CAT Prep: Profit, Loss, and Discount

Profit, Loss, and Discount - CAT Study Notes

1. Core Concepts and Definitions

2. Basic Formulas and Percentage Relationships

3. Discount and Marked Price

4. Advanced Concepts and Shortcuts

4.1. Relationship between CP and MP for a given Profit/Loss

When an article is sold after a discount, the profit/loss is based on CP, but the discount is based on MP. The key equation is:

4.2. Faulty Weights (Cheating the Customer)

4.3. Two Articles Sold at Same Selling Price

If two items are sold at the same SP, one at a profit of x% and the other at a loss of x%, there is always an overall loss.

4.4. Successive Profit/Loss Transactions

When an article is sold multiple times, each transaction's SP becomes the next transaction's CP.

5. Common CAT Problem Types & Strategies

Type 1: Finding CP when SP and Profit/Loss % are given after Discount

Strategy: Assume CP = 100 (or any convenient number) and work step-by-step via MP and discount.

Type 2: Maximizing Discount/Minimizing Cost Problems

Strategy: Compare final prices after applying different discount schemes (e.g., flat discount vs. successive discounts).

Type 3: Data Sufficiency in Profit/Loss

Strategy: Remember you need a relationship between CP, SP, MP, and any percentage to find profit%. Often, two statements connecting these variables are needed.

6. Quick Strategy for CAT Exam

When to Attempt: Most basic and moderate P&L questions are speed-setters. Attempt if the relationship between variables is clear. Questions involving only one transaction (CP, SP, P%) are usually quick.

When to Skip/Be Cautious: Skip lengthy word problems with multiple successive transactions, partnerships, or complex faulty weight problems if they seem to have many steps, unless you are very comfortable. Be cautious with Data Sufficiency questions; ensure you are not making assumptions.

Time Allocation: A straightforward P&L question should take 60-90 seconds. A moderate one with discount and profit may take 2 minutes. Hard ones (involving multiple conditions/algebra) allocate max 2.5 minutes, otherwise mark for review.

Mental Math Shortcuts:

Memorize fraction equivalents: 25% = 1/4, 20% = 1/5, 10% = 1/10, etc. This makes CP/SP calculations faster.
For successive discounts a% and b%, quickly calculate a*b/100 and subtract from a+b.
For profit/loss on selling two items at same SP, use (x^2/100)% loss directly.

[VIDEO: "CAT Profit Loss Discount successive transactions shortcut"]

[VIDEO: "CAT faulty weights profit percentage trick"]

[IMAGE: "Flowchart: Relationship between CP, MP, SP, Discount, and Profit"]

Profit and Loss, Discount