Understanding Painting Price Concepts

In commercial mathematics, understanding the relationship between marked price, selling price, and discount is crucial. The marked price (MP) is the price listed on an item. A discount is a reduction in the marked price offered to the customer. The price at which the item is finally sold after the discount is the selling price (SP).

The discount is usually calculated as a percentage of the marked price.

• Discount Amount = Discount % of Marked Price
• Selling Price = Marked Price - Discount Amount

So, the formula relating these terms is:

\( \text{Selling Price} = \text{Marked Price} - (\text{Discount \%} \times \text{Marked Price}) \)

This can be simplified to:

\( \text{Selling Price} = \text{Marked Price} \times (1 - \text{Discount \%}) \)

Or, to find the marked price:

\( \text{Marked Price} = \frac{\text{Selling Price}}{1 - \text{Discount \%}} \)

Calculating the Marked Price of the Painting

We are given the following information about the painting:

• Selling Price (SP) = Rs. 5,225
• Discount Percentage = 5%

We need to find the Marked Price (MP) of the painting.

Using the formula derived above:

\( \text{Marked Price} = \frac{\text{Selling Price}}{1 - \text{Discount \%}} \)

First, convert the discount percentage to a decimal:

\( 5\% = \frac{5}{100} = 0.05 \)

Now, substitute the given values into the formula:

\( \text{Marked Price} = \frac{5225}{1 - 0.05} \)

\( \text{Marked Price} = \frac{5225}{0.95} \)

Step-by-Step Calculation

To calculate \( \frac{5225}{0.95} \), we can remove the decimal from the denominator by multiplying both the numerator and the denominator by 100:

\( \text{Marked Price} = \frac{5225 \times 100}{0.95 \times 100} = \frac{522500}{95} \)

Now, perform the division:

\( \frac{522500}{95} \)

We can perform long division or simplify by dividing both numbers by a common factor, like 5.

• \( 522500 \div 5 = 104500 \)
• \( 95 \div 5 = 19 \)

So the expression becomes \( \frac{104500}{19} \).

Now, divide 104500 by 19:

\( 104 \div 19 \approx 5 \) (since \( 19 \times 5 = 95 \))

\( 104 - 95 = 9 \)

Bring down 5, forming 95.

\( 95 \div 19 = 5 \) (since \( 19 \times 5 = 95 \))

\( 95 - 95 = 0 \)

Bring down the two zeros. The result is 5500.

So, \( \frac{522500}{95} = 5500 \).

The Marked Price of the painting is Rs. 5,500.

Summary of Painting Price Calculation

Therefore, the marked price of the painting was Rs. 5,500.

Revision Table: Price Concepts

Additional Information: Profit and Loss

Understanding marked price and discount is often related to profit and loss calculations in commerce. While this question only involved discount and marked price, profit or loss is calculated on the Cost Price (CP) of an item.

• Cost Price (CP): The price at which an item is bought.
• Profit: Occurs when Selling Price > Cost Price. Profit = SP - CP.
• Loss: Occurs when Selling Price < Cost Price. Loss = CP - SP.
• Profit/Loss %: Calculated on the Cost Price. Profit % = (Profit / CP) * 100. Loss % = (Loss / CP) * 100.

Sometimes, questions involve multiple steps, such as calculating the cost price after finding the selling price based on a discount from the marked price, and then finding the profit percentage.