Problem Setup
We are given that the cost price (CP) of 28 mangoes is equal to the selling price (SP) of 25 mangoes. We need to find the profit percentage.
Let the cost price of one mango be \(CP\) and the selling price of one mango be \(SP\).
According to the question:
\( 28 \times CP = 25 \times SP \)
Calculating Price Ratio for Profit
To find the profit percentage, we first determine the ratio between the selling price and the cost price.
From the equation \( 28 \times CP = 25 \times SP \), we can rearrange it to find the ratio \( \frac{SP}{CP} \):
\( \frac{SP}{CP} = \frac{28}{25} \)
This ratio tells us that for every ₹25 spent (CP), the seller receives ₹28 (SP).
Determining Profit Percentage
The profit percentage is calculated using the formula:
\( \text{Profit \%} = \left( \frac{SP - CP}{CP} \right) \times 100 \)
We can rewrite this using the ratio we found:
\( \text{Profit \%} = \left( \frac{SP}{CP} - 1 \right) \times 100 \)
Substitute the value of \( \frac{SP}{CP} = \frac{28}{25} \):
\( \text{Profit \%} = \left( \frac{28}{25} - 1 \right) \times 100 \)
\( \text{Profit \%} = \left( \frac{28 - 25}{25} \right) \times 100 \)
\( \text{Profit \%} = \left( \frac{3}{25} \right) \times 100 \)
\( \text{Profit \%} = 3 \times \frac{100}{25} \)
\( \text{Profit \%} = 3 \times 4 \)
\( \text{Profit \%} = 12\% \)
Final Answer Verification
The calculated profit percentage is 12%. This matches Option A.
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