Calculating Cost Price from Selling Price and Profit Percentage

This problem involves finding the original cost price of an item when its selling price and the profit percentage are known. We are given that an item was sold at a profit of 23% relative to the cost price, and the selling price was Rs. 14022.

Understanding the relationship between cost price, selling price, and profit percentage is crucial here. Profit is calculated as a percentage of the cost price. When an item is sold at a profit, the selling price is the cost price plus the profit amount.

Let's define the terms:

• Cost Price (CP): The original price at which the item was bought or manufactured.
• Selling Price (SP): The price at which the item was sold.
• Profit Percentage (Profit%): The profit expressed as a percentage of the Cost Price.

The relationship between these is given by the formula:

\[ \text{SP} = \text{CP} + (\text{Profit} \text{ \% of CP}) \]

This can be written more concisely as:

\[ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit}\%}{100}\right) \]

In this problem, we are given:

• Selling Price (SP) = Rs. 14022
• Profit Percentage (Profit%) = 23%

We need to find the Cost Price (CP).

Using the formula, we can substitute the given values:

\[ 14022 = \text{CP} \times \left(1 + \frac{23}{100}\right) \]

First, let's simplify the term in the parenthesis:

\[ 1 + \frac{23}{100} = 1 + 0.23 = 1.23 \]

So the equation becomes:

\[ 14022 = \text{CP} \times 1.23 \]

To find the Cost Price (CP), we need to isolate CP. We can do this by dividing the Selling Price by 1.23:

\[ \text{CP} = \frac{14022}{1.23} \]

Now, we perform the division:

\[ \text{CP} = \frac{14022}{1.23} = \frac{14022 \times 100}{1.23 \times 100} = \frac{1402200}{123} \]

Dividing 1402200 by 123:

\[ 1402200 \div 123 = 11400 \]

So, the Cost Price (CP) is Rs. 11400.

Thus, the cost price of the item was Rs. 11400.

Revision Table: Profit and Loss Concepts

Additional Information on Profit and Loss

Profit and loss calculations are fundamental in commercial arithmetic. They help businesses determine profitability and set pricing strategies. The percentage of profit or loss is almost always calculated with respect to the cost price unless otherwise specified. Understanding these basic formulas allows you to solve various problems involving buying and selling goods.

Key points to remember:

• Profit occurs when Selling Price is greater than Cost Price.
• Loss occurs when Selling Price is less than Cost Price.
• The base for calculating profit or loss percentage is typically the Cost Price.
• A 23% profit means the Selling Price is 123% of the Cost Price.

Being comfortable with percentage calculations and algebraic rearrangement of formulas is very helpful for these types of problems.