Profit and Loss — Study Notes

Overview

Profit and Loss is a high-weightage topic in SSC GD Elementary Mathematics. Nearly every year, you will face 2–4 direct questions on cost price (CP), selling price (SP), marked price (MP), discount, and profit/loss percentage. These problems test your ability to quickly manipulate percentages and understand commercial arithmetic.

The core concept is simple: a shopkeeper buys goods at CP and sells at SP. The difference determines profit or loss. Real-world complications like marked price, discount, and successive transactions add layers, but the fundamentals remain unchanged. Mastering the standard formulas and recognizing problem patterns will fetch you easy marks.

Focus on speed and accuracy. Most questions require 2–3 step calculations. Practice mental percentage conversions (like 20% = 1/5, 25% = 1/4) to save precious seconds during the exam.

Key Concepts

• **Cost Price (CP)** is the amount paid to acquire an article. It includes purchase price plus any additional expenses like transport or repair (called overhead expenses).

• **Selling Price (SP)** is the amount received when the article is sold. Profit or loss is always calculated on the CP, not the SP.

• **Profit** occurs when SP > CP. Profit = SP − CP. Profit percentage = (Profit / CP) × 100.

• **Loss** occurs when SP < CP. Loss = CP − SP. Loss percentage = (Loss / CP) × 100.

• **Marked Price (MP)** is the price tag displayed on the article, often higher than CP. The seller announces discounts on this marked price.

• **Discount** is a reduction given on the marked price. Discount = MP − SP. Discount percentage is always calculated on MP: Discount% = (Discount / MP) × 100.

• In real transactions, first apply discount to MP to get SP, then compare SP with CP to find profit or loss. The two steps are independent.

• **Successive transactions**: If an article passes through multiple hands (A → B → B → C), calculate each person's gain/loss separately using their individual CP and SP.

Formulas / Key Facts

1. **Profit = SP − CP**; **Loss = CP − SP**

2. **Profit% = (Profit / CP) × 100 = [(SP − CP) / CP] × 100**

3. **Loss% = (Loss / CP) × 100 = [(CP − SP) / CP] × 100**

4. **SP = CP × (100 + Profit%) / 100** when profit is given.

5. **SP = CP × (100 − Loss%) / 100** when loss is given.

6. **CP = (SP × 100) / (100 + Profit%)** when SP and profit% are given.

7. **CP = (SP × 100) / (100 − Loss%)** when SP and loss% are given.