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]