Calculating the Marked Price: Understanding Discounts and Sales Tax

In any retail transaction, understanding how the final price is derived from the marked price, discount, and sales tax is essential for both consumers and business owners. Let's break down a typical scenario to understand how these elements interact. We will explore how a 30% discount on a marked price followed by a 10% sales tax results in a final selling price of Rs. 1000.

Scenario Overview

Consider an article with a marked price (m.p) of x. A discount of 30% is applied, and then a 10% sales tax is added to the discounted price, resulting in a final selling price of Rs. 1000. We need to find the marked price of the article.

Mathematical Calculation

Let's denote the marked price by MP and the selling price by SP.

1. A discount of 30% on the marked price reduces the price to 70% of the marked price.

2. A 10% sales tax is then applied to the discounted price.

3. The selling price is the result of applying the tax to the discounted price.

Mathematically, this can be represented as:

[ SP MP - (MP times 0.3) (MP times 0.3 times 0.1) ]

Simplifying, we get:

[ SP MP times (1 - 0.3) times (1 0.1) ] [ SP MP times 0.7 times 1.1 ]

Given that the selling price (SP) is Rs. 1000, we can set up the equation:

[ 1000 MP times 0.77 ]

Solving for MP (the marked price), we get:

[ MP frac{1000}{0.77} ]

which evaluates to approximately Rs. 1298.70.

Verification of Calculation

To verify, let's consider a simpler approach. If we assume the marked price MP is 100, then after a 30% discount, the discounted price would be:

[ 100 - 100 times 0.3 70 ]

Applying the 10% sales tax on the discounted price:

[ 70 70 times 0.1 77 ]

Clearly, Rs. 77 is not the selling price of Rs. 1000, so let's solve for the exact amount.

Using the formula:

[ SP MP times 0.77 ]

we set:

[ MP frac{1000}{0.77} approx 1298.70 ]

Conclusion

The marked price of the article, given a final selling price of Rs. 1000 and a 30% discount followed by a 10% sales tax, is Rs. 1298.70. This calculation is essential for understanding the pricing dynamics in retail businesses and for consumers to accurately assess the true cost.

Additional Tips for Retailers and Consumers

Understand Discounting: A discount of 30% on a marked price of Rs. 1000 would normally reduce the price to Rs. 700, but the tax on this price would result in a slightly higher final price due to the additional 10% tax. Tax Considerations: Including tax in the final price ensures consumers have a comprehensive understanding of the total cost of the product. Comparison Shopping: Understanding these calculations can help in comparing prices across different retailers and stores.

For more detailed calculations and further questions related to pricing in retail, feel free to explore additional resources or consult with financial experts.