Calculating Successive Discounts

This problem involves calculating the value of a second discount percentage applied successively after a first discount on the marked price of an article to reach the final selling price.

Let's break down the problem:

• The original marked price (MP) of the article is Rs. 740.
• A first discount of 15% is applied.
• A second successive discount of x% is applied.
• The final selling price (SP) after both discounts is Rs. 566.10.
• We need to find the value of x.

Step-by-Step Calculation of Successive Discounts

First, let's calculate the price of the article after the first discount of 15%.

Price after 1st discount = Marked Price - (15% of Marked Price)

This can be calculated as:

Price after 1st discount = $\text{MP} \times (1 - \frac{\text{Discount}_1}{100})$

Substituting the given values:

Price after 1st discount = $740 \times (1 - \frac{15}{100})$

Price after 1st discount = $740 \times (1 - 0.15)$

Price after 1st discount = $740 \times 0.85$

Price after 1st discount = Rs. 629

Now, this price (Rs. 629) becomes the new base price for the second successive discount of x%.

The final selling price (SP) is Rs. 566.10 after applying the second discount.

The formula for the second discount is:

Selling Price = (Price after 1st discount) - (x% of Price after 1st discount)

This can be written as:

$\text{SP} = (\text{Price after 1st discount}) \times (1 - \frac{x}{100})$

Substituting the known values:

$566.10 = 629 \times (1 - \frac{x}{100})$

Now, we need to solve this equation for x.

Divide both sides by 629:

$\frac{566.10}{629} = 1 - \frac{x}{100}$

Calculating the left side:

$0.90 = 1 - \frac{x}{100}$

Now, rearrange the equation to isolate the term with x:

$\frac{x}{100} = 1 - 0.90$

$\frac{x}{100} = 0.10$

Finally, multiply by 100 to find the value of x:

$x = 0.10 \times 100$

$x = 10$

So, the value of the second discount percentage (x) is 10%.

Verifying the Result

Let's check if applying a 15% discount followed by a 10% discount on Rs. 740 results in Rs. 566.10.

• Original Price = Rs. 740
• Price after 15% discount = $740 \times (1 - 0.15) = 740 \times 0.85 = \text{Rs. } 629$
• Price after next 10% discount on Rs. 629 = $629 \times (1 - 0.10) = 629 \times 0.90 = \text{Rs. } 566.10$

This matches the given selling price, confirming our calculation is correct.

The value of x is 10.

Revision Table: Successive Discounts

Additional Information on Pricing Concepts

Understanding terms like Marked Price, Selling Price, and Discount is crucial for solving problems related to profit and loss. Here's a bit more detail:

• Marked Price (MP): Also known as List Price. It's the price tag on the item. Retailers might offer discounts on this price.
• Selling Price (SP): This is the price the customer pays. It is usually the Marked Price minus the discount offered. If there are multiple discounts, they are applied successively, not added up directly.
• Discount: It's the reduction in the marked price given to the customer. It is usually calculated as a percentage of the Marked Price or the price after a previous discount.
• Calculating Price After Discount: If a discount of D% is given on a price P, the price after discount is $P \times (1 - \frac{D}{100})$. This is a quicker way than calculating the discount amount and subtracting it.
• Equivalent Single Discount: Two successive discounts are equivalent to a single discount, but it's not just the sum of the percentages. For discounts D1% and D2%, the equivalent single discount is $D1 + D2 - \frac{D1 \times D2}{100}$. This formula applies to the original Marked Price.

In this problem, we used the concept of applying discounts successively to find the unknown discount percentage.