The syllabus expects familiarity with basic formulas and their direct application rather than complex multi-step problems. Mastering this topic also builds the foundation for Simple Interest, which follows logically in the syllabus.

Understanding these concepts helps future primary teachers demonstrate practical mathematics to young learners using everyday examples from Assam's markets, tea gardens, and local businesses.

Key Concepts

• **Cost Price (CP)**: The price at which an article is purchased or the total expense incurred to acquire goods. This is your baseline for calculating profit or loss.

• **Selling Price (SP)**: The price at which an article is sold to a customer. Comparing SP with CP determines whether there is profit or loss.

• **Profit (Gain)**: When SP is greater than CP, the difference is called profit. Profit = SP − CP.

• **Loss**: When CP is greater than SP, the difference is called loss. Loss = CP − SP.

• **Marked Price (MP)**: The price written on the label or tag of an article before any discount is applied. Also called list price or catalogue price.

• **Discount**: The reduction given on the marked price to attract customers. Discount = MP − SP.

• **Profit and Loss are always calculated on Cost Price**: This is a fundamental rule. Percentage calculations use CP as the base, not SP.

• **Discount is always calculated on Marked Price**: Unlike profit/loss, discount percentage uses MP as the base.

Formulas / Key Facts

**Basic Profit and Loss Formulas:**

• Profit = SP − CP (when SP > CP)
• Loss = CP − SP (when CP > SP)
• Profit Percentage = (Profit / CP) × 100
• Loss Percentage = (Loss / CP) × 100

**Finding SP when Profit/Loss Percentage is given:**

• SP = CP × (100 + Profit%) / 100 [for profit]
• SP = CP × (100 − Loss%) / 100 [for loss]

**Finding CP when Profit/Loss Percentage is given:**

• CP = SP × 100 / (100 + Profit%) [for profit]
• CP = SP × 100 / (100 − Loss%) [for loss]

**Discount Formulas:**

• Discount = MP − SP
• Discount Percentage = (Discount / MP) × 100
• SP = MP × (100 − Discount%) / 100

**Key Facts to Remember:**

• No profit, no loss means SP = CP
• Two successive discounts of a% and b% give effective discount = a + b − (ab/100)
• If an article is sold at the same price at which it was bought, profit = loss = 0%

Worked Examples

**Example 1: Basic Profit Calculation**

A shopkeeper buys a bicycle for ₹2,500 and sells it for ₹2,800. Find the profit and profit percentage.

*Solution:*

• CP = ₹2,500, SP = ₹2,800
• Profit = SP − CP = 2,800 − 2,500 = ₹300
• Profit% = (Profit / CP) × 100 = (300 / 2,500) × 100 = 12%

**Example 2: Finding SP at a Given Loss**

A trader bought mangoes for ₹800 and had to sell them at 15% loss due to spoilage. Find the selling price.

*Solution:*

• CP = ₹800, Loss% = 15%
• SP = CP × (100 − Loss%) / 100
• SP = 800 × (100 − 15) / 100 = 800 × 85 / 100 = ₹680

**Example 3: Discount Problem**

A shirt has a marked price of ₹600. The shopkeeper offers a 20% discount. Find the discount amount and selling price.

*Solution:*

• MP = ₹600, Discount% = 20%
• Discount = (20 / 100) × 600 = ₹120
• SP = MP − Discount = 600 − 120 = ₹480

Alternatively: SP = 600 × (100 − 20) / 100 = 600 × 80 / 100 = ₹480

**Example 4: Combined Problem**

A book is marked at ₹250. After giving a 10% discount, the shopkeeper still makes a 12.5% profit. Find the cost price.

*Solution:*

• MP = ₹250, Discount% = 10%, Profit% = 12.5%
• SP = 250 × (100 − 10) / 100 = 250 × 90 / 100 = ₹225
• CP = SP × 100 / (100 + Profit%) = 225 × 100 / 112.5 = ₹200

Common Mistakes

• **Calculating profit% on SP instead of CP** → Always remember: Profit and Loss percentages are calculated on Cost Price only. The formula uses CP in the denominator, never SP.

• **Calculating discount% on SP instead of MP** → Discount percentage is always calculated on Marked Price. The tag price is your base for discount calculations.

• **Confusing Marked Price with Cost Price** → MP is what the seller writes on the tag (often inflated). CP is what the seller actually paid. These are different amounts.

• **Adding percentages directly in successive discounts** → Two discounts of 10% and 20% do not equal 30% discount. Use the formula: effective discount = 10 + 20 − (10 × 20)/100 = 28%.

• **Forgetting to convert percentage to decimal or fraction** → When calculating, either divide by 100 or use the fraction form. Writing 20% as 20 in multiplication gives absurd results.

Quick Reference

• Profit = SP − CP; Loss = CP − SP
• Profit% and Loss% are always on CP
• Discount% is always on MP
• SP = CP × (100 ± Profit or Loss%) / 100
• SP after discount = MP × (100 − Discount%) / 100
• No profit no loss: SP = CP