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:**

• Profit% and Loss% are always computed on CP.
• Discount% is computed on MP.
• If SP = CP, there is no profit and no loss.
• Successive discounts are not simply added; they must be applied one after another.

Worked Examples

**Example 1: Basic Profit Calculation**

A shopkeeper buys a shawl for ₹800 and sells it for ₹920. Find the profit and profit percentage.

*Solution:*

• CP = ₹800, SP = ₹920
• Profit = SP − CP = 920 − 800 = ₹120
• Profit % = (120 / 800) × 100 = 15%

**Example 2: Finding SP from Loss Percentage**

A trader buys apples for ₹500. Due to damage, he sells them at 12% loss. Find the selling price.

*Solution:*

• CP = ₹500, Loss% = 12%
• Loss = (12/100) × 500 = ₹60
• SP = CP − Loss = 500 − 60 = ₹440

Alternatively: SP = 500 × (1 − 12/100) = 500 × 0.88 = ₹440

**Example 3: Discount and Selling Price**

A jacket is marked at ₹1,200. A shop offers 20% discount during a winter sale. Find the discount amount and selling price.

*Solution:*

• MP = ₹1,200, Discount% = 20%
• Discount = (20/100) × 1200 = ₹240
• SP = MP − Discount = 1200 − 240 = ₹960

**Example 4: Combined Problem (Discount + Profit)**

A shopkeeper buys a bag for ₹400 and marks it at ₹600. He gives 10% discount to a customer. Find his profit percentage.

*Solution:*

• CP = ₹400, MP = ₹600, Discount% = 10%
• Discount = (10/100) × 600 = ₹60
• SP = 600 − 60 = ₹540
• Profit = SP − CP = 540 − 400 = ₹140
• Profit % = (140 / 400) × 100 = 35%

Common Mistakes

1. **Calculating percentages on the wrong base.**

• Wrong: Computing profit% on SP or discount% on CP.
• Correct: Profit% and Loss% are always on CP; Discount% is always on MP.

2. **Confusing Marked Price with Cost Price.**

• Wrong: Assuming MP is what the seller paid.
• Correct: MP is the tag price; CP is the purchase price. They are independent.

3. **Adding successive discounts directly.**

• Wrong: Two discounts of 10% and 5% treated as 15%.
• Correct: Apply 10% first, then 5% on the reduced amount. Effective discount < 15%.

4. **Forgetting to convert percentage to decimal or fraction.**

• Wrong: Writing SP = CP × (1 + 20) instead of (1 + 0.20).
• Correct: Always divide percentage by 100 before using in formulae.

5. **Sign errors in loss problems.**

• Wrong: Adding loss to CP to get SP.
• Correct: SP = CP − Loss (since loss means selling below cost).

Quick Reference

• **Profit = SP − CP; Loss = CP − SP.**
• **Profit% = (Profit/CP) × 100; Loss% = (Loss/CP) × 100.**
• **Discount% = (Discount/MP) × 100.**
• **SP after discount = MP × (100 − Discount%)/100.**
• **Base for Profit/Loss → CP; Base for Discount → MP.**
• **No profit, no loss ⇒ SP = CP.**