Profit, Loss and Discount

Overview

Profit, Loss and Discount forms the backbone of commercial mathematics at the primary level. This topic connects classroom learning directly to everyday transactions—buying groceries, selling items at a fair, or understanding shop discounts during festivals. For JTET Paper I, questions test both computational accuracy and conceptual clarity about how these terms relate to each other.

Students must understand the relationship between Cost Price (CP), Selling Price (SP), Marked Price (MP), and how profit, loss and discount percentages are calculated. Questions typically involve straightforward calculations but require careful attention to which price serves as the base for percentage computation. Mastery here also builds foundation for simple interest and ratio-proportion problems.

Expect 2–4 questions from this topic, often integrated with percentage calculations. Word problems dominate, requiring students to extract relevant data and apply the correct formula.

Key Concepts

• **Cost Price (CP)** is the price at which an item is bought or manufactured. All profit/loss calculations use CP as the base.

• **Selling Price (SP)** is the price at which an item is sold. Comparing SP with CP determines profit or loss.

• **Profit occurs when SP > CP.** The seller earns more than what was spent.

• **Loss occurs when SP < CP.** The seller receives less than what was spent.

• **Marked Price (MP)** is the price printed/labelled on an item before any discount. It is also called the list price or catalogue price.

• **Discount** is the reduction offered on MP. Discount is always calculated on MP, not on CP.

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

• **Break-even** means no profit, no loss—when SP exactly equals CP.

Formulas / Key Facts

| Concept | Formula | |---------|---------| | Profit | Profit = SP − CP | | Loss | Loss = CP − SP | | Profit Percentage | Profit % = (Profit / CP) × 100 | | Loss Percentage | Loss % = (Loss / CP) × 100 | | SP when Profit % is given | SP = CP × (100 + Profit%) / 100 | | SP when Loss % is given | SP = CP × (100 − Loss%) / 100 | | Discount | Discount = MP − SP | | Discount Percentage | Discount % = (Discount / MP) × 100 | | SP after Discount | SP = MP × (100 − Discount%) / 100 | | Successive Discounts (a% and b%) | Net SP = MP × (100 − a)/100 × (100 − b)/100 |

**Key facts to remember:**

• Profit % and Loss % are always calculated on CP.