Calculating Selling Price, J1, J2, and J2 - J1

The problem asks us to first calculate the selling price for various articles based on their marked price and discount percentage. Then we need to find the total selling price for certain combinations of articles (J1 and J2) and finally, the difference between J2 and J1.

Understanding Marked Price, Discount, and Selling Price

The marked price is the price listed on an article. A discount percentage is a reduction offered on the marked price. The selling price is the price at which the article is actually sold after the discount is applied.

The formula provided for calculating the selling price is:

\(Selling \ Price = Marked \ Price - \left(\frac{Marked \ Price \ \times \ Discount \ percent}{100}\right)\)

Alternatively, the selling price can be calculated directly if we consider the discount percentage. If the discount is \(D\%\), the article is sold for \((100 - D)\%\) of the marked price.

\(Selling \ Price = Marked \ Price \ \times \ \left(\frac{100 - Discount \ percent}{100}\right)\)

Analyzing the Provided Table

Let's look at the data given in the table for the five articles:

Calculating Selling Price for Each Article

Let's calculate the selling price for each article mentioned in the definitions of J1 and J2 (Articles P, R, Q, and T):

• Article P:

  Marked Price = 300, Discount = 20%

  Discount Amount = \(300 \times \frac{20}{100} = 3 \times 20 = 60\)

  Selling Price (P) = Marked Price - Discount Amount = \(300 - 60 = 240\)

  Alternatively, Selling Price (P) = \(300 \times \frac{100 - 20}{100} = 300 \times \frac{80}{100} = 3 \times 80 = 240\)

• Article Q:

  Marked Price = 600, Discount = 25%

  Discount Amount = \(600 \times \frac{25}{100} = 6 \times 25 = 150\)

  Selling Price (Q) = Marked Price - Discount Amount = \(600 - 150 = 450\)

  Alternatively, Selling Price (Q) = \(600 \times \frac{100 - 25}{100} = 600 \times \frac{75}{100} = 6 \times 75 = 450\)

• Article R:

  Marked Price = 400, Discount = 16%

  Discount Amount = \(400 \times \frac{16}{100} = 4 \times 16 = 64\)

  Selling Price (R) = Marked Price - Discount Amount = \(400 - 64 = 336\)

  Alternatively, Selling Price (R) = \(400 \times \frac{100 - 16}{100} = 400 \times \frac{84}{100} = 4 \times 84 = 336\)

• Article T:

  Marked Price = 800, Discount = 30%

  Discount Amount = \(800 \times \frac{30}{100} = 8 \times 30 = 240\)

  Selling Price (T) = Marked Price - Discount Amount = \(800 - 240 = 560\)

  Alternatively, Selling Price (T) = \(800 \times \frac{100 - 30}{100} = 800 \times \frac{70}{100} = 8 \times 70 = 560\)

Calculating J1 and J2

J1 is the total selling price of article P and R.

\(J1 = Selling \ Price(P) + Selling \ Price(R)\)

\(J1 = 240 + 336\)

\(J1 = 576\)

J2 is the total selling price of Q and T.

\(J2 = Selling \ Price(Q) + Selling \ Price(T)\)

\(J2 = 450 + 560\)

\(J2 = 1010\)

Finding the Value of (J2 - J1)

Finally, we need to find the difference between J2 and J1.

\(J2 - J1 = 1010 - 576\)

\(J2 - J1 = 434\)

The value of (J2 - J1) is 434.

Summary of Calculations

\(J1 = SP(P) + SP(R) = 240 + 336 = 576\)

\(J2 = SP(Q) + SP(T) = 450 + 560 = 1010\)

\(J2 - J1 = 1010 - 576 = 434\)

Revision Table: Selling Price Calculation

Additional Information: Profit and Loss Basics

This problem relates to basic concepts in profit and loss, specifically discount calculations. Here are a few related terms:

• Cost Price (CP): The price at which an article is purchased.
• Profit: When Selling Price > Cost Price. Profit = Selling Price - Cost Price.
• Loss: When Selling Price < Cost Price. Loss = Cost Price - Selling Price.
• Profit Percentage: \(\frac{Profit}{CP} \times 100\)
• Loss Percentage: \(\frac{Loss}{CP} \times 100\)
• Marked Price (MP): The price at which an article is listed for sale, often higher than the cost price to allow for discounts and profit.
• Discount: A reduction in the marked price.
• Selling Price (SP): The price at which the article is sold after applying the discount. \(SP = MP - Discount\).

Understanding these terms is crucial for solving problems involving commercial mathematics.