A book was sold for â¹27.50 with a profit of 10%. If it were sold for â¹25.75, then what would have been the percentage of profit or loss?

Points to Remember:

Profit and loss percentage calculation.
Cost price calculation.
Application of percentage formula.

Introduction:

This question involves a basic business mathematics problem concerning profit and loss percentage. Profit is the difference between the selling price and the cost price of a good, while loss is the difference when the cost price exceeds the selling price. Profit or loss percentage is calculated as a percentage of the cost price. The question provides a selling price and profit percentage in one scenario and asks to determine the profit or loss percentage in a different scenario with a revised selling price.

Body:

1. Calculating the Cost Price:

The book was sold for â¹27.50 with a 10% profit. This means that â¹27.50 represents 110% (100% cost price + 10% profit) of the cost price. To find the cost price (CP), we can use the following formula:

CP = (Selling Price / (1 + Profit Percentage/100))

CP = (27.50 / (1 + 10/100)) = (27.50 / 1.1) = â¹25

Therefore, the cost price of the book is â¹25.

2. Calculating Profit/Loss at â¹25.75 Selling Price:

If the book were sold for â¹25.75, we need to determine if it’s a profit or loss. Since the selling price (SP) is â¹25.75 and the cost price (CP) is â¹25, there is a profit.

Profit = SP – CP = 25.75 – 25 = â¹0.75

To calculate the profit percentage, we use the following formula:

Profit Percentage = (Profit / Cost Price) * 100

Profit Percentage = (0.75 / 25) * 100 = 3%

Therefore, if the book were sold for â¹25.75, there would have been a profit of 3%.

Conclusion:

In summary, by first calculating the cost price of the book based on the initial selling price and profit percentage, we were able to determine the profit or loss if the book was sold at a different price. The analysis shows that selling the book for â¹27.50 resulted in a 10% profit, while selling it for â¹25.75 would have resulted in a 3% profit. This highlights the direct relationship between selling price and profit margin. Businesses need to carefully consider pricing strategies to maximize profits while remaining competitive in the market. A holistic approach to pricing should consider factors such as production costs, market demand, and competitor pricing to ensure sustainable profitability.

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