Calculating Profit Percentage

This problem involves calculating the profit percentage on an item when its selling price changes, given the initial selling price and profit percentage. To solve this, we first need to find the cost price (CP) of the item using the information from the first sale. Once we have the CP, we can calculate the profit made in the second sale and then determine the new profit percentage.

Step-by-Step Profit Calculation

Here are the steps to find the new profit percentage:

1. Find the Cost Price (CP):

   We know that the shopkeeper sells the item at Rs. 2,700 and makes an 8% profit. The selling price (SP) is the cost price plus the profit. The formula relating SP, CP, and Profit Percentage is:

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

   Using the given values:

   $2700 = \text{CP} \times \left(1 + \frac{8}{100}\right)$

   $2700 = \text{CP} \times (1 + 0.08)$

   $2700 = \text{CP} \times 1.08$}

   Now, we can find the Cost Price:

   $\text{CP} = \frac{2700}{1.08}$

   $\text{CP} = 2500$}

   So, the cost price of the item is Rs. 2,500.

2. Calculate the Profit in the Second Sale:

   The item is now sold at Rs. 3,000. The profit is the difference between the new selling price and the cost price.

   $\text{Profit} = \text{New SP} - \text{CP}$

   $\text{Profit} = 3000 - 2500$}

   $\text{Profit} = 500$}

   The profit made when selling the item at Rs. 3,000 is Rs. 500.

3. Calculate the New Profit Percentage:

   The profit percentage is calculated on the cost price. The formula is:

   $\text{Profit \%} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100$}

   Using the profit from the second sale and the cost price:

   $\text{Profit \%} = \left(\frac{500}{2500}\right) \times 100$}

   $\text{Profit \%} = \left(\frac{1}{5}\right) \times 100$}

   $\text{Profit \%} = 0.2 \times 100$}

   $\text{Profit \%} = 20\%$}

   The percentage of profit if the item is sold at Rs. 3,000 is 20%.

Summary of Profit Calculation

Let's summarize the two scenarios:

The final profit percentage when selling the item at Rs. 3,000 is 20%.

Revision Table: Profit and Loss Formulas

Additional Information: Profit and Loss Problems

Profit and loss calculations are fundamental in business mathematics. Understanding the relationship between cost price, selling price, profit, loss, and their respective percentages is crucial. Problems often involve finding an unknown value when others are given, or dealing with successive transactions, discounts, and taxes. Always remember that profit and loss percentages are typically calculated based on the cost price unless otherwise specified.