Arun Sharma Summary: Profit , Loss & Discount | Quantitative Aptitude (Quant) - CAT PDF Download

Introduction

• Profit and Loss is a fundamental concept in commercial arithmetic, crucial for exams like CAT, SNAP, XAT, and NMAT. 
• It assesses financial outcomes in transactions, vital for business and individual contexts. 
• Key terms include Cost Price (CP), Selling Price (SP), profit, and loss, with calculations typically based on CP unless specified otherwise.

Key Terms &  Standard Language in Profit & Loss

• The amount a seller pays to acquire or produce an item.

2. Selling Price (SP)

•  The amount at which the seller sells the item to a buyer.

3. Profit (Gain)

•  Occurs when the selling price is greater than the cost price.
• Profit = Selling Price - Cost Price.
• Example: 
  Selling price = ₹250, 
  Cost price = ₹200, 
  So ,Profit = ₹250 − ₹200 = ₹50.

4. Loss

• Occurs when the selling price is less than the cost price.
• Loss = Cost Price - Selling Price.
• Example: 
  Selling price = ₹180, 
  Cost price = ₹200, so 
  Loss = ₹200 − ₹180 = ₹20.

5. Profit Percentage

• The profit is expressed as a percentage of the cost price.
•  Profit Percentage = (Profit ÷ Cost Price) × 100. 
• Example: 
  Profit = ₹50 on Cost price = ₹200, 
  so Profit Percentage = (50 ÷ 200) × 100 = 25%.

6. Loss Percentage

• The loss expressed as a percentage of the cost price.
• Loss Percentage = (Loss ÷ Cost Price) × 100.
• Example: 
  Loss = ₹20 on Cost price = ₹200, 
  so Loss Percentage = (20 ÷ 200) × 100 = 10%.

7. Marked Price (MP) or List Price

• The labeled price printed on an item before any discount.

8. Discount

• Reduction allowed from the marked price when selling.
• Discount = Marked Price - Selling Price.
• Example: Marked price = ₹300, Selling price after discount = ₹270, Discount = ₹300 − ₹270 = ₹30.

9. Discount Percentage

• The discount is expressed as a percentage of the marked price.
• Discount Percentage = (Discount ÷ Marked Price) × 100.
• Example: 
  Marked price = ₹300, 
  Discount = ₹30, 
  Discount Percentage = (30 ÷ 300) × 100 = 10%.

Profit & Loss( In Case of an Individual)

Profit: SP > CP, profit = SP - CP.
Loss: SP < CP, loss = CP - SP.

Percentage Profit/Loss:

• Percentage Profit =
• Percentage Loss =

Example: For an item with CP ₹100 and SP ₹120, profit = ₹20, percentage profit =

Profit & Loss as Applied to Commercial Transactions

1. Profit in Multiple Units of Products are Being Bought or Sold: 

Total CP = CP per unit × number of units, 
Total SP = SP per unit × number of units. 
Profit = Total SP - Total CP
2. Loss in Multiple Units of Products are Being Bought or Sold: 

If SP < CP per unit, 
loss = total CP - total SP.

Types of Costs 

1. Direct Costs (Variable Costs)

• Variable costs (e.g., transportation) are proportional to the number of units. Total CP includes these costs.
• Example: For 10 pens at CP ₹5 each, variable cost ₹1 per pen, 
  total CP = (₹5 + ₹1) × 10 = ₹60.

2. Indirect Costs (Overhead Costs or Fixed Costs)

• Fixed costs (e.g., rent) remain constant regardless of units sold. They are added to the total CP.
• Example: For 100 pens at CP ₹10 each, fixed cost ₹100, 
  total CP = 100 x₹10 + ₹100 = ₹1100. 
  SP = ₹12 each, 
  total SP = ₹1200, 
  Profit = ₹100.

3. Semi-Variable Costs

• Semi-variable costs combine fixed and variable components, increasing with sales volume.
• Example: A fixed rent of ₹500 plus ₹1 per unit transport for 100 units adds ₹100 variable cost, 
  Total CP = base CP + ₹500 + ₹100.

The Concept of the Break-Even Point

The break-even point occurs when total SP = total CP, resulting in no profit or loss.
Break-Even Sales: Total SP = Total CP.
Break-Even Units: Number of units sold where total revenue equals total cost.
Example: For 100 pens, CP = ₹8 each, total CP = ₹800. To break even at SP ₹10 each, sell

Profit Calculation on the Basis of Equating the Amount Spent and the Amount Earned

• Profit is determined by equating total CP (amount spent) and total SP (amount earned).
• Formula: Profit = Total SP - Total CP.
• Example: 
  For 100 pens, CP = ₹8 each, 
  SP = ₹10 each, 
  total CP = ₹800, 
  total SP = ₹1000, 
  Profit = ₹200, 
  Percentage Profit =

Table: Summary of Key Formulas and Examples