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
Rohit buys 8 pens and 4 pencils for Rs. 2400. He sells pencils at a profit of 20 percent and pens at the loss of 10 percent. If his overall profit is Rs. 240, then what is the sum of the cost price of one pen and one pencil?
The cost price of an article is Rs.6,450. If it sold at a profit 16%, how much would be its selling price?
If the selling price of 7 articles is equal to the cost price of 6 articles, then what is the percentage loss?
An article when sold at a gain of 5%, yields Rs. 15 more than when sold at a loss of 5%. The cost price will be
What will be cost price of an item which when sold at the profit of 5% and at the loss of 5% the difference of selling prices be Rs. 60?
