Video Lecture 1: Fractions in Disguise — Percentages, Discounts and Commercial Margins

# Video Lecture 1: Fractions in Disguise — Percentages, Discounts and Commercial Margins
**Speaker:** Prof. Arvind Swaminathan | **Duration:** ~05:50 mins

### Introduction: The Disguise of Fractions
What is a percentage? The word *percent* comes from the Latin *per centum*, meaning "out of one hundred."
A percentage is simply a fraction whose denominator is locked at $100$:
$$25\% = \frac{25}{100} = \frac{1}{4}$$

### 1. Marked Price ($MP$) and Discounts:
Retailers mark up goods with a **Marked Price ($MP$)** and offer a **Discount** to attract buyers:
$$\text{Discount} = \text{Marked Price} - \text{Selling Price}$$
$$\text{Discount}\% = \frac{\text{Discount}}{\text{Marked Price}} \times 100\%$$
Always remember: **Discount is ALWAYS calculated on the Marked Price**, never on the cost price!

### 2. Profit and Loss:
- **Cost Price ($CP$):** The buying price + overhead expenses (transportation, repairs).
- **Selling Price ($SP$):** The price at which the article is sold.
- If $SP > CP \implies \text{Profit} = SP - CP$
- If $CP > SP \implies \text{Loss} = CP - SP$
- **Profit / Loss Percentage:** ALWAYS calculated on the **Cost Price ($CP$)**:
$$\text{Profit}\% = \frac{\text{Profit}}{CP} \times 100\%, \quad \text{Loss}\% = \frac{\text{Loss}}{CP} \times 100\%$$