Profit Calculation: SP = 5/4 of CP
This problem requires calculating the profit percentage when the selling price (SP) is given as a fraction of the cost price (CP).
Understanding the Relationship
Let the Cost Price (CP) be represented by a variable, say $C$.
According to the question:
- Selling Price (SP) = $\frac{5}{4} \times \text{CP}$
- So, SP = $\frac{5}{4}C$
Calculating Profit
Profit is the difference between the Selling Price and the Cost Price.
- Profit = SP - CP
- Profit = $\frac{5}{4}C - C$
- To subtract, find a common denominator: Profit = $\frac{5}{4}C - \frac{4}{4}C$
- Profit = $(\frac{5}{4} - \frac{4}{4})C$
- Profit = $\frac{1}{4}C$
Calculating Profit Percentage
The profit percentage is calculated based on the Cost Price.
- Profit Percentage = $\frac{\text{Profit}}{\text{CP}} \times 100\%$
- Substitute the values: Profit Percentage = $\frac{\frac{1}{4}C}{C} \times 100\%$
- The $C$ terms cancel out: Profit Percentage = $\frac{1}{4} \times 100\%$
- Profit Percentage = $25\%$
Therefore, the profit obtained in the transaction is 25%.
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?
