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.
Similar Questions
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Important Questions from Profit and Loss
Ram bought a chair at 35% discount on its market price, Had Ram got no discount, he would have had to pay ₹245 more. How much did Ram pay for the chair?
A shopkeeper bought an item for Rs. 4,500 and sold it at a loss of 5%. From this money, he bought another item and sold it at a profit of 10%. What is his overall profit?
A man sells two articles at Rs. 9,180 each. He gains 8% on one article and loses 15% on the other. His overall profit or loss is:
A shopkeeper selling an article for ₹46 loses 8%. In order to gain 6%, what should be the selling price of the article?
Rahul purchased 80 items from the market. 25% items of the total items were defective and the remaining items were sold at 50% profit. What will be the overall profit percentage?
