Profit, Loss and Discount

Overview

Profit, Loss and Discount form the backbone of commercial mathematics and appear consistently in HP TET Mathematics sections. These concepts test your ability to apply percentage calculations to real-world trading scenarios—buying, selling, calculating gains or losses, and understanding how discounts affect final prices.

For HP TET, you must be comfortable with quick mental calculations involving cost price, selling price, marked price, and successive discounts. Questions typically involve straightforward formula application but may include twists like dishonest dealers, successive discounts, or finding the cost price when profit/loss percentages are given. Mastering this topic also strengthens your foundation for teaching commercial mathematics to elementary students using relatable market examples.

The key to success is understanding the relationships between different prices and always being clear about which price forms the base for percentage calculations—a common source of errors.

Key Concepts

• **Cost Price (CP)**: The price at which an article is purchased or manufactured. This is always the base for calculating profit or loss percentage.

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

• **Marked Price (MP)**: The price displayed on an article (also called list price or catalogue price). Discount is always calculated on MP, not on CP.

• **Profit occurs when SP > CP**; Loss occurs when SP < CP. The difference gives the absolute profit or loss amount.

• **Discount is a reduction from Marked Price** to arrive at Selling Price. A seller may still make profit even after giving discount if MP is sufficiently above CP.

• **Successive Discounts**: When multiple discounts are applied one after another, each discount is calculated on the reduced price from the previous discount, not on the original MP.

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

Formulas / Key Facts

**Basic Profit and Loss:**

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

**Finding SP from CP:**

• SP = CP × (100 + Profit%) / 100
• SP = CP × (100 − Loss%) / 100

**Finding CP from SP:**

• CP = SP × 100 / (100 + Profit%)