Solving Profit and Loss Problems in Cost Price Calculation for Watches

Introduction

Understanding the relationship between cost price, selling price, and profit or loss is crucial for businesses, especially in the retail sector. This article discusses how to calculate the cost price of a watch when the profit and loss incurred are approximately equal. Through algebraic manipulation, we will provide a step-by-step solution for solving such problems.

Problem Context

A watch is sold at two different prices, resulting in a loss of Rs. 600 and a profit of Rs. 650.

Selling Price (SP1) Rs. 600 Selling Price (SP2) Rs. 650

You are to determine the cost price (CP) of the watch when the loss and profit amounts are approximately equal.

Problem Analysis

Let the cost price of the watch be represented as CP. Loss when the watch is sold for Rs. 600: Loss CP - 600 Profit when the watch is sold for Rs. 650: Profit 650 - CP

According to the problem, the loss amount is approximately equal to the profit amount.

Loss ≈ Profit

CP - 600 ≈ 650 - CP

Now, to solve for CP:

CP - 600 650 - CP

Adding CP to both sides of the equation:

2CP 1250

CP 1250 / 2 Rs. 625

Thus, the cost price of the watch is approximately Rs. 625.

Verification

To verify the solution, we can use the following calculations:

Selling at Rs. 600 for a loss: Loss CP - 600 625 - 600 Rs. 25 (loss) Selling at Rs. 650 for a profit: Profit 650 - CP 650 - 625 Rs. 25 (profit)

The loss and profit amount are indeed approximately equal as Rs. 25.

Conclusion

Understanding the relationship between the cost price, selling price, and the resulting profit or loss is essential for running a retail business. By following the algebraic equations, we can determine the cost price accurately. In this case, the cost price of the watch is Rs. 625.

Additional Resources

For further assistance or similar problems, you may refer to the following resources:

Math-only-math - Loss and Profit - Percent-Problems