Oranges are purchased at the rate of 7 oranges for ₹3. At what price one hundred oranges should be sold so that the profit is 33% ?
₹57
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.
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