Profit, Loss and Discount

Overview

Profit, Loss and Discount form the backbone of commercial mathematics at the primary level. These concepts connect classroom learning to everyday transactions—buying groceries, selling goods, festival sales—making them highly relatable for young learners. For JKTET Paper I, this topic tests both your computational accuracy and your ability to teach these ideas to Classes I–V students.

Expect questions that involve calculating profit or loss amounts, finding percentages, determining selling price after discount, and occasionally two-step problems combining discount with profit/loss. The pedagogy angle may ask how to introduce these concepts using real-life examples from local markets in Jammu, Kashmir or Ladakh. Mastering the formulae and their logical foundation is essential—rote memorisation without understanding leads to errors in applied problems.

Key Concepts

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

• **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 > CP, the seller earns a profit. Profit = SP − CP.

• **Loss:** When SP < CP, the seller incurs a loss. Loss = CP − SP.

• **Profit/Loss Percentage:** Always calculated on Cost Price (not on SP). This standardises comparison across different transactions.

• **Marked Price (MP):** The price written on the label or tag before any discount is applied. Also called List Price or Catalogue Price.

• **Discount:** Reduction offered on Marked Price. Discount = MP − SP.

• **Discount Percentage:** Calculated on Marked Price, not on CP or SP.

• **Relationship chain:** CP → (add profit or subtract loss) → SP; MP → (subtract discount) → SP.

Formulas / Key Facts

| Concept | Formula | |---------|---------| | Profit | Profit = SP − CP | | Loss | Loss = CP − SP | | Profit % | Profit % = (Profit / CP) × 100 | | Loss % | Loss % = (Loss / CP) × 100 | | SP when profit | SP = CP + Profit = CP × (1 + Profit%/100) | | SP when loss | SP = CP − Loss = CP × (1 − Loss%/100) | | CP from SP and Profit% | CP = SP × 100 / (100 + Profit%) | | CP from SP and Loss% | CP = SP × 100 / (100 − Loss%) | | Discount | Discount = MP − SP | | Discount % | Discount % = (Discount / MP) × 100 | | SP after discount | SP = MP × (1 − Discount%/100) |

**Key facts to remember:**