Profit, Loss and Discount

Overview

Profit, Loss and Discount forms a crucial component of commercial mathematics in the OTET Paper I syllabus. This topic tests a candidate's ability to apply basic arithmetic operations to real-life buying and selling scenarios—something primary teachers must master to help young learners connect mathematics with everyday transactions.

In OTET, questions from this topic typically involve straightforward calculations of profit percentage, loss percentage, selling price, cost price, and discount. The difficulty level remains appropriate for primary mathematics, but the conceptual clarity required is high. Teachers need to understand these concepts deeply enough to explain them to children using relatable examples like shop transactions, market purchases, and festival sales.

Mastering this topic also builds a foundation for related concepts like simple interest and percentage, making it essential for overall exam success in the mathematics section.

Key Concepts

• **Cost Price (CP)**: The price at which an article is purchased or manufactured. This is the baseline for all profit/loss calculations.

• **Selling Price (SP)**: The price at which an article is sold to a customer. Comparison of SP with CP determines 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, also called list price or catalogue price. This is the price before any discount is applied.

• **Discount**: The reduction offered on the marked price. Discount = MP − SP. Discount is always calculated on MP, not on CP.

• **Successive Discounts**: When two or more discounts are applied one after another on the reduced price, not on the original marked price.

• **Break-even Point**: When SP equals CP, there is neither profit nor loss.

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 — when there is profit
• SP = CP × (100 − Loss%) / 100 — when there is loss

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

• CP = SP × 100 / (100 + Profit%) — when there is profit
• CP = SP × 100 / (100 − Loss%) — when there is loss

**Discount Formulas:**

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

**Important Facts:**

• Profit and loss percentages are always calculated on Cost Price
• Discount percentage is always calculated on Marked Price
• If an article is sold at cost price, profit = 0% and loss = 0%
• Two successive discounts of a% and b% equal a single discount of: a + b − (a × b)/100 percent

Worked Examples

**Example 1: Finding Profit Percentage**

A shopkeeper buys a toy for ₹80 and sells it for ₹100. Find the profit percentage.

*Solution:*

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

**Answer: 25% profit**

**Example 2: Finding Selling Price with Loss**

A fruit seller buys oranges for ₹500 and sells them at 10% loss. Find the selling price.

*Solution:*

• CP = ₹500, Loss% = 10%
• SP = CP × (100 − Loss%) / 100
• SP = 500 × (100 − 10) / 100 = 500 × 90 / 100 = ₹450

**Answer: ₹450**

**Example 3: Discount Calculation**

A shirt has a marked price of ₹600. The shopkeeper offers a 15% discount. Find the selling price and discount amount.

*Solution:*

• MP = ₹600, Discount% = 15%
• Discount = MP × Discount% / 100 = 600 × 15 / 100 = ₹90
• SP = MP − Discount = 600 − 90 = ₹510

**Answer: Discount = ₹90, SP = ₹510**

**Example 4: Combined Problem (Profit after Discount)**

A trader marks his goods 25% above cost price and allows a 10% discount. Find his profit percentage.

*Solution:*

• Let CP = ₹100
• MP = 100 + 25% of 100 = ₹125
• Discount = 10% of 125 = ₹12.50
• SP = 125 − 12.50 = ₹112.50
• Profit = SP − CP = 112.50 − 100 = ₹12.50
• Profit % = (12.50 / 100) × 100 = 12.5%

**Answer: 12.5% profit**

Common Mistakes

• **Calculating profit/loss percentage on SP instead of CP** → Always remember: profit and loss percentages are calculated on Cost Price, not Selling Price.

• **Calculating discount percentage on CP or SP** → Discount percentage is always calculated on Marked Price. The formula uses MP in the denominator, not CP.

• **Adding successive discounts directly** → Two discounts of 10% and 20% do not equal 30%. Apply the first discount, then apply the second discount on the reduced price. Use the formula: a + b − (ab)/100.

• **Confusing Marked Price with Selling Price** → MP is the labelled price before discount; SP is the actual price paid after discount. They are equal only when no discount is given.

• **Forgetting to convert percentage to decimal or fraction** → When calculating, convert 25% to 25/100 or 0.25. Many errors occur due to incorrect conversion.

• **Ignoring the direction of comparison** → For profit, SP must be greater than CP. For loss, CP must be greater than SP. Mixing these up leads to sign errors.

Quick Reference

• **Profit = SP − CP; Loss = CP − SP** — direction matters
• **Profit/Loss % always on CP; Discount % always on MP**
• **SP with profit: CP × (100 + P%) / 100**
• **SP with loss: CP × (100 − L%) / 100**
• **SP after discount: MP × (100 − D%) / 100**
• **No profit, no loss: SP = CP**