# Profit and Loss

**Profit and Loss**

Profit and loss is a fundamental concept in quantitative ability, often covered in various competitive exams and real-life business scenarios. It deals with the financial aspect of buying and selling goods or services, calculating the profit or loss incurred in a transaction.

Let's understand the key terms related to profit and loss:

Cost Price (CP): The price at which an article is purchased or the cost incurred to produce an item.

Selling Price (SP): The price at which an article is sold is known as Selling Price.

Profit (P): The amount earned when the Selling Price (SP) is higher than the Cost Price (CP).

Loss (L): The amount incurred when the Selling Price (SP) is lower than the Cost Price (CP).

Profit Percentage: The percentage of profit earned concerning the Cost Price.

Loss Percentage: The percentage of loss incurred concerning the Cost Price.

The general formulas for calculating profit and loss are as follows:

Profit (P) = Selling Price (SP) of a commodity- Cost Price (CP) of a commodity

Loss (L) = Cost Price (CP) of a commodity - Selling Price (SP) of a commodity

Profit Percentage = (Profit / Cost Price of a commodity) * 100

Loss Percentage = (Loss / Cost Price) * 100

Now, let's go through some examples to illustrate profit and loss calculations:

Example 1:

A shopkeeper bought a shirt for $40 and sold it for $60. Calculate the profit amount and profit percentage.

Solution 1:

Cost Price (CP) = $40

Selling Price (SP) = $60

Profit (P) = SP - CP = $60 - $40 = $20

Profit Percentage = (Profit / CP) * 100 = ($20 / $40) * 100 = 50%

Example 2:

A trader sold a book for $500, incurring a loss of $100. Calculate the cost price and loss percentage.

Solution 2:

Selling Price (SP) = $500

Loss (L) = $100

Cost Price (CP) = SP + L = $500 + $100 = $400

Loss Percentage = (Loss / CP) * 100 = ($100 / $400) * 100 = 25%

**Examples:**

Example 1:

A shopkeeper bought a smartphone for $300 and sold it for $400. Calculate the profit percentage.

Solution 1:

Cost Price (CP) = $300

Selling Price (SP) = $400

Profit (P) = SP - CP = $400 - $300 = $100

Profit Percentage = (Profit / CP) * 100 = ($100 / $300) * 100 = 33.33%

Example 2:

A vendor purchased a box of 50 pens for $20 and sold each pen at $1.50. Calculate the total profit or loss.

Solution 2:

Cost Price of 1 pen (CP) = $20 / 50 = $0.40

Selling Price of 1 pen (SP) = $1.50

Profit (P) = SP - CP = $1.50 - $0.40 = $1.10 (profit per pen)

Total Profit = Profit per pen * Number of pens sold = $1.10 * 50 = $55

Example 3:

A company bought a machine for $10,000, but due to its condition, it could only be sold for $8,500. Calculate the loss percentage.

Solution 3:

Cost Price (CP) = $10,000

Selling Price (SP) = $8,500

Loss (L) = CP - SP = $10,000 - $8,500 = $1,500

Loss Percentage = (Loss / CP) * 100 = ($1,500 / $10,000) * 100 = 15%

Example 4:

A bookshop bought a set of novels for $120 and sold it at a discount for $90. Calculate the loss percentage.

Solution 4:

Cost Price (CP) = $120

Selling Price (SP) = $90

Loss (L) = CP - SP = $120 - $90 = $30

Loss Percentage = (Loss / CP) * 100 = ($30 / $120) * 100 = 25%

Example 5:

A farmer sold a batch of vegetables for $800, making a profit of 25%. What was the cost price of the vegetables?

Solution 5:

Profit Percentage = 25%

Selling Price (SP) = $800

Let the cost price be CP.

Profit (P) = (Profit Percentage / 100) * CP

$800 - CP = (25 / 100) * CP

$800 = 0.25CP + CP

$800 = 1.25CP

CP = $800 / 1.25 = $640

These examples demonstrate how to calculate profit and loss amounts and percentages. It's essential to understand these concepts and practice various scenarios to become proficient in solving quantitative ability questions related to profit and loss. Additionally, real-life applications of these concepts include business calculations, pricing strategies, and investment decisions.