Calculating Selling Price with Successive Discounts

This problem involves calculating the final selling price of an article after two consecutive discounts are applied to its marked price. Understanding how successive discounts work is key here.

Understanding Successive Discounts

Successive discounts mean that the second discount is applied not on the original marked price, but on the price that results after the first discount has been applied. It's not simply adding the two discount percentages together and applying a single discount.

• First discount reduces the price from the Marked Price (MP).
• Second discount reduces the price from the reduced price obtained after the first discount.

Given Information

• Marked Price (MP) = Rs. 25,500
• First Discount = 15%
• Second Discount = 12%

Step-by-Step Calculation of Selling Price

We can calculate the price after each discount sequentially, or use a formula that directly calculates the final selling price after successive discounts.

Method 1: Step-by-Step Calculation

1. Calculate the price after the first discount (15%):

   The price remaining after a 15% discount is $(100 - 15)\% = 85\%$ of the marked price.

   Price after 1st discount $= \text{MP} \times \left(1 - \frac{15}{100}\right)$

   Price after 1st discount $= 25500 \times (1 - 0.15) = 25500 \times 0.85$

   Price after 1st discount $= 21675$

2. Calculate the price after the second discount (12%) on the reduced price:

   The second discount of 12% is applied to Rs. 21,675. The price remaining after a 12% discount is $(100 - 12)\% = 88\%$ of the price after the first discount.

   Selling Price (SP) $= (\text{Price after 1st discount}) \times \left(1 - \frac{12}{100}\right)$

   Selling Price (SP) $= 21675 \times (1 - 0.12) = 21675 \times 0.88$

   Selling Price (SP) $= 19074$

Method 2: Using a Combined Factor

When successive discounts of $d_1\%$ and $d_2\%$ are applied, the final selling price is a percentage of the marked price. The price remaining after a $d\%$ discount is $(100-d)\%$ of the original price, or $\left(1-\frac{d}{100}\right)$ times the original price.

For two successive discounts of $d_1\%$ and $d_2\%$, the final selling price is:

$\text{SP} = \text{MP} \times \left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right)$

Plugging in the given values:

$d_1 = 15\%$, $d_2 = 12\%$

$\text{SP} = 25500 \times \left(1 - \frac{15}{100}\right) \times \left(1 - \frac{12}{100}\right)$

$\text{SP} = 25500 \times (1 - 0.15) \times (1 - 0.12)$

$\text{SP} = 25500 \times 0.85 \times 0.88$

$\text{SP} = 25500 \times 0.748$

$\text{SP} = 19074$

Both methods yield the same result. The selling price of the article after two successive discounts of 15% and 12% is Rs. 19,074.

Conclusion on Selling Price

Based on the calculations using successive discounts, the final selling price of the article is Rs. 19,074.

Revision Table: Price and Discount Concepts

Additional Information: Equivalent Single Discount

Sometimes, it's useful to know what single discount would be equivalent to two successive discounts. If two successive discounts are $d_1\%$ and $d_2\%$, the selling price is $MP \times (1 - d_1/100) \times (1 - d_2/100)$.

Let the equivalent single discount be $D\%$. Then, $\text{SP} = \text{MP} \times (1 - D/100)$.

So, $(1 - D/100) = (1 - d_1/100) \times (1 - d_2/100)$

$D/100 = 1 - (1 - d_1/100) \times (1 - d_2/100)$

$D = 100 \left[ 1 - \left(1 - \frac{d_1}{100}\right) \left(1 - \frac{d_2}{100}\right) \right]$

For the given discounts 15% and 12%:

$d_1 = 15$, $d_2 = 12$

$D = 100 \left[ 1 - \left(1 - \frac{15}{100}\right) \left(1 - \frac{12}{100}\right) \right]$

$D = 100 \left[ 1 - (0.85) \times (0.88) \right]$

$D = 100 \left[ 1 - 0.748 \right]$

$D = 100 \times 0.252$

$D = 25.2\%$

So, successive discounts of 15% and 12% are equivalent to a single discount of 25.2%.

Applying a single discount of 25.2% on Rs. 25,500:

$\text{SP} = 25500 \times \left(1 - \frac{25.2}{100}\right)$

$\text{SP} = 25500 \times (1 - 0.252)$

$\text{SP} = 25500 \times 0.748$

$\text{SP} = 19074$

This confirms the previous calculation for the selling price.