Calculating Successive Discounts for a Given Selling Price

When dealing with sales and pricing in the retail industry, understanding how discounts work is crucial for successful pricing strategies. This article aims to discuss the process of finding the successive discounts applied to a marked price to reach a certain selling price. Specifically, we will explore a scenario where an article was sold for Rs. 512 after two equal successive discounts on a marked price of Rs. 800.

Understanding Successive Discounts

Successive discounts refer to a series of discounts applied consecutively to a product's marked price. Each discount reduces the price further before the next one is applied. In this case, we will calculate the percentage discount offered for each of the two successive discounts.

Formulating the Problem

Let the percentage discount be (x). This means the discount factor for each discount is (1 - frac{x}{100}).

Step 1: First Discount

After the first discount, the price becomes:

[text{First Discounted Price} text{Marked Price} times 1 - frac{x}{100} 800 times 1 - frac{x}{100}]

Step 2: Second Discount

After the second discount, the price becomes:

[text{Final Price} text{First Discounted Price} times 1 - frac{x}{100} 800 times 1 - frac{x}{100}^2]

Setting the final price equal to Rs. 512:

[800 times 1 - frac{x}{100}^2 512]

Solving for the Discount Percentage

Divide both sides by 800:

[1 - frac{x}{100}^2 frac{512}{800}]

Simplify the fraction:

[1 - frac{x}{100}^2 frac{64}{100} 0.64]

Take the square root of both sides:

[1 - frac{x}{100} sqrt{0.64} 0.8]

Solve for (x):

[frac{x}{100} 1 - 0.8 0.2]

]Multiply by 100:

[x 0.2 times 100 20]

Therefore, the percentage discount offered is 20%.

Verification Using Different Methods

There are a few different methods to verify the same result:

Algebraic Method

[SP 512, MP 800]

[512 800 times (1 - frac{x}{100})^2]

[1 - frac{x}{100} sqrt{frac{512}{800}} frac{sqrt{64}}{sqrt{100}} 0.8]

[frac{x}{100} 1 - 0.8 0.2]

[x 0.2 times 100 20]

Shortcuts and Alternative Verification

Given:

MP 800 SP 512

Now, MP : SP 800 : 512 400 : 256

Since two equal successive discounts have been given, after one discount, the ratio becomes:

MP : SP sqrt{400} : sqrt{256} 20 : 16

Discount is 20 - 16 / 20 times 100 20%.

Conclusion

By understanding and applying the successive discount formulas and different methods, we can accurately determine the percentage discount offered on an article. This knowledge is valuable for businesses to adjust their pricing strategies effectively and ensure competitive pricing in the market.

Keywords: consecutive discounts, discount factor, percentage calculation, marked price, selling price