Calculating Selling Price with Successive Discounts

This problem involves calculating the final selling price of an item after two successive discounts are applied to its original listed price. Successive discounts mean that the second discount is calculated on the price after the first discount has been applied, not on the original listed price.

Understanding the Terms

• Listed Price (Marked Price): The original price of the item as displayed. In this case, it is Rs. 5000.
• Discount: A reduction in the price of an item. It is usually given as a percentage of the current price.
• Successive Discounts: Applying one discount after another on the reduced price.
• Selling Price: The final price at which the item is sold after all discounts.

Step-by-Step Calculation of Selling Price

We need to apply the two successive discounts of 20% and 10% to the listed price of Rs. 5000.

Step 1: Apply the First Discount (20%)

The first discount is 20% on the listed price of Rs. 5000.

Discount Amount 1 = 20% of Rs. 5000

Discount Amount 1 $= \frac{20}{100} \times 5000$

Discount Amount 1 $= 0.20 \times 5000$

Discount Amount 1 $= 1000$

Price after First Discount = Listed Price - Discount Amount 1

Price after First Discount $= 5000 - 1000$

Price after First Discount $= 4000$

So, after the first 20% discount, the price of the dining set is Rs. 4000.

Step 2: Apply the Second Discount (10%)

The second discount is 10%. This discount is applied to the price *after* the first discount, which is Rs. 4000.

Discount Amount 2 = 10% of Rs. 4000

Discount Amount 2 $= \frac{10}{100} \times 4000$

Discount Amount 2 $= 0.10 \times 4000$

Discount Amount 2 $= 400$

Selling Price = Price after First Discount - Discount Amount 2

Selling Price $= 4000 - 400$

Selling Price $= 3600$

Thus, after applying both successive discounts, the final selling price of the dining set is Rs. 3600.

Alternative Method: Using Percentage Multipliers

When a discount of d% is given, the selling price is $(100-d)\%$ of the price. For successive discounts, we can multiply the remaining percentages.

• After a 20% discount, the price is $(100 - 20)\% = 80\%$ of the original price.
• After a 10% discount, the price is $(100 - 10)\% = 90\%$ of the price after the first discount.

So, the final selling price will be $90\%$ of $80\%$ of the original listed price.

Selling Price $= 90\%$ of $(80\%$ of $5000)$

Selling Price $= \frac{90}{100} \times (\frac{80}{100} \times 5000)$

Selling Price $= 0.90 \times (0.80 \times 5000)$

Selling Price $= 0.90 \times 4000$

Selling Price $= 3600$

Both methods yield the same result, confirming the selling price is Rs. 3600.

Summary of Discounts and Price Calculation

The selling price of the dining set after successive discounts of 20% and 10% is Rs. 3600.

Revision Table: Successive Discounts

Additional Information: Equivalent Single Discount

Instead of applying successive discounts one by one, we can calculate a single equivalent discount that would result in the same final selling price. If the successive discounts are $d_1\%$ and $d_2\%$, the single equivalent discount ($D\%$) is calculated as:

$D = d_1 + d_2 - \frac{d_1 \times d_2}{100}$

In this problem, $d_1 = 20\%$ and $d_2 = 10\%$.

Equivalent Single Discount $= 20 + 10 - \frac{20 \times 10}{100}$

Equivalent Single Discount $= 30 - \frac{200}{100}$

Equivalent Single Discount $= 30 - 2$

Equivalent Single Discount $= 28\%$

This means that successive discounts of 20% and 10% are equivalent to a single discount of 28% on the original marked price. Let's verify this:

Selling Price = Marked Price - 28% of Marked Price

Selling Price $= 5000 - \frac{28}{100} \times 5000$

Selling Price $= 5000 - 0.28 \times 5000$

Selling Price $= 5000 - 1400$

Selling Price $= 3600$

The selling price calculated using the equivalent single discount is also Rs. 3600, confirming the method.