Calculating Profit Percentage for Sharpeners Sale

This problem involves calculating the profit percentage Veer made on selling sharpeners. We are given the cost price per dozen and the selling price per individual sharpener. To find the profit percentage, we first need to determine the cost price per sharpener and then use the profit and cost price to calculate the percentage.

Step 1: Determine the Cost Price (CP) per Sharpener

Veer bought the sharpeners at a rate of ₹180 per dozen. Since one dozen consists of 12 items, we can calculate the cost price of a single sharpener:

$ \text{Cost Price per dozen} = ₹180 $

$ \text{Number of sharpeners in a dozen} = 12 $

$ \text{CP per sharpener} = \frac{\text{Cost Price per dozen}}{\text{Number of sharpeners in a dozen}} $

$ \text{CP per sharpener} = \frac{₹180}{12} $

$ \text{CP per sharpener} = ₹15 $

So, the cost price for one sharpener is ₹15.

Step 2: Determine the Selling Price (SP) per Sharpener

The problem states that Veer sold each sharpener for ₹23.

$ \text{SP per sharpener} = ₹23 $

Step 3: Calculate the Profit per Sharpener

Profit is the difference between the selling price and the cost price. A profit occurs when the selling price is greater than the cost price.

$ \text{Profit per sharpener} = \text{SP per sharpener} - \text{CP per sharpener} $

$ \text{Profit per sharpener} = ₹23 - ₹15 $

$ \text{Profit per sharpener} = ₹8 $

Veer made a profit of ₹8 on each sharpener.

Step 4: Calculate the Profit Percentage

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

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

Substituting the values we found:

$ \text{Profit Percentage} = \left( \frac{₹8}{₹15} \right) \times 100 $

$ \text{Profit Percentage} = \left( \frac{8}{15} \right) \times 100 $

Now, let's perform the calculation:

$ \frac{8}{15} \approx 0.53333... $

$ \text{Profit Percentage} \approx 0.53333... \times 100 $

$ \text{Profit Percentage} \approx 53.333... \% $

Step 5: Round the Profit Percentage

The question requires the profit percentage to be rounded off to two decimal places.

Rounding $ 53.333... \% $ to two decimal places gives $ 53.33 \% $.

Summary of Calculation

Therefore, Veer's profit percentage is approximately 53.33 %.