Calculating Selling Price with Multiple Discounts

This problem involves calculating the final selling price of an item after applying two successive discounts: a trade discount and a cash discount. It's important to remember that successive discounts are applied one after the other, with the second discount being calculated on the price remaining after the first discount has been applied.

Here, we have a list price of Rs. 1,200, a 20% trade discount, and a 30% cash discount.

Step 1: Apply the Trade Discount

The trade discount is given on the list price. The list price is Rs. 1,200, and the trade discount rate is 20%.

• List Price = \( \text{Rs. } 1,200 \)
• Trade Discount Rate = \( 20\% \)

The amount of trade discount is calculated as:

\( \text{Trade Discount Amount} = \text{List Price} \times \frac{\text{Trade Discount Rate}}{100} \)

\( \text{Trade Discount Amount} = 1,200 \times \frac{20}{100} \)

\( \text{Trade Discount Amount} = 1,200 \times 0.20 \)

\( \text{Trade Discount Amount} = \text{Rs. } 240 \)

The price after applying the trade discount is:

\( \text{Price after Trade Discount} = \text{List Price} - \text{Trade Discount Amount} \)

\( \text{Price after Trade Discount} = 1,200 - 240 \)

\( \text{Price after Trade Discount} = \text{Rs. } 960 \)

Alternatively, the price after a 20% trade discount is 100% - 20% = 80% of the list price:

\( \text{Price after Trade Discount} = \text{List Price} \times (1 - 0.20) \)

\( \text{Price after Trade Discount} = 1,200 \times 0.80 \)

\( \text{Price after Trade Discount} = \text{Rs. } 960 \)

Step 2: Apply the Cash Discount

The cash discount is applied to the price remaining after the trade discount has been deducted. This price is Rs. 960, and the cash discount rate is 30%.

• Price after Trade Discount = \( \text{Rs. } 960 \)
• Cash Discount Rate = \( 30\% \)

The amount of cash discount is calculated as:

\( \text{Cash Discount Amount} = \text{Price after Trade Discount} \times \frac{\text{Cash Discount Rate}}{100} \)

\( \text{Cash Discount Amount} = 960 \times \frac{30}{100} \)

\( \text{Cash Discount Amount} = 960 \times 0.30 \)

\( \text{Cash Discount Amount} = \text{Rs. } 288 \)

Step 3: Calculate the Final Selling Price

The selling price is the final price after deducting the cash discount from the price after the trade discount.

\( \text{Selling Price} = \text{Price after Trade Discount} - \text{Cash Discount Amount} \)

\( \text{Selling Price} = 960 - 288 \)

\( \text{Selling Price} = \text{Rs. } 672 \)

Alternative Method: Successive Percentage Calculation

We can also calculate the final price by directly applying the remaining percentages. After a 20% trade discount, 80% of the list price remains. After a 30% cash discount on that amount, 70% of that amount remains.

\( \text{Selling Price} = \text{List Price} \times (1 - \frac{\text{Trade Discount Rate}}{100}) \times (1 - \frac{\text{Cash Discount Rate}}{100}) \)

\( \text{Selling Price} = 1,200 \times (1 - 0.20) \times (1 - 0.30) \)

\( \text{Selling Price} = 1,200 \times 0.80 \times 0.70 \)

\( \text{Selling Price} = 1,200 \times 0.56 \)

\( \text{Selling Price} = \text{Rs. } 672 \)

Both methods yield the same final selling price.

Summary of Discount Calculation

Here is a summary of the price progression:

The final selling price is Rs. 672.

Revision Table: Key Pricing Terms

Additional Information: Why Discounts Matter in Trading

Understanding how to calculate discounts is essential for traders and businesses. Trade discounts help manage pricing structures for different types of buyers or sales volumes, while cash discounts encourage faster payments, improving cash flow. Correctly calculating the final selling price ensures profitability while offering competitive pricing.

Successive discounts are common in wholesale and retail trade. It's crucial not to simply add the discount percentages, as this would lead to an incorrect (usually lower) selling price. Always apply the discounts sequentially to the diminishing price base.