In-Depth: Profit, Loss and Discount

CLAT Application & Relevance

Importance: HIGH. This topic is frequently integrated into Data Interpretation sets, particularly those dealing with business financials, sales reports, or economic data. Questions often require you to calculate profit/loss percentages, compare profitability across different years or products, or determine original prices based on given profit/discount.

How it's tested: Identifying profit margins from a company's revenue and cost data (caselet); comparing profit percentages of different products in a table; calculating the selling price after a discount.

Section 1: Core Concepts & Formulas

Profit and Loss concepts are fundamental to understanding financial transactions. Discount is a reduction in the marked price.

Key Definitions

Cost Price (CP): The price at which an item is purchased or manufactured. This is your base for all profit/loss calculations.
Selling Price (SP): The price at which an item is sold.
Marked Price (MP) / List Price: The price at which an article is marked. Discounts are always given on the MP.
Profit (Gain): Occurs when SP > CP.
Loss: Occurs when CP > SP.
Discount: A reduction offered on the Marked Price.

Fundamental Formulas

Crucial Rule: Profit or Loss percentage is ALWAYS calculated on the Cost Price (CP) unless specifically stated otherwise. Discount % is ALWAYS calculated on the Marked Price (MP).

Profit = SP - CP
Loss = CP - SP
Discount = MP - SP
Profit % = (Profit / CP) * 100
Loss % = (Loss / CP) * 100
Discount % = (Discount / MP) * 100

Relationships between Prices and Percentages

If there's Profit: SP = CP * (100 + Profit%) / 100
If there's Loss: SP = CP * (100 - Loss%) / 100
After Discount: SP = MP * (100 - Discount%) / 100
To find CP from SP and Profit/Loss%:
- If Profit: CP = SP * 100 / (100 + Profit%)
- If Loss: CP = SP * 100 / (100 - Loss%)

Section 2: Solved CLAT-Style Examples

Example 1: Calculating Profit/Loss Percentage from a Table

Passage Context: A table shows the financial performance of a legal publishing house for two books:

Book	Cost Price (₹)	Selling Price (₹)
"Legal Insights"	800	1000
"Judicial Review"	1200	1080

Question: "What is the net profit or loss percentage for the publishing house considering both books together?"

Detailed Solution:
1. Calculate Total CP: 800 + 1200 = ₹2000
2. Calculate Total SP: 1000 + 1080 = ₹2080
3. Determine Net Profit/Loss: Since Total SP (2080) > Total CP (2000), there is a net profit.
Net Profit = 2080 - 2000 = ₹80
4. Calculate Net Profit Percentage: (Net Profit / Total CP) * 100
= (80 / 2000) * 100
= (8 / 20) = 4%.
Answer: The net profit percentage for the publishing house is 4%.

Example 2: Discount and Profit Relationship (Caselet)

Passage Context: A legal textbook publisher marks a book 25% above its cost price. They then offer a discount of 10% on the marked price to university students.

Question: "What is the publisher's overall profit percentage on the sale of this book?"

Detailed Solution:
1. Assume a convenient CP: Let CP = ₹100.
2. Calculate Marked Price (MP): Marked 25% above CP.
MP = CP * (100 + Mark-up%) / 100 = 100 * (100 + 25) / 100 = ₹125.
3. Calculate Selling Price (SP) after Discount: Offered 10% discount on MP.
SP = MP * (100 - Discount%) / 100 = 125 * (100 - 10) / 100
SP = 125 * 90 / 100 = 125 * 0.9 = ₹112.50.
4. Calculate Overall Profit: Profit = SP - CP = 112.50 - 100 = ₹12.50.
5. Calculate Overall Profit Percentage: (Profit / CP) * 100
= (12.50 / 100) * 100 = 12.5%.
Answer: The publisher's overall profit percentage is 12.5%.