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