Commercial Mathematics

Overview

Commercial Mathematics forms a significant portion of the WB TET Paper II Mathematics section, testing your ability to apply arithmetic concepts to real-world financial scenarios. This topic bridges abstract number operations with practical situations involving buying, selling, borrowing and lending — skills every upper-primary teacher must convey clearly to students.

Expect 3–5 questions from this topic, typically presented as word problems requiring you to calculate profit percentages, find selling prices after discount, or compare simple and compound interest amounts. Mastery here demands not just formula recall but the ability to quickly identify what quantity is being asked and which base value (cost price, marked price, principal) to use for percentage calculations.

The concepts interlink tightly: discount problems use the same percentage logic as profit/loss, and compound interest builds upon simple interest. A student who grasps the underlying percentage framework can handle all variations confidently.

Key Concepts

• **Cost Price (CP)** is the price at which an article is purchased; **Selling Price (SP)** is the price at which it is sold. Profit or loss is always calculated on CP.

• **Profit** occurs when SP > CP; **Loss** occurs when SP < CP. Profit% and Loss% are always expressed as a percentage of CP, never of SP.

• **Marked Price (MP)** is the price displayed on an article before any discount. Discount is calculated on MP, not on CP.

• **Successive discounts** are applied one after another on the reduced price, not added together on the original marked price.

• **Simple Interest (SI)** is calculated on the original principal only, remaining constant each year for a fixed rate.

• **Compound Interest (CI)** is calculated on the principal plus accumulated interest, so interest "earns interest" in subsequent periods.

• **The difference between CI and SI for 2 years** equals P × (R/100)², a frequently tested shortcut.

• **Effective rate** in compound interest increases with more frequent compounding (half-yearly, quarterly).

Formulas / Key Facts

**Profit and Loss**

• Profit = SP − CP
• Loss = CP − SP
• Profit% = (Profit / CP) × 100
• Loss% = (Loss / CP) × 100
• SP = CP × (100 + Profit%) / 100 — when profit is made
• SP = CP × (100 − Loss%) / 100 — when loss is made
• If a trader uses false weights: Gain% = (Error / True Value − Error) × 100