Calculating Profit Percentage
The problem states that the cost price (CP) of 10 articles is equal to the selling price (SP) of 9 articles. We need to find the profit percentage.
Relating Cost Price and Selling Price
Let the cost price of one article be CP and the selling price of one article be SP.
According to the question:
$ 10 \times \text{CP} = 9 \times \text{SP} $
From this equation, we can express the cost price in terms of the selling price:
$ \text{CP} = \frac{9}{10} \times \text{SP} $
Calculating Profit
Since the cost price ($\frac{9}{10} \times \text{SP}$) is less than the selling price (SP), there is a profit.
Profit = Selling Price - Cost Price
Profit = $ \text{SP} - \text{CP} $
Substitute the value of CP:
Profit = $ \text{SP} - \left( \frac{9}{10} \times \text{SP} \right) $
Profit = $ \left( 1 - \frac{9}{10} \right) \times \text{SP} $
Profit = $ \frac{1}{10} \times \text{SP} $
Calculating Profit Percentage
The formula for profit percentage is:
Profit % = $ \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\% $
Substitute the values for Profit and CP:
Profit % = $ \left( \frac{\frac{1}{10} \times \text{SP}}{\frac{9}{10} \times \text{SP}} \right) \times 100\% $
Simplify the expression:
Profit % = $ \left( \frac{1}{9} \right) \times 100\% $
Profit % = $ \frac{100}{9} \% $
Convert the improper fraction to a mixed number:
Profit % = $ 11 \frac{1}{9} \% $
Similar Questions
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Important Questions from Profit and Loss
By selling an article for Rs. 2,200, a profit of 10% is earned. If the same article is sold for Rs. 2,600, then what will be the gain percentage?
By selling an article for Rs. 640, a person loses 15% of its selling price. At what price (in Rs.) should he sell it to gain 15% on its cost price?
The selling prices of articles A and B are the same. A is sold at a profit of 28 percent and B is sold at a loss of 24 percent. If the total selling price of the both articles is Rs. 48640, then what is the cost price of A and B, respectively ?
The cost price of an article is Rs. 2800. Profit as a percentage of selling price is 20 percent. What is the actual profit (in Rs.) ?
A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?
