Question

A dealer buys a product at Rs. 1920, He sells at a discount of \(20 \%\) still he gets the profit of \(20 \%\). What is the selling price of that product? (a) Rs. 2304 (b) Rs. 1536 (c) Rs. 2200 (d) it is not possible

Short answer

Answer: (d) it is not possible

Step-by-step solution

Calculate the Cost Price after adding Profit Percentage

To calculate the cost price after adding the profit percentage, we can use the formula: Cost Price After Profit = Cost Price * (1 + Profit Percentage) Here, the cost price is Rs. 1920 and the profit percentage is \(20 \%\). Cost Price After Profit = 1920 * (1 + 0.20) = 1920 * 1.20 = Rs. 2304

Calculate the Selling Price after applying the Discount Percentage

Now that we have the cost price after adding the profit percentage, we can calculate the selling price by subtracting the discount percentage from the new cost price. We can use the formula: Selling Price = Cost Price After Profit * (1 - Discount Percentage) Here, the cost price after the profit is Rs. 2304 and the discount percentage is \(20 \%\). Selling Price = 2304 * (1 - 0.20) = 2304 * 0.80 = Rs. 1843.20 Since this is a multiple-choice question and Rs. 1843.20 is not one of the given options, we can conclude that the selling price is not possible among the given options. Our answer is: (d) it is not possible

Key concepts

Percentage Calculations

Understanding percentage calculations is essential in many business math problems, such as calculating profit and discounts. Percentages represent a proportion out of 100, simplifying comparisons and calculations. To find the percentage of a number, you multiply the number by the percentage in decimal form. For example, a 20% increase on a cost implies multiplying the original cost by 1.20.
For the given exercise, we had to increase the cost price by 20%, indicating a profit. This calculation is done by multiplying the initial cost, Rs. 1920, by 1.20, leading to Rs. 2304 after the applied profit percentage. Similarly, we decrease the selling price by the discount percentage, converting 20% to 0.20 and then multiplying the reduced selling cost by 0.80.
Calculating percentages effectively involves understanding how to shift from a percentage to a decimal and correctly applying it to the given values, ensuring mathematical operations are done in the right sequence.

Cost Price and Selling Price

The concepts of cost price and selling price are foundational in evaluating transactions involving buying and selling goods. The cost price (C.P.) is the amount a seller pays to purchase a product, while the selling price (S.P.) is the price at which the seller sells the product to a buyer.
In the exercise, the cost price is Rs. 1920. The profit percentage signifies that the seller expects a monetary gain over the cost price. If the selling price is higher than the cost price, the seller achieves a profit. If it is lesser, there is a loss.
Here, an additional factor of a discount complicates the final selling price. After accommodating the profit percentage, the selling price ought to be Rs. 2304. However, the application of a 20% discount necessitates further calculation, which results in a final potential selling price that was checked against the available answer options.

Discount and Profit Relations

It is crucial to understand the relationship between discount and profit to solve pricing problems effectively. The profit refers to the financial gain made when an item is sold for more than its cost price. Discounts are reductions applied to encourage sales, presented as a percentage decrease in the selling price.
In the scenario provided, the seller achieves a profit of 20% on the cost price but also offers a 20% discount on the marked-up price. The complexity arises because discount and profit affect the final selling price differently. The profit calculation is based on the original cost, increasing the initial price, while the discount is applied to this new price, decreasing it afterward.

• Calculate profit: Increase original price by profit percentage.
• Apply discount: Reduce marked-up price by discount percentage.

These steps show how profit and discounts compound, sometimes leading to non-intuitive results, such as finding selling prices incompatible with provided options.