Profit Loss Discount | Session 01 | Basic to Advanced | CAT - Arithmetic | Udit Saini #cat2024

Summary

Udit Saini introduces profit, loss, and discount, starting with basic definitions and applying them to exam-style questions. He recommends studying percentages first, since percentage calculations and fraction conversions are used throughout the topic.

Core concepts and formulas

• Cost Price (CP): The amount spent to make or acquire an item.
• Selling Price (SP): The amount for which the item is sold.
• Marked Price (MP): The listed or asking price, often shown as the MRP.
• Profit: Occurs when the selling price is greater than the cost price.
  • Profit = SP − CP
  • Profit percentage = (Profit ÷ CP) × 100
• Loss: Occurs when the cost price is greater than the selling price.
  • Loss = CP − SP
  • Loss percentage = (Loss ÷ CP) × 100
• Discount: The reduction from the marked price to the selling price.
  • Discount = MP − SP
  • Discount percentage = (Discount ÷ MP) × 100

Profit and loss percentages are normally calculated on CP, while discount percentage is calculated on MP. If a question explicitly says profit is calculated on SP, use SP as the base.

Percentage-to-ratio method

The instructor emphasizes converting percentages into fractions or ratios to make calculations quicker and clearer.

• A 20% profit on CP means the profit is one-fifth of CP. If CP is represented as 5 parts, profit is 1 part and SP is 6 parts.
• A 20% profit on SP means profit is one-fifth of SP. CP is then 4 parts and SP is 5 parts, making the profit 25% of CP.
• Apply the same approach to losses, using the stated loss percentage to relate loss, CP, and SP.
• For unusual percentages, convert the percentage into a fraction when possible before forming the price ratio. Examples include percentages corresponding to fractions such as 1/6 or 1/12.

Approach to solving questions

1. Identify which quantities are given: CP, SP, MP, profit or loss, or discount.
2. Check what the percentage is calculated on; do not assume the base if the question specifies otherwise.
3. Convert the percentage into a fraction or ratio, then express CP and SP in matching parts.
4. For questions involving multiple items or quantities, find the per-item prices or costs first, then scale up to the total.
5. Check the basic price relationships to confirm whether the result represents a profit or a loss.

The lesson progresses from foundational definitions to basic and more involved applications, including questions involving multiple items and quantities.

Illustrative example

If an item has a marked price of ₹15 and is sold for ₹12, the discount is ₹3. The discount percentage is calculated using the marked price as the base:

₹3 ÷ ₹15 × 100

Speakers and source

• Udit Saini — instructor and principal speaker.
• MBA Pathshala — the YouTube channel identified in the lesson.