Calculating the Marked Price of a Watch: A Comprehensive Guide

When purchasing a watch, the question of its marked price often arises. Given that the selling price of a watch is Rs 220 and a 10% profit is included in the marked price, how do we calculate the marked price?

Understanding the Concepts

To find the marked price (MP) of a watch, we need to understand the relationship between the selling price (SP), the marked price, and the profit. The profit margin is given as 10%, which means the profit is 10% of the cost price (CP).

Calculating the Cost Price (CP)

First, we determine the cost price (CP). The selling price (SP) is Rs 220, and it includes a 10% profit. We can represent this relationship using the formula:

SP CP 0.1 × CP 1.1 × CP

To find the cost price, we rearrange this equation:

CP SP / 1.1 220 / 1.1 200

Calculating the Profit

With the cost price determined, we can calculate the profit as follows:

Profit 0.1 × CP 0.1 × 200 20

The marked price (MP) is the cost price plus the profit:

MP CP Profit 200 20 220

However, it's important to note that the selling price (SP) is the marked price minus the discount. Since no discount is mentioned, we can assume that the selling price is the marked price. Nevertheless, if we consider the profit margin, the marked price can be calculated as follows:

Marked Price SP / (1 - Profit Margin) 220 / (1 - 0.1) 220 / 0.9 ≈ 244.44

Conclusion and Verification

From the calculations above, the marked price of the watch should be approximately Rs 244.44. However, given that the profit is included in the marked price, we can verify this by checking:

SP Marked Price - Profit 244.44 - 24.44 220

This verification confirms that the marked price is indeed Rs 244.44.

Additional Insights

Some sources might suggest that the marked price is Rs 220, by treating the profit as a discount from the marked price. However, this approach is not consistent with the given information that the profit is included in the marked price. Therefore, the most accurate calculation is based on the marked price being the price after including the profit.

Frequently Asked Questions

What is the difference between selling price and marked price?
The selling price (SP) is the final price at which a product is sold. The marked price (MP) is the price at which the product is listed before any discounts are applied, including profit margins. How do you calculate profit margin?
Profit margin is calculated as: Profit Margin (Profit / CP) × 100. In this case, it is given as 10%. Why is the marked price important?
The marked price is crucial as it helps in determining the final selling price and ensures that the seller covers the cost and profit margin. It also helps in negotiating discounts and understanding the true value of the product.

By understanding these concepts and following the steps above, you can accurately calculate the marked price of a watch or any other product when given the selling price and profit margin.