Calculating Selling Price for Oranges with Profit

The problem requires finding the selling price (SP) for 100 oranges to achieve a 33% profit, given the cost price (CP) rate.

Step 1: Determine the Cost Price (CP) of One Orange

Oranges are purchased at 7 for ₹3.

Therefore, the Cost Price (CP) of 1 orange is:

$ \text{CP per orange} = \frac{₹3}{7} $

Step 2: Calculate the Selling Price (SP) for 33% Profit

A profit of 33% means the selling price must be 100% + 33% = 133% of the cost price.

Selling Price (SP) per orange = CP per orange $ \times (1 + \text{Profit Percentage}) $

$ \text{SP per orange} = \left( \frac{₹3}{7} \right) \times (1 + 0.33) $

$ \text{SP per orange} = \left( \frac{₹3}{7} \right) \times 1.33 $

$ \text{SP per orange} = \frac{₹3.99}{7} $

Step 3: Calculate the Selling Price for 100 Oranges

To find the selling price for 100 oranges, multiply the SP per orange by 100.

$ \text{SP for 100 oranges} = \left( \frac{₹3.99}{7} \right) \times 100 $

$ \text{SP for 100 oranges} = \frac{₹399}{7} $

$ \text{SP for 100 oranges} = ₹57 $

Thus, one hundred oranges should be sold at ₹57 to achieve a 33% profit.