If the cost price of 150 shirts is equal to the selling price of 120 shirts, find the profit in percentage.

Points to Remember:

• Profit is calculated as Selling Price (SP) – Cost Price (CP).
• Profit percentage is calculated as (Profit/Cost Price) * 100.
• The problem involves a direct relationship between cost price and selling price.

Introduction:

This question is a basic profit and loss problem in mathematics. Profit and loss calculations are fundamental to understanding business operations and financial management. Understanding these calculations is crucial for businesses to determine pricing strategies, assess profitability, and make informed decisions. The core concept revolves around comparing the cost incurred in producing or acquiring goods (Cost Price) with the revenue generated from selling those goods (Selling Price). A positive difference indicates profit, while a negative difference indicates a loss.

Body:

1. Defining Variables and Establishing Relationships:

Let’s denote:

• CP_shirt = Cost price of one shirt
• SP_shirt = Selling price of one shirt

The problem states that the cost price of 150 shirts equals the selling price of 120 shirts. This can be expressed mathematically as:

150 * CP_shirt = 120 * SP_shirt

2. Calculating the Selling Price per Shirt:

We can rearrange the equation above to find the relationship between the cost price and selling price of a single shirt:

SP_shirt = (150/120) * CP_shirt = (5/4) * CP_shirt = 1.25 * CP_shirt

This shows that the selling price of one shirt is 125% of its cost price.

3. Calculating the Profit per Shirt:

Profit per shirt = SP_shirt – CP_shirt = 1.25 * CP_shirt – CP_shirt = 0.25 * CP_shirt

4. Calculating the Profit Percentage:

Profit percentage is calculated as:

Profit Percentage = (Profit/Cost Price) * 100

Substituting the values, we get:

Profit Percentage = (0.25 * CP_shirt / CP_shirt) * 100 = 0.25 * 100 = 25%

Conclusion:

The profit percentage on the sale of shirts is 25%. This indicates a healthy profit margin. Businesses can use this type of calculation to optimize pricing strategies, ensuring sufficient profit while remaining competitive in the market. Understanding profit and loss calculations is essential for sustainable business growth and responsible financial management. Further analysis could involve considering factors like overhead costs, market demand, and competitor pricing to refine the pricing strategy and maximize profitability while maintaining ethical business practices.

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